Appeasement has few defenders. Ever since Neville Chamberlain's
famous piece of paper failed to stop the Nazi advances in the 1930s,
making concessions to an aggressor in the hope of preventing war has
seemed to most observers rather foolish. Winston Churchill ridiculed
appeasement as the strategy of “one who feeds a crocodile, hoping
it will eat him last.”1
Reasons for distrusting
the policy were, in fact, noticed long before Munich. Classical
political thinkers from Thucydides to Machiavelli offer many statements
of the anti-appeasement view.
Appeasement, many argue, is not just futile: it is self-destructive.
The danger is most acute when many potential challengers exist.
Acceding to one challenger undermines the appeaser's reputation
for resolve and encourages others to attack, starting a cascade of
dominoes. The argument received a compelling game theoretic formulation
in the solutions of Kreps and Wilson and Milgrom and Roberts to
Reinhard Selten's “chain-store paradox.”2
This article argues that the common presumption against appeasement
is far too strong. The standard treatments leave out one factor that is
crucial in international politics—resource constraints. If
resources are limited and a state faces many potential threats,
appeasing one challenger may actually increase a state's ability
to deter others. When conflict is costly, defenders face a trade-off:
fighting may enhance their reputation for resolve, but it will deplete
their resources to fight—or deter—future challenges.3
In fact, if all types appease, none loses
face by doing so.
Often, the latter effect outweighs the
former, prompting a strategy I call “rational appeasement.”
If even highly resolved incumbents rationally appease, observers do not
impute low resolve to appeasers. Moreover, when fighting depletes
enforcement resources, a refusal to appease can undermine the
state's deterrent. This insight applies to actors as diverse as
states facing international challenges, empires fearing subject
rebellions, federations concerned about possible regional tax revolts,
and monopolists eager to deter entry.
Below, I demonstrate this point formally. First I present a benchmark
model of the interaction between one “central” and two
“local” actors assuming no resource constraint, and I show
how investing in reputation can be rational (and appeasement
irrational) à la Kreps and Wilson and Milgrom and Roberts. I
show that a deterrence equilibrium will often exist in which
“weak” central actors fight to preserve a reputation for
“strength.” I then show how the logic changes if the
central actor's resources are limited. Now fighting the first
challenger to demonstrate resolve is often self-destructive: it weakens
the center so much that this actually prompts the second to attack. The
conditions for this depend on whether the stakes of conflict can be
manipulated by the center or are exogenous. If they are exogenous,
fighting is self-destructive when the stakes are either high or low; if
endogenous, this is true if fighting is very costly to the center. By
contrast, under these conditions appeasing the first challenger will
conserve resources sufficient to deter the second.
Social psychologists have distinguished two types of appeasement:
reactive appeasement strategies—that “reduce
extant conflict”—and forms of anticipatory
appeasement—that “prevent potential conflict from
occurring.”4
Borrowing their terminology, I show in a third model that both types of
appeasement can be rational in international relations and other
settings. I assume here that the central actor can tailor its demands
(for tax revenues, international respect, policy adherence, or market
protection) to characteristics of the local actor, and I label the
deliberate lowering of demands on more aggressive local actors
“anticipatory appeasement.” I show that in all equilibria
in which local actors pay the transfer demanded, the maximum level of
this transfer is lower for actors for whom fighting is less costly.
Even when the center fights an early challenge to demonstrate resolve,
it will subsequently appease by demanding lower transfers of those who
are more bellicose.
I then apply the model's insights to two historical cases. I
discuss how a strategy of selective appeasement apparently slowed the
disintegration of the British Empire, whereas an attempt to invest in
reputation regardless of the cost accelerated the decline of Habsburg
Spain. While appeasement policies certainly do not always succeed in
the sense of reversing a state's or empire's decline, they
often seem to work better than a policy of fighting to demonstrate
resolve.
My argument differs from several others. First, various historians
and international relations scholars have defended the weaker thesis
that policies of conciliation and compromise are rational. Some have
even labeled such compromise strategies “appeasement.” In
an influential series of works, Kennedy contended that British foreign
policy between 1865 and 1939 embraced a strategy of appeasement on a
global scale.5
Appeasement in Kennedy's
definition is “the policy of settling international (or, for that
matter, domestic) quarrels by admitting and satisfying grievances
through rational negotiation and compromise.”
6 My
definition—the policy of making unilateral concessions to a
challenger or potential challenger in the hope of avoiding or delaying
conflict—does not require any rational negotiation or compromise.
On the contrary, the concessions envisioned are
unilateral.
7 I agree, however,
that Britain engaged in appeasement, not just by Kennedy's
definition but also by mine (see the section entitled
“Britain” below).
Similarly, Rock defines
appeasement as “the policy of reducing tensions with one's
adversary by removing the causes of conflict and disagreement,” a
definition that does not require concessions on the part of an
appeaser, and that renders the term a close synonym for
“conciliation” or even “negotiation.”
8
In this definition, it is easy to see why appeasement might sometimes
be a good thing. My claim is much stronger: that unilateral concessions
to a challenger just to avoid war are sometimes a rational and
effective survival strategy.
Second, many treatments of appeasement focus on the hope of
socializing or reforming the aggressor. Mine does not. Given multiple
threats, one should often appease even if one views the aggressor as
unreformable. The goal is not to change the challenger but to deter
others from imitating the aggressor.
Third, my analysis concerns the strategic dilemma for states facing
multiple potential challenges. Two recent articles show it can be
rational to appease when there is only one potential challenger.
Hirshleifer argues that appeasement can be effective if aggression is
an inferior good for the opponent state, so the opponent's demand
for it drops as that state is bought off.9
Powell
presents an argument based on asymmetric information.
10 A declining state faces a challenger with unclear
aims. If the challenger's aims are unlimited, the first state
would prefer to fight—and fight as soon as possible. There is a
strategic cost to delay. However, if the challenger's aims are
limited, the first state would prefer to appease. In equilibrium, the
state trades off the loss of strategic advantage against the chance of
acquiring information about its adversary's objectives.
Both these articles make compelling points about how appeasement can
be rational in isolated interactions. But they do not address the
arguments about reputation and deterrence that inform most critiques of
appeasement. When there is only one challenger, such questions cannot
arise—there is no one to deter. An isolated domino cannot start a
cascade. If the Hirshleifer or Powell models were adapted to include
many potential challengers, appeasement would—by the usual
chain-store logic—erode the appeaser's reputation for
resolve and provoke challenges, even if aggression were an inferior
good or the first challenger had clearly limited aims. By contrast, I
show how, given resource constraints, appeasement can be rational for
states facing multiple potential challengers where questions of
reputation are critical.11
If one views
the models I present as rounds in a repeated game and limits
consideration to stationary strategies, then the models can also
rationalize appeasement even when a challenger's long-run aims are
known to be unlimited, so long as the challenger's demand in any
given round is limited. Although appeasing in such circumstances only
postpones the fight, it may help the state survive longer (by
preserving sufficient resources to deter other challenges) than
fighting immediately (in which case, the state's weakness provokes
other challenges.) Of course, if a challenger seeks to destroy its
adversary in a single round, then acquiescing is never rational. On
this point, my analysis concurs with that of Powell and all others. My
model also differs from Powell's in that it does not rely on
asymmetric information about the challenger's type. One could
derive similar results under asymmetric information. But I am able to
show that appeasement can be rational even in the harder case of
complete information about challengers' types, where appeasing
confers no informational benefit.
Because state leaders do
usually face multiple threats and worry about international reputation
and deterrence, this renders the model broadly relevant.
Rational deterrence theory—and the presumption that states must
always fight to preserve reputation—has come under more
fundamental criticism in recent decades. Empirically, scholars have
found only sketchy evidence that states that fail to fight challenges
are judged irresolute. Backing out of confrontations, averting
one's eyes, and offering secret concessions have been common
practices of all the great powers. Reputations appear far more
context-dependent and resilient than the standard models suggest.12
One response has been to reject the rationalistic
assumptions of deterrence models and explain behavior as the result of
cognitive biases.
13 While such biases may indeed exist, the approach in this article is
less radical. I show that minor modifications of current rational
reputation models can render them substantially more realistic and
convincing.14
Even if one accepts the
social psychological critiques, this exercise may be valuable for two
reasons. First, to assess the persuasiveness of psychological theories,
it would be useful to test them against more realistic models of
rational signaling. Second, whatever the validity of rational
deterrence theories, many decision makers use their concepts and claims
to choose policies and anticipate their adversaries' reactions.
This alone is reason to examine their logic.
Many points that
classical deterrence theorists are criticized for neglecting can be
incorporated quite naturally. In fact, once resource constraints are
introduced, predictions about reputation formation become sensitive to
key aspects of the context—the central actor's initial
reputation, the stakes involved, the costs of fighting, and how rapidly
conflict depletes resources. Fighting and appeasing have very different
consequences for a state's reputation—and payoffs—when
these circumstances are different. Appeasing in one context does not
imply one will appease in others.
