2. Stakes and leverage of interest groups in trade policy regimes

Assume, just for the moment, that there are two economies, Home and Foreign, with population in both of them normalized to unity. We will discuss an upscaled version featuring a mass of countries in Section 4. Assume furthermore that, in this world economy of two, there are two goods (good 1 and 2) that are potentially subject to trade restrictions, whereas a third good that serves as numéraire is freely traded. The latter assumption follows the tradition in trade analysis by primarily ensuring that international trade flows are balanced. As such, it will not be considered in more detail. Both goods whose trade is potentially restricted are produced in both of the countries with supply, however, inelastic in order to simplify the analysis. Notice that the kind of trade restriction that is imposed on these goods is of secondary importance. Countries may impose duties on imports, but since other trade restrictions carry a tariff equivalent, it is not necessary to be more specific at this point.

As for trade, we will assume without loss of generality that Home enjoys a comparative advantage in the production of good 2 while Foreign has an advantage in good 1, with supply of both of these export goods inelastic at unity. Simplifying again, the competitive disadvantage in good 1 (Home) and good 2 (Foreign) can be expressed by parameter λ with 0 < λ < 1 and with the disadvantage decreasing as the parameter approaches unity. Measuring the lack in competitiveness, λ is thus also an index of the stake import-competing interest groups have in protection. This supply side ensures that, given the same downward sloping demand curve in Home and Foreign, prices of these goods in autarky are higher, the smaller λ and, naturally, also higher than abroad (and so are local rents). Supply (X) in Home and Foreign is thus

(1)\begin{equation} \begin{array}{l} X_1 = \lambda ;\quad X_1^* = 1 \\ X_2 = 1;\quad X_2^* = \lambda , \\ \end{array}\end{equation}

with subscripts 1 and 2 for goods 1 and 2 respectively. We follow common practice in that variables with an asterisk refer to Foreign. With λ < 1, Home (Foreign) is thus a natural importer of good 1 (2). Because of the inelastic supply and the rents associated therewith, Home's import substitution industry (good 1) has a vested interest in protection while its export industry (good 2) would benefit from free access to markets abroad. The same applies with respect to Foreign, there, however, with the sign reversed.

Suppose furthermore that demand (D) is in any case a simple downward sloping curve of domestic prices p, that is, prices including tariffs or tariff equivalents of other import restrictions:

(2)\begin{equation} \begin{array}{l} D_1 \left( {p_1 } \right) = 1 - p_1 ;\quad D_1^* \left( {p_1^* } \right) = 1 - p_1^* \\ D_2 \left( {p_2 } \right) = 1 - p_2 ;\quad D_2^* \left( {p_2^* } \right) = 1 - p_2^* . \\\end{array}\end{equation}

With trade, albeit restricted, arbitrage conditions are thus p ₁ = p*₁ + τ and p*₂ = p ₂ + τ*, with τ, τ* nominal protection (tariff equivalent) rates in Home and Foreign, respectively. Markets for both goods are cleared via trade, implying that supply equals demand for each of them:

(3)\begin{equation} X_1 \left( \lambda \right) + X_1^* = D_1 \left( {p_1 } \right) + D_1^* \left( {p_1^* } \right);\quad X_2 + X_2^* \left( \lambda \right) = D_2 \left( {p_2 } \right) + D_2^* \left( {p_2^* } \right).\end{equation}

Market-clearing prices depend inter alia on the competitiveness of the import-substitution industry as measured by parameter λ, as does the import-substitution industries’ stake in protection. The natural coalition partner in the quest for protection is either the government (when collecting tariff revenue) or all those political groups that receive the equivalence of the tariff revenue in the form of rents. The potential opposition is, as usually, formed by the export industry and the consumers whose real income would be higher because of cheaper imports, in case tariffs were removed.