15 Sartori (2002) makes a related
argument, suggesting that states may appease adversaries to preserve a
reputation for honesty. Her model differs from mine in that she assumes
that players' types change randomly between interactions, and so
investing in a reputation for resolve is ruled out by assumption.
Because her aim is to show that “cheap talk” in diplomacy
can be rendered meaningful by the honesty-reputation effect, this lies
beyond the scope of her article.
I do not claim to be discovering a completely new idea. Since the
time of Thucydides, many writers have noted the usefulness of what I
call appeasement. However, such notions have largely been eclipsed by
the elegant formulations of theorists such as Schelling and the general
horror at the consequences of Munich. By presenting a simple model that
includes resource constraints and rationalizes selective appeasement, I
hope to suggest the need for reconsideration.
Two Traditions
Distrust of appeasement dates at least to the Peloponnesian War. In
the Athenian view, leniency toward hostile or even neutral city-states
risked eroding the city's reputation for toughness, thus
undermining its empire. As the Athenian envoys told the people of
Melos: “if we were on friendly terms with you, our subjects would
regard that as a sign of weakness in us, whereas your hatred is
evidence of our power.”16
Fighting—and
eventually massacring the male population—demonstrated resolve. A
hint of such thinking appears also in Pericles's speech warning
against accepting the Spartan ultimatum: “If you give in, you
will immediately be confronted with some greater demand, since they
will think that you only gave way on this point out of fear. But if you
take a firm stand you will make it clear to them that they have to
treat you properly as equals.”
17 Much later, Machiavelli laid out the anti-appeasement argument in
The Discourses:
[I]f you yield to a threat, you do so in order to
avoid war, and more often than not, you do not avoid war. For those
before whom you have thus openly demeaned yourself by yielding, will
not stop there, but will seek to extort further concessions, and the
less they esteem you the more incensed will they become against you. On
the other hand, you will find your supporters growing cooler towards
you, since they will look upon you as weak or pusillanimous.18
This logic of interdependent threats and fragile reputation came to
dominate postwar American strategic thinking. Chamberlain's
failure seemed to have proved it correct. Successive presidents invoked
similar arguments to justify the use of force in distant countries,
from Harry S. Truman's call to arms over Korea to George W.
Bush's warnings to Europe not to appease terrorists.19
Bush, addressing the German parliament in
May, 2002, compared the threat of global terrorism to that of Nazism
and warned that it “cannot be appeased or … ignored”
(transcript available at
〈www.whitehouse.gov/news/releases/2002/05/20020523-2.html〉).
For many earlier examples, see Gaddis 1982,
Rock 2000, and Jervis
1991. Some have questioned whether policymakers sincerely
believe in the vulnerability of reputation or merely employ such
arguments for rhetorical effect (see, for example, Snyder 1991a and 1991b).
But there are enough examples of policymakers expressing such views in
private conversations or diaries to make it likely they do shape
thinking to a considerable extent.
Modern theoretical
underpinnings were supplied first by the intuitions of Schelling and
other early analysts of nuclear diplomacy.
20 Schelling 1966 discussed the
interdependence of threats and the importance of demonstrating
commitment.
The modeling innovations of Harsanyi, Spence, and
other pioneers of the economics of asymmetric information later opened
up opportunities for formal development.
21 Game theoretic discussions of the problem began in earnest with
Selten's “chain-store paradox.”22
A
monopolist operating in a number of markets fears the entry of
competitors and threatens to respond in each case with a price war. As
Selten showed, if the number of markets is finite it is irrational for
the monopolist to fulfill its threats. The only subgame perfect
equilibrium is for all competitors to enter and the monopolist to
acquiesce.
The model assumed complete information and so left no room for
reputation, the key element in arguments about deterrence and
appeasement. The reason actual chain stores fight, as Selten
intuitively understood, is to deter other possible competitors from
entering. As Kreps and Wilson and Milgrom and Roberts argued in their
responses to Selten's puzzle, when information is asymmetric
failure to fight can reveal the chain store's type.23
If potential entrants do not know the chain
store's payoffs and there is even a small chance it is
“tough”—that is, actually enjoys fighting—then
“weak” chain stores may deter subsequent entry by fighting
early in the game. Similarly, even irresolute states can deter military
challenges by imitating resolute ones.
24 Kreps
and Wilson (1982, 275) suggest their reputation
argument could apply to international diplomacy.
Acquiescing
to a challenge—appeasing—would reveal the state to be
irresolute, prompting challenges from all other possible entrants.
The anti-appeasement argument has had an enormous influence on both
theorists and practitioners of international politics. But a second
tradition of thought, not always distinct from the first, recognizes a
strategic value in appeasement. The Athenians did not treat all
opponents as they did the Melians. In the case of Mytilene, the
assembly favored Diodotus's argument that “the right way to
deal with free people is … not to inflict tremendous punishments
on them after they have revolted, but to take tremendous care of them
before this point is reached, to prevent them even contemplating the
idea of revolt.”25
This is the strategy
that, following Keltner, I call “anticipatory
appeasement.”
26 Even
Pericles in the speech already quoted urged a strategic
retreat—the Athenians should abandon their land to the Spartans
to preserve military resources. If they fought the Spartans on land,
their colonies would “immediately revolt if we are left with
insufficient troops to send against them.”
27
Thus, to preserve their deterrent against colonial rebellions, the
Athenians should temporarily yield their homeland without a fight.
Machiavelli also recognized the dangers of an exaggerated concern for
reputation. The forceful argument against appeasement already quoted is
undercut by a caveat in the next paragraph. “This applies,”
he adds, “where you have but one enemy. If you have more, the
wiser course is to hand over some of your possessions to one of them so
as to win him to your side even after war has been declared, and that
you may detach a member of the confederation which is hostile to
you.”
Both Pericles—in Thucydides's rendering—and
Machiavelli recognized that when resources are limited, the logic of
deterrence and appeasement changes. In such conditions, selective
appeasement can become necessary for deterrence. This second logic,
neglected since 1938, is the one I seek to model.
Modeling Deterrence and Appeasement
Rational Deterrence
I introduce here a benchmark model that reproduces in a simpler
context the finding of Kreps and Wilson and Milgrom and Roberts that if
information is asymmetric “weak” actors may invest in a
reputation for “strength” to deter future challenges.28
Two “local” actors (L1 and
L2) decide sequentially whether to challenge a
“central” actor (C). This central actor might be a
hegemonic state facing two rising powers; a federal government taxing
two regions; an empire with two colonies; or a monopolist with two
potential competitors. One key assumption, as in all models of
reputation, is that actors are of different “types.” At
time 0, Nature determines whether C is “strong” or
“weak” (denote the strong C
“CS” and the weak C
“CW”). Only C knows
its type. It is common knowledge that the probability of a
“strong” C is π, where π ∈ (0,1).
At time 1, the first local actor, L1, chooses an
action {c,a} where “c” stands for “challenge”
and “a” for “acquiesce.” A
“challenge” might consist of a rising power confronting the
hegemon, a territory refusing to remit taxes, or a commercial
competitor entering a protected market. If L1
acquiesces, it makes a payment of t to C, where
t ∈ (0,∞) is for now assumed to be exogenously
fixed (I relax this assumption in the section titled “Endogenous
Stakes” below). This transfer of utility might represent payment
of a tax, acquiescence to the hegemon's demands, or the increase
in rents when a monopoly goes unchallenged.29
Although theory does not require the monopolist's
benefit to equal the forgone profits to an entrant, I assume this here
for simplicity.
(Although
t is assumed strictly
positive, this is just a normalization. One could assume instead that
C provides some positive benefit,
b, to
L1 and
L2, and that the
net transfer paid by them to
C when they acquiesce,
t −
b, is negative.)
If L1 challenges, then at time 2, C
chooses an action {A,F}, where “A” stands for
“appease” and “F” for “fight.” If
C fights, both C and L1 suffer a
fixed cost of fighting, k (k > 0)30
In the section “Endogenous
Stakes” below, I let players have different fixed costs.
As a result of the fight,
t is divided between
C and
L1. If
C is “strong,” it
expropriates
t from
L1; if
“weak,” it gets nothing.
31 This is for convenience; one could derive the same results
assuming CS and
CW both get some fraction of t
when they fight (ss and
sw, respectively, where 0 ≤
sw ≤ ss
≤ 1). The key point is that in the last interaction,
CW always appeases. If
CW fought in the last interaction, the
state would not need to invest in a (false) reputation for strength to
deter challenges—the state's true preferences would be
sufficient deterrent.
At time 3, L2 chooses its action {c,a}. If it
chooses “c,” C then chooses at time 4 whether to
appease it or fight. The payoffs from confrontation are derived
analogously to those at time 2. A strong C who fights gets
t − k from this interaction, (added to the
payoff from the interaction with L1); a weak
C who fights gets −k (again added to the payoff
from the first interaction). If a strong C fights
L2's challenge, L2 gets
−t − k; if a weak C fights,
L2 gets −k. After C chooses
an action, the game ends and payoffs are realized. Figure 1 shows the game tree.
The game's interest derives from the possible difference between
the decisions C makes at time 2 and time 4. In any
equilibrium, CS fights at time 4 if
t > k, while CW
always appeases at time 4. At time 2, however, equilibria exist in
which even weak central actors fight to preserve their reputation and
deter challenges at time 3.
To show this, I define two terms. A deterrence equilibrium
(DE) is a pure strategy sequential equilibrium in which either: (1)
L1 challenges, both CS
and CW fight at time 2, and
L2 acquiesces at h1; or (2)
L1 acquiesces at time 1, because it correctly
believes that off the equilibrium path both
CS and CW
would fight at time 2. In case (1), the investment in reputation must
be made. In case (2), the correct belief that C would fight
deters the challenger from challenging in the first place.32
In the second case, fighting challenges occurs off the equilibrium
path. Sequential equilibrium places few restrictions on beliefs off the
equilibrium path—beliefs need only be derivable “using
Bayesian inference from arbitrarily small trembles.”
33 To focus on cases in which
reputation—rather than just strength—deters challenges, I
require that weak as well as strong
Cs would actually fight if
challenged by
L1, to preserve their reputation.
34 If only CS
fought such challenges, then any deterrence would be explained just by
a high prior probability that C is strong: reputation building
would have nothing to do with it.
I call type (1) cases
“on-equilibrium-path” DEs (because fighting for reputation
occurs on the equilibrium path), and type (2) cases
“off-equilibrium-path” ones. Notice that the definition of
a DE deliberately leaves many actions unspecified to encompass a
variety of possible strategy and belief profiles. Any pure strategy
sequential equilibrium that includes the play defined in (1) or (2) is
a DE. Thus, the proofs seek to characterize conditions that any DE must
meet; where space permits, I also illustrate with a fully specified
example.
Second, a partial deterrence equilibrium (PDE) is a mixed
strategy sequential equilibrium in which (1) L1
challenges, CS and
CW both fight at time 2 with positive
probability (ps ≤
1,pw < 1, respectively), and
L2 acquiesces at h1 with positive
probability (“on-equilibrium-path PDE”); or (2)
L1 acquiesces because it correctly believes that,
off the equilibrium path, both Cs would fight with
sufficiently high probability at time 2 to make it prefer acquiescing
(“off-equilibrium-path PDE”).
Proposition 1: In the game without resource constraints: (1) If
the stakes are neither too low nor too high relative to the cost of
fighting and π is sufficiently high (k ≤
t ≤ kπ/(1 − π)) at least one
(off-equilibrium-path) deterrence equilibrium exists. No DE exists if
t > kπ/(1 − π). (2) A partial
deterrence equilibrium may exist even if t >
kπ/(1 − π). If it does, the frequency,
pw, with which CW
fights an initial challenge in order to deter the second challenger is
lower the higher are the stakes: pw =
πk/[(1 − π)t]. (See proofs
in Appendix.)
Thus, for an intermediate range of the stakes, an equilibrium exists
in which weak central actors always fight an initial challenge to
preserve a reputation for strength. This deters the first challenger.
If stakes are higher, weak central actors only sometimes fight an
initial challenge, and less frequently as the stakes rise. These
results are quite intuitive. If the stakes are too high, deterrence
will not be very effective, and a weak C will wish to reduce
its costs by only fighting on occasion. By contrast, when t is
so low that no central actors would bother to fight (t <
k), attempting to build reputation is pointless.35
It might seem odd to include t
≥ k as a boundary condition for equilibrium, because this
essentially states that there are at least some Cs for whom
fighting is beneficial. Absent such “tough” players,
reputation-building cannot occur. However, a main point of this article
is that whether or not there are “tough” players in this
sense is itself endogenous and depends on previous moves in the game.
To restrict attention to either games in which there are
“tough” players or those in which there are none precludes
analysis of the strategies players rationally adopt when they recognize
that one game can change endogenously into the other.
Effective and consistent efforts to build reputation are most likely
when the stakes are neither too low nor too high relative to the cost
of fighting.
Rational Appeasement
But what if the central actor's enforcement resources are
exhaustible? Suppose now that if a strong C fights against
L1, it still extracts t units from
L1. But if C fights against
L2, having already fought against
L1, it receives only t/α units
from L2 where α ∈ (1,∞).
C's resources are depleted in the first fight, leaving it
weaker in the second; α measures how severely C is
weakened in each fight. The payoffs are identical to those in Figure 1, with one exception: if
L1 and L2 both challenge and
CS fights both challenges, the payoff to
CS is t + t/α
− 2k instead of 2(t − k), and
the payoff to L2 is −t/α
− k instead of −t − k.
Proposition 2: In the game with resource constraints, a
deterrence equilibrium only exists if αk ≤ t
≤ αkπ/(α − π). A partial
deterrence equilibrium only exists if αk ≤ t ≤
αk/(α − 1).
Thus, if fighting depletes the central actor's resources
sufficiently (αk > t), it is never rational
for weak Cs to fight to preserve reputation. Nor is it
rational to fight to preserve reputation if the stakes are too high. In
some cases, a quite different strategy may be optimal. When resources
are limited, conserving resources by appeasing the first challenge will
sometimes deter a second challenge more effectively than fighting.
Because in these conditions strong central actors prefer to appease, a
weak central actor cannot improve its reputation by fighting.
To show this formally, I define an appeasement equilibrium
(AE) as a sequential equilibrium in which L1
challenges, both CS and
CW appease, and L2
acquiesces.36
Notice that this
definition, again, deliberately leaves many actions unspecified: any
pure strategy sequential equilibrium that includes the play defined
above is an AE.
Note that there cannot be any
“off-equilibrium-path” appeasement equilibria, because if
L1 believes
C would appease, it always
challenges. Because I want to establish that
even pure
appeasement sometimes deters attacks, it is not relevant here to
consider mixed strategies, in which a weak center only appeases part of
the time (or in which
L2 is only deterred part of
the time). Such equilibria almost certainly exist but are not germane
to the stronger point I wish to demonstrate.
Proposition 3: In this game, an appeasement equilibrium only
exists if k ≤ t ≤
min[2αk,kπ/(1 −
π)].
Thus, if the stakes are high—but not too high—relative to
the fixed cost of fighting, and the central actor's initial
reputation is sufficiently strong (high enough π), it can be
effective and optimal for weak centers to appease a challenge. Because
strong central actors appease in such conditions, the weak cannot do
better than to imitate them—rational appeasement.37
What is interesting is not that states with
limited resources sometimes appease. After all, “the strong do
what they will, and the weak do what they must.” The novelty is
that appeasing reduces the risk of subsequent challenges.
Appeasement equilibria always exist for lower values of
t than
deterrence equilibria (when
k ≤
t <
α
k). If α > 3π/2, they also exist at higher
values of the stakes than DE's. If α > 2π, no DE
exists. (AEs can only exist if π > 1/2.) When fighting
weakens the fighter sufficiently, it is not possible to deter by
fighting.
38 For appeasement to make
sense, the cost of fighting, k, must be relatively large. If
costs are low, a central actor could fight many times without losing
credibility. This renders the analysis less relevant to, say,
monopolists controlling many small markets (although not monopolists
with a few large ones). But it seems to fit well the realities of
international politics, when even a “hyperpower” such as
the United States only claims to be able to fight two wars
simultaneously.
Note that in the game found above in the section entitled
“Rational Deterrence,” in which C faced no
resource constraint, no appeasement equilibrium existed (except in the
borderline case in which t = k). For
L2 to acquiesce at h2, it must be that
k ≤ t ≤ kπ/(1 − π).
But for CS to appease at time 2 (given
that k ≤ t ≤ kπ/(1 −
π)), it must be that t ≤ k, which contradicts
the previous condition if t ≠ k.
Endogenous Stakes
Sometimes the stakes of conflict, t, are not under the
central actor's control. If a rival firm steals a
monopolist's market, the rents lost to the monopolist are
predetermined by demand in the market and costs of supply. If an
invader occupies certain territories, the incumbent's loss is
determined by the value of the territories. But sometimes the central
actor itself determines the level of t. For instance, central
authorities often decide themselves what tax rates to set for regions
or subject territories. A hegemon might choose to demand greater or
smaller concessions from a minor power in an international negotiation.
In this section, I consider how the analysis changes if t is a
choice of the central actor.
This makes it possible to examine a second kind of appeasement. So
far, I have considered only appeasement in the sense of deciding not to
fight a challenge—reactive appeasement. But when t is
chosen by the central actor, C may appease some adversaries in
advance by lowering its demands on them to forestall a
challenge—anticipatory appeasement.39
Recall that t > 0 is just a normalization. A
central actor might also appease in advance not just by lowering a
demand but by providing a positive transfer to the local
actor.