It might be clear who is the potential winner and who is the potential loser when markets are opened up. Yet, it is much less clear how preferences are aggregated in the political process. We will thus distinguish between stakes of vested interests in a particular political regime and their political leverage: as for a general approach, and for reasons mentioned in the introduction, we will assume that preferences are amalgamated into political objective functions V (V* for Foreign) by means of parameter μ with 0 < μ < 1. Hence, parameter μ is a measure of the leverage of protectionist interests versus free-trade interests (that is, the import-substitution industry and recipients of tariff revenue versus the consumers and export industry) – which may well differ from their stake in protection as parameterized by λ. However, notwithstanding problems of aggregation, the respective stakes continue to be measured by consumer (CS) and producer surpluses (PS) as they depend on λ. Consumer surplus is the difference between the maximum willingness to pay and the actual market price. In our case of linear demand and prices as previously outlined, CS, for example, in the consumption of good 1 in Home is the triangle c ₁(1 − p ₁)/2, with c ₁ actual consumption according to equation (2), p ₁ market price of good 1 and unity the maximum willingness to pay. Because of the assumptions concerning supply, producer surplus PS can be simply proxied by sales revenue, that is X ₁p ₁. Finally, with imports M ₁ ≡ D ₁ − X ₁, government collects tariff revenue τM ₁ (similar in Foreign).Footnote ⁴

(4)\begin{equation} \begin{array}{l} V = \left( {1 - \mu } \right)\left( {CS_1 + CS_2 + PS_2 } \right) + \mu \left( {PS_1 + \tau M_1 } \right) \\ V^* = \left( {1 - \mu } \right)\left( {CS_1^* + CS_2^* + PS_1^* } \right) + \mu \left( {PS_2^* + \tau ^* M_2^* } \right). \\ \end{array}\end{equation}

Note that this does not imply that politicians act on behalf of their constituents with complete knowledge of their preferences and foresight as regards the implications of policies. The contrary might be the case: the parameterization with respect to the stakes and the leverage not only covers a wide range of possible ways as to how special interests feed into the political will, it can also be interpreted as a fuzziness with respect to perceptions. With these quite general assumptions concerning the aggregation of interests, we can take a closer look at the incentives (and thus the chances) for sustaining a particular trade regime in the presence of interest groups with stakes λ and political leverage μ.

3. When does a prisoner's dilemma arise?

We will start out with the main argument that is often advanced in support of formal international institutions such as the WTO, namely that otherwise countries would wind up in a prisoner's dilemma from which they cannot free themselves as no country (or policy maker) is ready to make a first move. As alluded to in the introduction, removing barriers to trade while others keep their markets protected, so the argument, would imply a worsening of the terms-of-trade respectively a loss of political support. Given a situation like this, countries are thus stuck with protectionist regimes, and, one might add, with world output smaller than otherwise.

However, a scenario thus bleak need not materialize. Consider the ranking of strategies in a ‘one-shot game’ of two policy makers (from Home and Foreign) with preferences V, V* driven by domestic political support. This is the typical setting under which a prisoners’ dilemma in the governance of trade is said to loom large. Figure 1 displays the basic scenario with politically perceived pay offs conditional on policies as indicated by subscripts, that is, for example, .V|_{τ > 0; τ* = 0} in case of an asymmetric protection of Home's import-substitution industry.

Figure 1. Pay offs: ‘one-shot trade policies’

Whether protectionism really prevails depends on the two aforementioned parameters in particular: (i) the international competitiveness of the local industry (as measured by parameter λ) and (ii) the leverage of domestic interests seeking protection (as measured by parameter μ). They are both crucial to the ranking and sustainability of policy regimes. Although domestic interests seeking protection have a saying in policy formation and although the chance that Foreign's policy makers might reciprocate does not have a bearing on Home's policy makers’ strategy, protectionism need not obtain. Hence, on a conceptual basis, the prisoner's dilemma does not always reflect governance issues in trade. Note though, that this conjecture is not based on a welfare-theoretic account but on pay offs as politically perceived; those pay offs need by no means coincide with the underlying welfare-theoretic account.