The multiple equilibria that characterize most
signaling models mean that one can only derive comparative statics on
the maximum
t that
C could set in equilibrium. I show
that this upper bound will be lower for those local actors that have a
lower fixed cost of fighting. If one accepts a refinement that rules
out some implausible off-equilibrium-path beliefs, the result holds for
all equilibrium tax rates. Anticipatory appeasement will occur in all
equilibria in which any local actor acquiesces—including the
classic deterrence equilibrium in which the center's readiness to
fight deters any challenge. When fighting is costly and resources
limited, rational players will often moderate their demands to avoid a
fight. They will do so even if their reputations for toughness are at
stake.
I adapt the game as in Figure 2. Now
C sets t for L1—denoted
t1—at time 0.5, right after Nature determines
C's type. C sets t for
L2—denoted t2—at
time 2.5, right after C has taken any action against
L1. I assume there is a maximum level of
t, t, so that
t1,t2 ∈
[0,t] . Otherwise,
CS could always increase its payoff by
raising its demand and would set t infinitely high. To make
the game more realistic, I also allow each actor to have a different
fixed cost of fighting, labeled k1,
k2, and kc.
Deterrence game with limited resources and endogenous stakes
In the endogenous stakes model, I define a deterrence
equilibrium as a pure strategy sequential equilibrium in which
either (1) L1 challenges, both
CS and CW
fight and set strictly positive t2's, and
L2 acquiesces; or (2) L1
acquiesces because it correctly believes that if it challenged, both
CS and CW
would fight. The requirement that t2 > 0 rules
out cases in which L2 acquiesces simply because no
sacrifice is asked of it. To attribute such acquiescence to deterrence
would be odd.40
Because of the complexity
of the game—with continuous tax rates and multiple
decisions—I defer consideration of mixed strategy equilibria to
future work. The results of this section should therefore be viewed as
suggestive rather than definitive.
Similarly, I define an
appeasement equilibrium as a pure strategy sequential
equilibrium in which
t1,
t2 >
0,
L1 challenges, both
CS and
CW
appease, and
L2 acquiesces. (As before,
off-equilibrium-path appeasement equilibria cannot exist, because if
L1 believes
C will appease,
L1 will always challenge, given
t1 > 0.) Again, I require that
t1 > 0 and
t2 > 0 to
avoid merely proving that actors acquiesce when nothing is asked of
them.
Propositions 4 to 6 establish two things. First, when stakes are
endogenous, reactive appeasement can still occur; and (pure strategy)
AEs exist at higher values of the center's fixed cost,
kc, than (pure strategy) DEs. Second,
whenever actors acquiesce in equilibrium, some degree of anticipatory
appeasement must also occur. This is true even in deterrence equilibria
in which both types of C fight an early challenge in order to
invest in a reputation for resolve.
Proposition 4: In the game with endogenous stakes, a deterrence
equilibrium can exist only if the center's fixed cost of fighting,
kc, is in the range:
t/α −
απk2 /(α − π) ≤
kc ≤
min[πk2 /(α −
π),t/α].
Proposition 5: At least one appeasement equilibrium exists if
t − πk2 /(1
− π) ≤ kc ≤
πk2 /(1 − π) and either
max[t/2α,t(1 +
α)/2α − πk2 /[2(1
− π)]] ≤ kc <
t/α, or kc
≥ t/α.41
Proofs of Propositions 4 and 5 are omitted here because of
space constraints; they are available at
〈http://www.sscnet.ucla.edu/polisci/faculty/treisman/〉.
Proposition 6: In any equilibrium in which a local actor pays a
positive transfer, the maximum level of that transfer must decrease
with decreases in that actor's cost of fighting.
The less sensitive to conflict an actor is, the lower is the maximum
transfer that can be required of it in equilibrium. Anticipatory
appeasement, in this sense, appears quite rational. Because this result
concerns the upper bound on equilibrium tax rates, it does not
imply that actual equilibrium transfer rates will be lower for local
actors with lower values of k. This will depend on
off-equilibrium-path beliefs. However, if one is prepared to rule out
certain beliefs as unreasonable, the predictions become sharper.
Consider equilibria in which on the upper branch the equilibrium
t2 ≡
t2t <
αk2π/(α − π). To sustain
such equilibria, L2 must respond to any
t2 set above
t2t by increasing its estimate
of the probability that C is weak. But is this plausible?
L2's model tells it that neither
CS nor CW
will set t2 >
t2t. One might argue that
because this unexpected event can reveal no information (given
L2's model), it should not change
L2's beliefs. Restricting beliefs in this way
would narrow the prediction for
t2t to the upper bound of the
previous range. (Because t2 does not affect
L2's beliefs and future actions, utility
maximization requires this, at least in equilibria in which
C's payoff is related to the tax rate.) Similarly,
t1 should be set at its upper bound, and one can
rewrite Proposition 6 as a proposition about the actual transfer
demanded in equilibrium rather than the upper bound of possible
demands.
Discussion
Several points emerge from the analysis. First, under certain
conditions appeasement equilibria—but not deterrence
equilibria—will exist. By appeasing a first challenge, a weak
central actor will deter a second; had the weak actor fought the first
challenge, its weakened state would actually have precipitated the
second.
The conditions differ depending on whether the stakes of conflict,
t, are exogenous or endogenous. If the stakes are exogenous,
only appeasement—and no deterrence—equilibria will exist if
t is low relative to the costs of fighting. If k ≤
t < αk, even a “strong” central
actor will not be able to deter the second challenge if weakened by
fighting the first. The actor's gain from fighting the second,
given its weakened state, will be too low for it credibly to threaten
to do so. However, if a strong center appeases the first challenge, it
will stay strong enough to deter the second. Weak centers, by
pretending to be strong and appeasing the first challenge, can also
deter the second.42
I assume throughout
that fighting depletes the center's military resources. There
might, however, be cases in which fighting actually strengthens the
center. The defeated power might have raw materials or industrial
capacity that enhance the victor's military capacity by more than
fighting depletes it. In such cases, appeasement is never an
equilibrium. But nor, strictly speaking, is deterrence—the center
will always prefer to fight whether or not it is challenged; and each
time it fights it will become stronger, until it has defeated all other
states. In such a situation, the questions discussed in this paper
simply do not arise. Reputation and information are irrelevant. That
state leaders do usually seek to avoid conflicts suggests that this
possibility is an exception rather than the rule. If it were generally
true that the net effect of fighting were to strengthen the aggressor,
the world would by now consist of a single state.
Appeasement may also be the unique rational strategy when the stakes
are high relative to the cost of fighting. So long as fighting
weakens the center sufficiently (α > 3π/2), there is a
higher range of t for which only appeasement—and no
deterrence equilibria—exist (απk/(α
− π) < t ≤
min[2αk,kπ/(1 − π)]).
In this range, fighting all challenges to preserve reputation is not
rational. At still higher stakes it becomes irrational for a weak
center ever to fight to preserve reputation (when t >
kα/(α − 1)). When so much is at stake, the
second local actor would rather fight a weakened central actor than
give in. However, it may still be possible to deter future challenges
by appeasing the initial challenger (so long as α > 3/2 and
π > 1/2).43
This is a
different case from the “low-prior” one that most
interested Kreps, Wilson, Milgrom, and Roberts. But in international
relations the moderate-to-high prior is often the most relevant. One
can safely assume that a state will respond militarily to, say,
incursions on its territory. It is precisely in such contexts that
questions of reputation are most frequently raised.
Both DEs
and AEs can exist for intermediate values of the stakes.
If the stakes are endogenous, conditions are best framed in terms of
the costs of fighting. There will be appeasement—but no
deterrence—equilibria at high values of the fixed cost to the
center, kc, for instance when
t/α < kc
≤ k2π/(1 − π). Thus, if the
maximum stakes, t, are not too high and the second
challenger's fixed cost of fighting, k2, is
not too low relative to the center's fixed cost of fighting,
kc, a weak center will be able to deter
future challengers by appeasing the first, but not by fighting. If the
second challenger's cost of fighting is too low, then it will not
be possible to deter this challenger by either fighting or appeasing.
If the maximum stakes are too high relative to the center's fixed
cost, then a DE may also exist (because the second challenger will
expect even a weakened center to fight it).44
Here, AEs do not appear to exist for lower values of
kc than DEs.
Second, if stakes are exogenous, the range of stakes for which a DE
is possible narrows as the weakening effect of fighting, α, gets
larger.45
For DEs, this range is
απk/(α − π) − αk;
for PDEs, it is αk/(α − 1) −
αk. Both these expressions decrease with increases in
α.
If α > 2π, no DE exists. The range of values
of the stakes for which appeasement is rational either increases as
α increases (if the upper bound is 2α
k) or remains the
same (if the upper bound is π
k/(1 − π)). If
stakes are endogenous, the range of values of the center's fixed
costs for which a DE exists narrows as α gets larger so long as the
maximum level of the stakes,
t, is not too high
(
t <
[
k2α
2π(1 +
π)]/[(α − π)
2]).