In order for protection to be politically perceived superior despite both parties being better off in case of mutual trade liberalization, the leverage μ of vested interests must fall within a certain range, with the range in turn conditional on the stake λ those interests may have in a protectionist regime. Under Nash assumptions, protectionism is perceived a strictly dominant strategy iff .V|_{τ > 0; τ* = 0} > .V|_{τ = 0; τ* = 0} and .V|_{τ > 0; τ* > 0} > .V|_{τ = 0; τ* > 0}. This condition implies a lower bound on the leverage of vested interests μ: inserting the respective values of consumer and producer surplus, and, if applicable, tariff revenues or related rents into the objective function of policy makers, according to equation (4) shows that outcomes .V|_{τ > 0; τ* = 0} and .V|_{τ = 0; τ* = 0} as perceived by policy makers depend on interest-group parameters μ and λ. Solving the inequality for political weights μ then yields pivotal values μ for protection to outperform trade liberalization, even if subjective. Hence, defection (protection) politically outperforms cooperation (trade liberalization) iff

(5)\begin{equation} \mu > \frac{{3 + 2\lambda - 5\lambda ^2 }}{{7 + 2\lambda - 9\lambda ^2 }},\end{equation}

thus implying a lower bound on the leverage μ. The pivotal leverage increases in the competitiveness λ of the import-substitution industry: the more competitive the industry, the higher must be the leverage in order to overcome the smaller stakes of their clientele in a protectionist regime (with ∂μ/∂λ = 8/(9λ + 7)² > 0 for all values of 0 < λ < 1). The same applies with respect to the ranking of outcomes .V|_{τ > 0; τ* > 0} and .V|_{τ = 0; τ* > 0}.

The nexus between both of the parameters, however, is much richer than the focus on dominant strategies suggests. This is because for a ‘pure’ prisoner's dilemma (Kuhn and Moresi, Reference Kuhn and Moresi1995: 335; Rapoport and Chammah, Reference Rapoport and Chammah1965: 34) to obtain, expected outcomes in case of mutual cooperation (here: in trade liberalization) must be considered even better, thus reflecting the ‘true dilemma’. Henceforth, the situation is perceived as a ‘pure’ prisoner's dilemma when the following ranking obtains: .V|_{τ > 0; τ* = 0} > .V|_{τ = 0; τ* = 0} > .V|_{τ > 0; τ* > 0} > .V|_{τ = 0; τ* > 0} and 2.V|_{τ = 0; τ* = 0} > (.V|_{τ > 0; τ* = 0} + .V|_{τ = 0; τ* > 0}). Both of these conditions yield an upper bound on the political leverage μ of domestic interest groups: inserting again values of consumer and producer surpluses, and, if applicable, tariff revenues into equation (4) yields politically expected outcomes of the respective strategies. Solving for the critical μ for which inequalities hold then requires μ not to be too large:

(6)\begin{equation} \mu < \frac{{3 - 2\lambda - \lambda ^2 }}{{5 - 2\lambda - 3\lambda ^2 }}.\end{equation}

Here, the condition on the leverage μ is decreasing in the stake λ: the higher the competitiveness of the import-substitution industry, the smaller must be the leverage of protectionist interests in order for the strategic interaction to give rise to a ‘true dilemma’ in the sense that mutual liberalization would have been better (that is ∂μ/∂λ = −4/(3λ + 5)² < 0 for all values of 0 < λ < 1).

Figure 2 displays pivotal values of interest-group parameters according to equations (5) and (6). The perception of protectionism to pay off politically (that is equation (5)) corresponds to the upward sloping curve, with all combinations (λ, μ) above implying that protection is politically preferred over liberalization (and for all values below the reverse). The upper bound on the leverage μ (that is equation (6)) corresponds to the downward sloping curve, with all combinations (λ, μ) below reflecting that mutual trade liberalization would have been considered even better an outcome.

Figure 2. Strategy space with leverage factor μ

The hatched area indicates the parameter combinations for which cooperation in trade liberalization obtains despite the presence of groups sharing an interest in protectionism; the area between the upward and the downward sloping boundary shows the range for which the situation is perceived as in a ‘pure dilemma’. The range shows the value of a rigorous formal analysis, as does the fact that the parameters have somewhat of a different impact, which also comes out of the analysis.