46 The range is either
αk2π/(α − π) or ((1 +
α)k2π)/(α − π) −
t/α. The derivative of the first with
respect to α is always negative; the derivative of the second is
negative so long as t <
(k2α2π(1 + π))/((α
− π)2).
Third, an important point follows
from the previous two. The rationality of investing in reputation or
appeasing challengers depends on the value of the stakes and the costs
of fighting. What inferences are drawn about resolve depends on the
particular circumstances in which one fights or appeases. One cannot
conclude from observing a state appease in one setting that it will do
so when the stakes or costs of fighting are different. In fact, given
that both appeasement and deterrence equilibria exist across a wide
range of parameter values, one cannot even conclude that a given actor
will behave the same way when objective features of the setting are
identical, if the actor thinks the beliefs of observers are different
in the two cases. If the stakes are exogenous, one does not have to
fight in either low or high stakes conflicts to preserve one's
reputation for fighting when the stakes are intermediate. Actually,
fighting when stakes are relatively high or relatively low will not
improve one's reputation (because even strong actors should
appease in those circumstances), and will merely produce fixed
costs.
47 If resolve were modeled as
continuous rather than as two types, appeasement at high or low stakes
would reveal that one was not of the small minority of extreme
conflict-seekers. But the slight loss in reputation would often be
offset by the gain in conserved resources.
If the stakes are
endogenous, the fact that a state appeases when the cost of fighting is
high tells observers nothing about whether it would fight when the cost
is lower, because even highly resolute states will appease when costs
are high.
48 This confirms the insight of
Jervis (1991, 27): “If a country retreats
rather than pay an enormous price for an object of little intrinsic value,
it is not clear that others should or will expect it to back down on issues
that matter more to it.” The model shows that others should not make
such inferences.
Thus, when Oliver Harvey, principal private secretary to Lord
Halifax, wrote in the late 1930s that: “It is not possible to
take a strong line in one quarter and an apparently weak one in another
indefinitely,” he was wrong. Such inconsistency is just what a
rational model of reputation formation would prescribe.49
Nor does Ronald Reagan's assertion that it
was necessary to defeat the Nicaraguan Sandinistas to prevent a
“collapse” of U.S. credibility worldwide make sense, if one
views Nicaragua as a low-stakes case.
50 New York Times, 28 April 1983, A12, quoted in
Walt 1991.
On the other hand,
Margaret Thatcher's comment that if Britain failed to defend the
Falklands, it might prompt similar challenges in places such as
Gibraltar and Belize is not so absurd, because the stakes would
probably be viewed as quite similar.
51 New York Times, 22 April 1982.
The way reputation-formation incorporates consideration of costs of
fighting provides more leeway for leaders than is usually recognized.
As the fixed cost of fighting increases, one passes a threshold at
which appeasement becomes the only pooling equilibrium. Because strong
players would not fight at this point, weak ones no longer need to
fight to impersonate them. Were North Korea to acquire nuclear weapons
and the United States to appease it, this might send all sorts of
dangerous messages to the world. But it would not indicate that the
United States lacked resolve to fight challenges from nonnuclear
powers. Nor would appeasing the Soviet Union in the Cuban Missiles
Crisis have implied a softness on the United States's part in
cases where nuclear escalation was less likely.52
Robert Kennedy's rhetorical question “if
Americans did not stop Communism in South Vietnam, how could people
believe that we would stop it in Berlin?” actually has a
straightforward answer. If the United States could demonstrate that for
it the objective stakes were higher in Berlin than in Vietnam—as
even the Soviets clearly believed at the time—that would be
sufficient (quoted in Ball 1982,
382).
Fourth, whether fighting to invest in reputation makes sense depends
not just on characteristics of the central actor,
kc, but also on those of its future
challengers, k2. The way it does so is
counterintuitive. Given kc, the more
bellicose a future challenger is expected to be (the lower is
k2), the more likely it is that the central
actor's only equilibrium strategy will be to appease in the first
interaction.53
More precisely, for a
given kc, as k2 falls
one passes from the range in which both deterrence and appeasement
equilibria are possible into the range in which only appeasement
equilibria exist (that is, from kc <
k2π/(α − π) to
k2π/(α − π) <
kc < k2π/(1
− π)).
It might seem that the prospect of facing a
more bellicose challenger in the next stage should make weak states
fight all the harder to boost their reputation for resolve. However,
even strong states will do better in such cases to conserve
resources—and so weak states should do the same. Only when states
anticipate facing challengers that are not too bellicose (relatively
high
k2) is it rational to fight to invest in
reputation.
54 This also suggests that
scholars who seek to predict the outcome of crises by focusing on the
relative power of just those states in conflict may be missing
something: whether or not a state fights should depend also on the
relative power and vulnerability of future opponents.
Fifth, anticipatory appeasement—deliberately placing lower
demands on opponents that have less to lose from fighting—is
rational in models of reputation-building that take into account
limited resources. In such cases, even the classic deterrence model
must include some element of anticipatory appeasement.55
It might seem that this part of the model,
which assumes the center knows the challenger's type,
underpredicts conflict. As Fearon (1995), has
pointed out, interstate conflicts can arise because of two-sided
incomplete information about states' net benefit from fighting.
This is quite compatible with the model presented here. One might
assume a small, zero-mean, stochastic element, e, in the
center's perception of the second challenger's cost of
fighting, so that k2 =
k2t + e, where
k2t is the true value of the second
challenger's fighting cost. This would render Fearon-type
conflicts possible without changing the predictions: the center would
still engage in anticipatory appeasement.
Sixth, as critics of rational deterrence theory have noted, a great
deal depends on the central actor's initial reputation, π. But
there is no straightforward relationship between π and equilibrium
strategy. It is not the case that central actors with a strong initial
reputation are more likely to fight to preserve it—this depends
on the stakes, the costs, and the weakening factor. In fact, sometimes
higher initial reputation increases the range of parameter values for
which appeasement rather than fighting is the equilibrium response. AEs
continue to exist—and sometimes DEs do not—at high values
of π.
Within the range of parameter values for which both appeasement and
deterrence equilibria exist, which equilibrium is played depends on the
players' beliefs. Critics of game theoretic analyses are right to
point out that theory tells one little about how these beliefs form.
Despite substantial efforts to refine equilibrium concepts, assumptions
about off-equilibrium-path beliefs remain rather arbitrary. But it is
not true that the importance of such unconstrained beliefs renders game
theoretic analysis irrelevant: one needs to analyze the games to know
when and how exogenous beliefs matter.
Imperial Appeasement and Deterrence: Two
Cases
Empires have adopted different strategies toward external aggressors
(and their own rebellious subjects). The British after 1865 achieved
considerable success by appeasing challengers.56
The Roman Empire also survived in part by appeasing
challengers on its vast periphery to preserve military forces that
could respond to threats elsewhere. See Treisman
2002.
In Spain in the first half of the seventeenth
century, an attempt to build reputation by fighting accelerated the
empire's decline.
57 Thus, this is a
case of “off-equilibrium-path” play. Why Spanish leaders
apparently got the model wrong is best left to historical experts. That
officials do sometimes make mistakes seems hard to deny. In this case,
Spain suffered consequences consistent with the structure of the games
sketched above.
The following brief discussions do not pretend
to summarize the abundant historical scholarship on these cases. Nor do
they offer in any sense a test of the main argument, which must stand
or fall on the validity of its logic. My aim is just to show its
relevance. Certain historical episodes that seem puzzling when viewed
from the perspective of the chain-store model make a lot more sense
once the possibility of rational appeasement is recognized. In these
two important cases, selective appeasement was more—and
reputation-building less—effective than conventional wisdom and
previous models would imply.
In the British case, the chain-store logic—or perhaps some
adaptation of it such as that in Alt, Calvert, and Humes—would
predict that Britain's acts of appeasement would trigger immediate
challenges by other potential adversaries.58
Alt, Calvert, and Humes's case 3′′ appears to
be the relevant one (1988, 452). In this case, the
first challenger challenges; if the hegemon appeases, the second challenger
also challenges. Yet in the British case, France did not immediately
challenge Britain after it appeased the United States. Instead, it
backed off without a fight at Fashoda. My point is not to criticize the
Alt et al. model for failing to explain cases the authors never claimed
to address; it is just to show that certain historical cases appear
inconsistent with the chain-store logic but are illuminated by the
models of this article.
Similarly, conventional models of
deterrence would predict that Spain's repeated military responses
to perceived challenges would deter others. In both cases, events
unfolded differently, in ways consistent with rational appeasement
models. British appeasement in one arena made deterrence credible in
others. Spain's aggressive reputation-building left it vulnerable
to attacks from other quarters. Britain's appeasement of Germany
was the main case that Powell addressed, and it is likely that British
uncertainty about Adolph Hitler's aims was—as he
argued—part of the story.