4. Evolutionary stable strategies in reciprocating trade policies: what are the chances for the emergence of cooperation in trade liberalization?

However, in evolutionary perspective, outcomes also depend on the expected pay off from a continuing trade relationship. This raises the bars for protectionism because in case of TFT trade relationships are at risk. The risk of a protectionist regime facing retaliation is to be included as a cost in any comparison of strategies. In line with repeated interaction models let parameter q thus denote the expected frequency of trade in the future.

Parameter q may include a discount rate or not. Adding another, explicit, time-specific element, however, does not change the calculus in any substantial way. Therefore, we will leave open what kind of information or characteristics of preferences enter q and instead interpret q as an amalgamation of (eventually) highly subjective considerations. Presumably, initial behavior triggers either cooperation in trade liberalization or retaliation of protectionist strategies along TFT lines. Figure 3 has the expected pay offs in repeated interaction, with .V|_{τ = 0; τ* = 0}, .V|_{τ > 0; τ* = 0}, .V|_{τ = 0; τ* > 0}, .V|_{τ > 0; τ* > 0}, as previously noted (see equations (8) in the Appendix).

Figure 3. Pay offs: ‘trigger strategies in trade policies’

Trigger strategies then imply a lower bound on the (subjective) frequency parameter q for reciprocating trade liberalization to obtain. According to Axelrod and Hamilton (Reference Axelrod and Hamilton1981: 1393), TFT must outperform three alternative strategies, namely

• - a strategy of always cooperating (liberalizing),

• - a strategy of defection (protection) despite cooperation of the opposite party, which eventually triggers protection, and

• - a strategy of alternating between defection (in this case: protection), and cooperation (liberalization).

Since, in effect, the first strategy can be expected to yield the same outcome as TFT, Axelrod and Hamilton (Reference Axelrod and Hamilton1981: 1393) assume that it does not crowd out an established TFT. They thus consider only two strategies potentially threatening TFT, namely those listed second and third. Accordingly, evolutionary stability requires that TFT does better than those. Maynard Smith (Reference Maynard Smith1976: 42; Reference Maynard Smith1982: 14–24) and Maynard Smith and Price (Reference Maynard Smith and Price1973: 17), by contrast, do not consider doing equally well a sufficient condition for non-invasion, as, for instance, the mutants might do better than the established strategy when facing another mutant. In addition, they account for the possibility of randomly mixed strategies. While these modifications might be important in some circumstances, they are less relevant in a trade-policy nexus. A strategy of ‘always cooperate’ amounts to unilateral trade liberalization. Yet, it is exactly for political-economy reasons why unilateralism is seldom, if ever, observed. Randomness will be an issue when we embed the bilateral perspective into an n-country setting. For the time being, we can thus safely follow Axelrod and Hamilton by considering the two remaining alternatives to carry over to trade policy, however, here, in modified form, so as to reflect international interdependence. That is, pay offs are endogenous (as are trade flows and rents). TFT in trade regimes then outperforms the two alternative trigger strategies iff:

\begin{equation*} \left. V \right|_{\tau = 0;\tau ^* = 0} /\left( {1 - q} \right) > \left. V \right|_{\tau > 0;\tau ^* = 0} + \left( {\left. V \right|_{\tau > 0;\tau ^* > 0} } \right)q/\left( {1 - q} \right),\end{equation*}

\begin{equation*} \wedge \left. V \right|_{\tau = 0;\tau ^* = 0} /\left( {1 - q} \right) > \left( {\left. V \right|_{\tau > 0;\tau ^* = 0} } \right)/\left( {1 - q^2 } \right) + \left( {\left. V \right|_{\tau = 0;\tau ^* > 0} } \right)q/\left( {1 - q^2 } \right).\end{equation*}