59 But this was not the only
reason Britain appeased. The record of policy debates suggests that
British leaders were very concerned about the overstretching of
military forces and the danger of provoking challenges elsewhere in the
empire if they diverted resources to combat Germany. There was a side
to British appeasement—even that of Hitler—that most
closely fits the models of this article.
Britain
When Argentina invaded the Falkland Islands, British leaders argued
that a forceful response was essential to deter attacks on the
country's other imperial remnants—Gibraltar and Hong Kong.
British strategy at the height of empire, however, was quite different.
Whitehall showed a persistent willingness to appease some challengers
to retain resources to deter others. Administering an empire on which
the sun never set meant one simply could not respond to all challenges
for, as the Earl of Rosebury put it in 1895, “did we not strictly
limit the principle of intervention we should always be simultaneously
engaged in some forty wars.”60
Kennedy has argued that British policy not just in 1938 but from 1865
to 1939 was essentially a policy of appeasement. This did not prevent
the empire's decline. But it does appear to have slowed the
inevitable disintegration far more than attempting to fight on many
fronts simultaneously would have. Moreover, Britain's reputation
for resolve does not appear to have been seriously damaged by its
public willingness to concede in various contests.
The most striking case of British appeasement concerned concessions
to the United States in the late nineteenth century. In 1895, President
Grover Cleveland intervened in a boundary dispute between Venezuela and
the colony of British Guiana, warning that the United States would
“resist, by every means in its power” any British attempt
to occupy the disputed territory.61
In 1898–99, the
United States threatened to abrogate the Clayton-Bulwer Treaty with
Britain and build a Central American canal. In 1902, President Theodore
Roosevelt sent cavalry to resolve a border dispute between Alaska and
Canada. In all three cases, the British backed down, agreeing to submit
the Venezuelan dispute to arbitration, recognizing the U.S. right to
build the canal, and essentially accepting the U.S. position on the
Alaskan dispute.
Why did they do so? A war against the United States at this point
would have been difficult to win. Objectively, the stakes were
relatively low for Britain. But what about its reputation? One British
newspaper, the Saturday Review, argued against appeasement on
just these grounds: “perpetual surrender only means further
demands, and either more concession or an aggravation of ill-feeling as
a result of unexpected resistance.”62
Lord Salisbury and the British
ambassador in Washington both advocated a tougher line on the
Venezuelan dispute.
The decisive consideration was probably Britain's need to
stretch military resources to deal with other more important crises
elsewhere.63
Lobell
2001 also argues that Britain was forced to choose its fights
carefully during this period and relates the country's dilemma to
the chain-store paradox.
The U.S. disputes coincided with the
outbreak of the Boer War, which at its height diverted 300,000 British
troops to South Africa, leaving the empire's defenses elsewhere
“severely weakened.”
64 Even South Africa was
not the most urgent priority. As Kennedy notes:
Perhaps the most interesting aspect of the Venezuelan and
Transvaal clashes was that they were not with the powers which
most British imperialists considered to be the country's really
serious rivals. Lurking in the background, the Cabinet and the press
knew, was that formidable Franco-Russian combination, whose
battlefleets were almost as large as the Royal Navy's and whose
ambitions clashed with Britain's everywhere from the Mediterranean
to the China Sea. If the Dual Alliance was the real foe, could the
country afford the luxury of quarrelling with the other powers?65
The British and French in 1898 were racing each other to the source
of the Nile. In June 1900, the Boxer uprising in China prompted a great
power intervention, which the British feared the Russians would exploit
to grab Chinese territory. Had Britain been fighting the United States,
it would have been harder to scare off the French at Fashoda in the
Sudan. The empire would have stood in peril as other great powers
sought to inflame its weak spots.
The British-U.S. conflicts meet the criteria under which appeasement
will not undermine a state's reputation for resolve. The stakes
were low relative to the cost of fighting. These costs—given the
distances involved—were potentially high. Britain's future
challengers were perceived to be bellicose. Under these conditions,
even a “strong” state would appease. Understanding this,
Britain's global adversaries did not infer lack of resolve from
its acquiescence to U.S. demands. The standard chain-store model
implies that any act of appeasement reveals the appeaser to be
“soft.” Other challengers should therefore attack. This
patently did not happen. Britain's retreat in the Venezuelan
crisis in 1895–96 did not embolden France to take on the British
in 1898 when its expeditionary force faced Kitchener's at Fashoda.
The contrast is striking. On this occasion, the Royal Navy mobilized
for war. It was the French who backed down.66
Ibid., 112–13. In fact, not even the U.S. side
viewed the British concessions as a sign of “softness.” In
January 1896 the Philadelphia Press wrote of the British
moderation on Venezuela that: “No American has dreamed of
attributing this to cowardice” (quoted in Rock
2000, 43). Rock concludes there is no evidence that
Britain's “capitulation on one matter elicited harsher
demands on another.”
As relations with Germany deteriorated in the 1930s, British military
planners continued to worry about the country's global exposure.
Although Hitler's intentions were certainly debated, policymakers
also expressed another concern—that a diversion of forces to
Europe would undermine Britain's ability to deter challenges in
the East. The British Chiefs of Staff warned in December 1937:
“we cannot foresee the time when our defence forces will be
strong enough to safeguard our trade, territory and vital interests
against Germany, Italy and Japan at the same time” and urged the
government to “reduce the number of our potential enemies and to
gain the support of potential allies.”67
When Italy invaded Ethiopia in 1935,
the British admiralty was determined to stay out of a Mediterranean
conflict that would threaten its ability to “get an effective
fleet to Singapore if a crisis developed in the Far East.”
68 British strategy had traditionally prioritized
the defense of India, Burma, the Middle Eastern countries and African
colonies over fighting in Europe. International conflict would threaten
the empire's internal cohesion. As Lord Lothian put it:
“Nehru is openly awaiting the next world war to let loose
revolution in India.”
69 The choice in the 1930s was stark: continue to try to defend the
empire, or concentrate on deterring the growing German threat. In a
great irony, Chamberlain, as chancellor of the exchequer, was among the
first to argue for the latter. He proposed to the cabinet in 1934 that
they reduce expenditures on imperial defense to build an air force
capable of deterring Hitler, and even suggested Britain should give up
defending the naval base in Singapore. “This,” Howard
notes, “was even more than the former pacifist Ramsay MacDonald
was prepared to accept.”70
That Chamberlain could make this remarkable suggestion in 1934
suggests that uncertainty about Hitler's aims (as emphasized by
Powell) was not the only reason the British opted for appeasing
Germany. In fact, Chamberlain appears to have had quite a realistic
view of the Nazi threat from the start.71
In 1934, Chamberlain urged the Air Ministry to come up
with a plan “based on the consideration that Germany might become
a major threat within five years” (Hughes
1988).
His eagerness to appease seems to have increased
as the evidence of Hitler's global ambitions mounted. The episode
highlights the context of severe resource constraints within which all
strategic decisions were made. Chamberlain's arguments with the
military planners in the mid-1930s were not over appeasement versus
deterrence, but whether to spend available funds on warships to deter
Japan or aircraft to deter Germany.
72 Unfortunately, he lost the debate.
Spain
Around 1615, the Spanish Habsburg Empire spanned the globe—from
the Netherlands, Portugal, and Spanish Italy to Brazil, Mexico, Peru,
and the Far East. Within Europe, Spain had achieved “undisputed
primacy.”73
Just sixty years later,
the state had become “the sick man of Europe.”
74 Several reasons have
been suggested for this precipitous decline. Droughts, plagues, and
economic depression—although not unique to Spain—all took
their toll. In large part, the country's failure appears the
result of a misguided preoccupation with the need always to fight to
preserve reputation. This led to “fatal over-commitment …
to foreign wars at a time when Castile lacked the economic and
demographic resources to fight them with success.”
75 Rather than increasing its security—as simple
models of deterrence would predict—Spain's aggressive
responses to challenges united all powers against it, while provoking
internal rebellions and eroding public finances.
76 In Kennedy's image, “Spain resembled a large
bear in the pit: more powerful than any of the dogs attacking it, but
never able to deal with all of its opponents and growing gradually
exhausted in the process” (1987,
49).
The case illustrates how resource constraints can undermine
the effectiveness of attempts to deter by demonstrating resolve, as
formalized in the previous models.
Spain's ascendancy early in the century owed much to the careful
policies of Philip III's key minister, the Duke of Lerma. In 1604,
Lerma made peace with England; in 1609, he signed a truce with the
Dutch, who had been rebelling against Spanish rule since the 1560s; and
in 1611, he arranged a marriage alliance with France. While
neutralizing threats to the North, he redirected Spanish foreign policy
toward the Mediterranean.77
This changed with Lerma's replacement in 1618 by Don Baltasar de
Zúñiga and his nephew, the Count-Duke of Olivares.