Solving for q yields

(7)\begin{equation} \left. {\begin{array}{*{20}c} {q \ge \frac{{\left. V \right|_{\tau > 0;\tau ^* = 0} - \left. V \right|_{\tau = 0;\tau ^* = 0} }}{{\left. V \right|_{\tau > 0;\tau ^* = 0} - \left. V \right|_{\tau > 0;\tau ^* > 0} }}} \\[7pt] { \wedge q \ge \frac{{\left. V \right|_{\tau > 0;\tau ^* = 0} - \left. V \right|_{\tau = 0;\tau ^* = 0} }}{{\left. V \right|_{\tau = 0;\tau ^* = 0} - \left. V \right|_{\tau = 0;\tau ^* > 0} }}} \\ \end{array}} \right\} = \frac{{\left( {5\lambda ^2 - 2\lambda - 3} \right) + \mu \left( {7 + 2\lambda - 9\lambda ^2 } \right)}}{{\left( {1 - \mu } \right)3\left( {1 - \lambda } \right)^2 }}.\end{equation}

Figure 4 displays pivotal values for q. The LHS panel of Figure 4 shows the nexus between the competitiveness of the import-competing industry and the threshold level of q that must be attained for mutual trade liberalization to be considered politically superior to protection. Parameter combinations above a particular curve (with each curve corresponding to a particular leverage μ of protectionist interests and with μ increasing from the bottommost to the topmost curve) sustain cooperation in trade liberalization with the trade regime evolutionary stable while those below do not. At the horizontal line, i.e. at μ = 0.5, q is independent of the interest groups’ stakes as measured by λ, with protectionism prevailing for all q below one third and trade liberalization above.

Figure 4. Evolutionary stable strategies with leverage factor μ

For values of μ below 0.5 (dashed lines), the lower bound on q for trade liberalization being evolutionary stable decreases in λ for any given leverage μ (i.e. along a particular dashed line); for all values of μ above 0.5 (dotted lines), it increases in λ. The former result obtains because of dead-weight losses weighing more heavily in case of μ < 0.5 while increasing in λ whereas in case of the latter the opposite holds. In any case, the lower bound on q increases in μ for any given λ. However, the shadow of the future as represented by the frequency q continues to play an important role, even with the political weight of special interests μ and the stake parameter λ as intervening parameters. While the pattern is much richer when special interest driven it is still very much in line with the Axelrod-literature on cooperation. There is thus more to TFT than just a fest for vested interests.

The RHS panel of Figure 4 switches perspective by displaying the nexus in μ–q-space. Curves rotate clockwise around the point (q = 1/3; μ = 0.5) as competitiveness decreases, with λ = 0.75 (dotted line), λ = 0.5 (dashed line), λ = 0.25 (solid line). Hence, for any given subjective frequency parameter q, the range of μ, for which TFT is evolutionary stable, is larger the lower λ, provided q is larger than one third; with q smaller, the reverse applies. Note the difference that shows up in formal analysis as regards both of the interest-group parameters, which turns out to be conditional on the actual value of q.

However, environments may be more hostile than previously assumed, hosting outright protectionist countries. How, then, do vested interests influence TFT? Answering this question requires to embed trade regimes and resulting trade flows into the ‘fitness of groups’ as outlined by Maynard Smith (Reference Maynard Smith1976: 42). Suppose, therefore, that, at most, a fraction Q follows TFT whereas the complementary set, (1 – Q), does not.

In this world, it must be that TFT fares better in the eyes of the policy maker whomever he faces. Hence,

\begin{eqnarray*} Q\frac{{\left. V \right|_{\tau = 0;\tau ^* = 0} }}{{\left( {1 - q} \right)}} + \left( {1 - Q} \right)\left( {\left. V \right|_{\tau = 0;\tau ^* > 0} + \frac{q}{{\left( {1 - q} \right)}}\left. V \right|_{\tau > 0;\tau ^* > 0} } \right)\nonumber\\ \quad > Q\left( {\left. V \right|_{\tau > 0;\tau ^* = 0} + \frac{q}{{\left( {1 - q} \right)}}\left. V \right|_{\tau > 0;\tau ^* > 0} } \right) + \left( {1 - Q} \right)\frac{{\left. V \right|_{\tau > 0;\tau ^* > 0} }}{{\left( {1 - q} \right)}}.\end{eqnarray*}