Henceforth, foreign policy focused on the need to preserve Spain's
prestige. According to Zúñiga: “a monarchy that has
lost its reputación, even if it has lost no territory,
is a sky without light, a sun without rays, a body without a
soul.”78
This goal came to justify massive
accumulation of public debt, for, as the marquis of Montesclaros,
president of the state's Council of Finance, put it in 1625,
“the lack of money is serious, but it is more important to
preserve reputation.”
79 Preoccupation with reputation turned any international crisis into a
test, failure at which would start the dominoes falling. According to
Olivares in 1635, “the first and most fundamental dangers
threaten Milan, Flanders and Germany. Any blow against these would be
fatal to this monarchy; and if any one of them were to go, the rest of
the monarchy would follow, for Germany would be followed by Italy and
Flanders, Flanders by the Indies, and Milan by Naples and
Sicily.”80
This
logic prompted a series of Spanish interventions that ultimately led to
fifty years of war. First, Philip IV intervened to aid the Habsburg
Emperor against Bohemian rebels. Spain renewed conflict with the Dutch,
attempted disastrously to influence the Mantuan succession, and went to
war with England and France. Efforts to centralize administration and
squeeze additional revenues out of the Spanish heartland to finance
these wars provoked uprisings in Catalonia and Portugal in 1640,
followed by revolts of Naples and Sicily in 1647. War losses trimmed
the empire's outlying territories, while regional fragmentation
accelerated in the heartland, until the French Bourbons won control of
the throne in 1701.
Other policies had been possible. The Count of Humanes had proposed a
course of strategic retreat similar to Lerma's. He argued in 1635
that Spain should abandon the Netherlands, make Milan an independent
duchy, and use the money thus saved to enhance defenses of peninsular
Spain and the Indies. Much later, in the 1660s, Olivares's
son-in-law, the Duke of Medina de las Torres, advocated a conciliatory
approach. In Medina's view, “the true reputation of states
does not consist of mere appearances, but in the constant security and
conservation of their territories, in the protection of their subjects
and the well-being thereof, in the respect which other princes have for
their authority and military strength.”81
To a traditional deterrence theorist, the futility of Spain's
efforts to nurture its reputation should seem puzzling. Philip
IV's evident readiness to fight might have been expected to deter
subsequent challenges. Sending troops to Bohemia should have
intimidated the Dutch rebels. It did not. Instead, the Dutch, under the
“war party” of Maurice of Nassau, refused to extend the
Twelve Year Truce with Spain when it ended in 1621 and sent support to
the Habsburgs' Protestant opponents.82
According
to the conventional logic, Spain's intervention in the Mantuan
crisis should also have deterred the Dutch. The opposite occurred.
Whatever it did for Philip's
reputación, his
Italian campaigns absorbed resources. He was forced to sharply reduce
support to Spanish forces in the Netherlands, where total financing
dropped from 39 million florins in 1621–25 to 29 million in
1626–30.
83 The Dutch responded by
stepping up attacks, capturing the Spanish treasure fleet in 1628,
taking towns in the Rhineland and Brabant in 1629, and occupying the
Brazilian province of Pernambuco in 1630.
The trade-off Spain faced under Philip IV was exactly that captured
by the rational appeasement model. Foreign interventions may indeed
have enhanced the state's reputation. However, these actions tied
up troops that could not simultaneously deter attacks elsewhere and
helped undermine Madrid's fiscal solvency, inviting additional
challenges. Spain was sometimes engaged on three fronts
simultaneously.84
Fighting the French on
the continent and intervening in Italy, it had fewer resources to
protect its overseas possessions from Dutch penetration. By 1640, the
monarchy could not even deter internal revolts as close to home as
Catalonia.
Conclusion
For actors with limited resources facing multiple potential
challenges, selective appeasement can be rational. If the stakes of
conflict are either high or low, or if the costs of fighting are high,
it may be the only rational strategy. Fighting an early challenge is
sometimes unnecessary to deter later ones—and sometimes
counterproductive. If even “tough” states would appease, it
is unnecessary; if the loss of resources outweighs any reputational
gains, it is counterproductive. Even when it is rational to fight an
early challenge, it will be optimal to lower future demands on more
bellicose potential challengers.
Recognizing this—and modeling the point formally—serves
several purposes. First, it has implications for security policy. In
defending—and sometimes devising—policies, U.S. leaders
have often appealed to a view of reputation as fragile and universally
exposed. If such arguments are sincerely believed, a closer look at the
logic suggests they need to be rethought. If they are mostly
rhetorical, an understanding of their logical weaknesses should help
guard listeners against political manipulation. Adversaries do not have
reason to draw far-reaching conclusions about U.S. resolve from
settings in which the stakes are very high or very low. Realizing this
might help reduce the dissonance strategic planners must feel as they
promise to “meet every threat” while budgeting for just two
major wars.
In practice, most state leaders must realize there is a trade-off
between losing reputation and losing enforcement resources. Yet many
still seem to find themselves stuck, unwilling to bear what they
perceive to be large reputational costs. This surely was the main
reason Richard Nixon and Henry Kissinger delayed leaving Vietnam. But
there is a saving grace in such situations that few leaders seem to
notice: the higher are the resource costs of intervening, the lower the
reputational costs of withdrawing. To leave Vietnam, given how costly
it had become, would signal little about American resolve because
almost any rational regime—even highly resolute ones—would
do the same.85
George Ball cautioned at
the time that fighting when the costs were so high that even resolute,
rational players would withdraw could even damage a state's
reputation—for rationality: “What we might gain by
establishing the steadfastness of our commitments, we could lose by an
erosion of confidence in our judgment” (Ball
1982, 382).
Similarly, states that withdraw from
low-stakes conflicts should suffer only minimal loss of credibility.
Objectively, Lebanon in the 1980s had little obvious importance for the
United States. Thus, when George Shultz claimed after the 1983 marine
barracks bombing that: “If America's efforts for peaceful
solutions [in Lebanon] are overwhelmed by brute force, our
role in the world is that much weakened everywhere,” he was
stating the point in far too general terms.
86
Other terrorist groups hoping to dislodge the United States from bases
in the Middle East might indeed take heart.
87 Osama bin Laden, in 1996, called the U.S. pullout from
Beirut a sign of American softness. Saddam Hussein also mentioned the
Beirut bombing in a speech in early 1990. If he deduced from this that
the United States would not oppose his invasion of Kuwait, he was
misreading the stakes in the two cases. While Lebanon produces little
oil, the Gulf states' output is important for the world
economy.
But Soviet leaders did not draw inferences about
American resolve.
88 The model also has implications for theory and empirical testing in
international relations. The rather extreme—and often empirically
unsupported—predictions of deterrence theory have prompted some
to reject rationalist explanations of conflict behavior. I show that
introducing resource constraints into the standard model leads to more
nuanced and plausible results. At the same time, this model—like
most others of international signaling—highlights the importance
of what game theorists call “off-equilibrium-path
beliefs”—hypothetical interpretations of events that
players believe will not occur. To study the formation of such beliefs,
it may indeed be necessary—as critics of rationalist analysis
argue—to turn to the social psychologists.
On the empirical side, the model suggests some hypotheses that might
be tested against those of psychological models of reputation
formation. One could test whether observers generalize more readily
between cases in which stakes or costs of fighting are similar. One
might explore whether states in fact have multiple reputations,
conditioned on the stakes. Most empirical studies try to trace the
incidence of violent conflict to characteristics of the states
involved. The model suggests this is incomplete. A state's motive
to fight challenges should depend also on the expected bellicosity of
future challengers. Including some estimate of this might improve
predictive power.
Finally, however, the analysis suggests both that one should not
expect too much from rational reputation models and that one should not
conclude too quickly that they are wrong. Because both appeasement and
deterrence equilibria are often possible for the same parameter values,
most behavior could be rationalized in some way. To generate models
with more predictive power and the fragility necessary for easy
falsification, scholars may have to incorporate insights from
psychology about how beliefs form and test for the existence of
specific beliefs. In short, even those who keep the rationalist
approach to explaining international behavior may need to learn more
about the human mind as well as about deductive logic.
Appendix: Proofs of Propositions
Proof of Proposition 1. Note that it is sufficient to
identify perfect Bayesian equilibria (PBEs), because Fudenberg and
Tirole (1991) establish that any PBE in a
game of this type (a multiperiod game with observed actions in which
players each have no more than two types, and types are independent and
have nonzero probability) is also a sequential equilibrium. A PBE (in
the sense of Fudenberg and Tirole 1991) of
this game is a profile of behavioral strategies and beliefs such that:
(1) each player maximizes its expected utility from each information
set onward, given the player's beliefs at that information set,
(2) beliefs at all information sets that are reached with positive
probability in equilibrium are derived using Bayes' Rule, and (3)
beliefs about player i at period t + 1 depend only on
the history of play up to t − 1 and player
i's period-t action.
1. If t < k, even CS
appeases at time 4. Knowing this, L2 always
challenges at time 3, so there can be no DE. Denote the belief at
information set hi “μi.”
In a DE, both CS and
CW must fight at time 2, on or off the
equilibrium path. Given this, the only consistent belief at
h1 is μ1 = π. Thus,
L2's expected payoff from challenging,
π(−t − k), is only less than or equal
to that from acquiescing, −t, if t ≤
kπ/(1 − π). This is required for either
on- or off-equilibrium path DE.
For any k ≤ t ≤ kπ/(1 −
π), the following behavioral strategies and beliefs constitute a DE:
L1 plays a; L2 plays a at
h1, c at h2, a at h3;
CS plays F at all its choice nodes (time 2
and 4); CW plays F at its time-2 choice node,
and A at its three time-4 choice nodes. Beliefs are at h1,
μ1 = π; at h2, μ2 = 0; at
h3, μ3 = π.
2. The definition of on-equilibrium-path PDE requires
CW to mix at time 2, which requires that
CW get the same expected payoff from A and F.
For this, L2 must also mix at h1,
h2, or both. (CW's payoff from
F is a convex combination of −k and t −
k; that from A is a convex combination of 0 and t.)
There are two ways C's expected payoffs from A and F could be
equalized: (1) L2 always plays a at h1, and
mixes at h2; (2) L2 mixes at h1,
and either always plays c or mixes at h2. Case (1) is impossible
because if L2 always plays a at h1,
CS would always play F at time 2; given
this, any C who plays A at time 2 must be weak and
L2 will prefer always to play c at h2
rather than mixing as supposed. So in any on-equilibrium-path PDE,
L2 mixes at
h1.
CS must play F at time 2 in this equilibrium.
To see this, note that for CW to mix, as
supposed, it must be that x − y =
−k/t, where x is the probability that
L2 plays c at h1 and y the probability
L2 plays c at h2. If this is true,
CS must play F at time 2, because its
expected payoff from A, y(t − k) + (1
− y)t, is less than that from F,
2x(t − k) + (1 −
x)(2t − k) = 2t −
k(x + 1), given x − y =
−(k/t). For L2 to mix at
h1, it must get equal expected utility from a and c. This
implies μ1 = t/(t + k).
The belief at h1 must be derived by Bayes' Rule from
the equilibrium strategies. This implies: μ1 =
Pr(strong|F at time 2) = π/(π + (1 −
π)pw). In equilibrium,
π/(π + (1 − π)pw) =
μ1 = t/(t + k) [hArr ]
t = (π/(1 −
π))(k/pw). This condition
is required in any on-equilibrium-path PDE.
In an off-equilibrium-path PDE, CW must,
by definition, mix off the equilibrium path at time 2. As before, this
requires that L2 mix at h1. For this,
L2's expected utility from c must equal that
from a, given its belief μ1. This implies
μ1 = t/(t + k).
Consistency of beliefs, required by sequential equilibrium, means that
μ1 must be arbitrarily close to the belief that would be
derived using Bayes' Rule from a slight perturbation of the
equilibrium strategies in which L1 plays c with
positive probability. Note that, off the equilibrium path as well as
on, for CW to mix as assumed implies that
CS plays F at time 2. Thus, this limiting
belief derived by Bayes' Rule must be π/(π + (1
− π)pw). In sequential
equilibrium again μ1 = π/(π + (1 −
π)pw) = t/(t +
k), and t = (π/(1 −
π))(k/pw).
Proof of Proposition 2. If t < αk,
even CS appeases at time 4. Knowing this,
L2 always challenges at time 3, so in any DE
t ≥ αk. In a DE, both
CS and CW
must fight at time 2, on or off the equilibrium path. Given this, the
only consistent belief at h1 is μ1 = π.
L2's expected payoff from challenging at
h1, π(−(t/α) − k),
is only less than or equal to that from acquiescing, −t,
if t ≤ αkπ/(α − π). This
is required for either on- or off-equilibrium-path DE.
For any αk ≤ t ≤
αkπ/(α − π), the following
behavioral strategies and beliefs constitute a DE:
L1 plays a; L2 plays a at
h1, c at h2, and a at h3;
CS plays F at all its choice nodes (time 2
and 4); CW plays F at its time-2 choice
node, and A at its 3 time-4 choice nodes. Beliefs are at h1,
μ1 = π; at h2, μ = 0; at
h3, μ3 = π.
The definition of PDE requires that, either on or off the equilibrium
path, CW mix at time 2, which requires
that it get the same expected payoff from A and F. As in the proof of
Proposition 1, this requires that L2 mix at
h1, which here implies μ1 =
αt/(t + αk). For
L2 to mix requires t ≥ αk,
because if t < αk, even
CS appeases at time 4, and
L2 challenges at time 3. Denote the probability
CS plays F at time 2: 0 ≤
ps ≤ 1. On the equilibrium path, belief
μ1 must be derived by Bayes' Rule, which here
implies Pr(strong|F at time 2) =
πps
/(πps + (1 −
π)pw). In equilibrium
πps
/(πps + (1 −
π)pw) = μ1 =
αt/(t + αk), which implies
t =
πpsαk/(α(1
− π)pw +
πps(α − 1)) ≤
αk/(α − 1). In an off-equilibrium-path PDE,
consistency requires that μ1 be arbitrarily close to the
belief that would be derived using Bayes' Rule from the
equilibrium strategies if these were perturbed so that
L1 played c with arbitrarily small positive
probability. This, again, implies μ1 =
πps
/(πps + (1 −
π)pw), so t =
πpsαk/(α(1
− π)pw +
πps(α − 1)) ≤
αk/(α − 1). Thus, t ≤
αk/(α − 1) in any PDE.
Proof of Proposition 3. If t < k, even
CS appeases at time 4. Knowing this,
L2 challenges at time 3, so AE requires t
≥ k. As noted in the text, no off-equilibrium-path AEs
exist. In an on-equilibrium-path AE, both
CS and CW
appease at time 2. Because both types appease at time 2, the belief at
h2 is μ2 = π. L2 will
only play a if π(−t − k) ≤
−t [hArr ] t ≤ kπ/(1 −
π). Given that L2 acquiesces at h2,
for CS to play A there must be a belief
associated with playing F that makes this unattractive. Sequential
equilibrium permits arbitrary choice of belief here. I am interested in
the broadest range of parameter values for which AE is possible. It is
easy to check that μ1 = 0 yields the loosest condition
on t. If μ1 = 0, L2
challenges at h1, resulting in a payoff for
CS of max[t +
t/α − 2k, t −
k] . Playing A yields t. Thus, if either
αk ≤ t ≤ 2αk or k
≤ t < αk, CS
may play A. Because L2 plays a at h2,
CW will also prefer A at time 2. Finally,
given that C plays A at time 2, L1 prefers
to challenge. So an on-equilibrium-path AE exists for any t
such that k ≤ t ≤ kπ/(1
− π), and t ≤ 2αk.
For instance, for any k ≤ t ≤
min[2αk,kπ/(1 − π)] ,
the following will be an AE: L1 challenges;
L2 plays c at h1, a at h2, a
at h3; CW plays A at all its
decision nodes; CS plays A at time-2 and F
at its time-4 nodes. Beliefs are at h1 : μ1 =
0; h2 : μ2 = π; h3 :
μ3 = π.
The belief that a C who deviates from the equilibrium path
to fight is “weak” might seem unreasonable. Kreps and
Wilson call such beliefs “implausible.”89
If, by contrast, any
C that fights at time 2 is
believed “strong” (while the belief about appeasers remains
π), the conditions for AE are not so different: either (1)
t ≤
kπ/(1 − π) and
k
≤
t ≤ α
k, or (2)
t ≤
kπ/(1 − π), α
k ≤
t
≤ 2α
k, and
t ≥ α
k/(α
− 1). The only change is that a range of
t from
α
k <
t < α
k/(α −
1) is excluded.
Propositions 4 and 5. Because of space constraints, proofs
are omitted here. They are available at
〈http://www.sscnet.ucla.edu/polisci/faculty/treisman〉.
Proof of Proposition 6. At h1,
L2 plays a only if
αkc ≤ t2 ≤
αk2 μ1 /(α −
μ1) (given t2 > 0), so the upper
bound on t2 such that L2
acquiesces increases with k2. At hi,
i = 2,3, L2 plays a only if
kc ≤ t2 ≤
k2 μi /(1 −
μi) (given t2 > 0).
Again, the upper bound on t2 increases with
k2. At h4,
L1 plays a (given
t1 > 0) only if (1) it expects
CS to play F and CW
to play A at time 2, and t1 ≤
k1μ4 /(1 − μ4) or
(2) it expects both Cs to play F at time 2 and t1
≤ k1 /(1 − μ4). The upper
bound on t1 such that L1
acquiesces increases with k1.