Inserting .V|_{τ = 0; τ* = 0}, .V|_{τ > 0; τ* = 0}, .V|_{τ = 0; τ* > 0}, .V|_{τ > 0; τ* > 0} as previously and solving for Q yields

\begin{equation*} Q > \frac{1}{2}\frac{{\left[ {5\lambda ^2 - 2\lambda - 3 + \mu \left( {7 + 2\lambda - 9\lambda ^2 } \right)} \right]}}{{\left[ {3 - 2\lambda - \lambda ^2 + \mu \left( {3\lambda ^2 + 2\lambda - 5} \right)} \right]}}\frac{{\left( {1 - q} \right)}}{q}.\end{equation*}

Figure 5 displays results. To display results in two dimensions, we assume without loss of generality that λ = 0.5. The vertical line in the LHS panel shows results for Q = 1, μ = 0.5, with q > 1/3 the pivotal value for trade liberalization to be evolutionary stable. This corresponds with a world of TFT-players as previously outlined. The solid downward sloping line displays the lower bound on q for values of Q < 1, that is, in a more hostile world, with the lower bound on q higher the smaller the probability Q, provided μ = 0.5. The nexus Q, q thus reflects a trade off between the mass of countries with TFT strategies and subjective frequency q in trade. Starting from a situation in which μ = 0.5, it rotates clockwise around the point (Q = 0; q = 1) for values of μ > 0.5 and increasing (dotted lines) and counterclockwise for values of μ < 0.5 and decreasing (dashed lines).

Figure 5. Lower bounds on q, Q with leverage factor μ parameterized

The RHS panel of Figure 5 shows the nexus between the leverage of protectionist groups μ and frequency parameter q. The upward sloping solid line displays pivotal combinations (q, μ) in a world of TFT as previously outlined (i.e. Q = 1). A lower fraction Q, i.e. moving horizontally from left to right, is more demanding on the pivotal value q for catering to a regime of free trade. Hence, TFT tends to unfold a disciplining force with respect to cooperation in trade liberalization, and establishes a trajectory towards effective multilateralization of trade regimes – even in a world populated by special interests and (some) generally protectionist countries.

Hence, this paper takes a different tack on protection than much of (normative) welfare economics. There are certainly also a number of normative reasons put forward as to why the verdict on protection might differ from its traditional welfare-theoretic account according to which it is costly for those imposing as well as those facing restrictions (on this see, for instance, Gomory and Baumol, Reference Gomory and Baumol2001 and the discussion following Chang, Reference Chang2011). Notwithstanding the arguments pro and con in this strand of the literature, we have presented another, political-economy cum institutional-economics perspective, on protection. In this perspective, protection serves to enforce compliance with a set of rules. In a world of sovereign states, where there is no external power, enforcement must come from within. TFT is one such strategy that is, in principle, capable of sustaining institutions.

From this perspective, WTO membership is a signal to employ a strategy of TFT for enforcing rules-based behavior (thus effectively increasing Q). However, TFT is equally widespread in bi- and pluri-lateral conflicts. And, as shown, it is fairly robust vis-à-vis the political economy of domestic interests, which might try to capture trade policy to serve their special interests rather than the common good. This property, in addition to the strategy being fairly simple to understand, caters to its frequent use, with the threat of retaliation often sufficient to ensure compliance. Notably, this is not an excuse for any kind of protection in any kind of situation. Far from it. However, the fact that conflicts usually do not escalate and degenerate into trade wars is in line with our perspective on TFT. Whether the time of the great depression is an exception to the rule is fiercely debated (Irwin, Reference Irwin1998; Kindleberger, Reference Kindleberger1986: Ch.10). Notably, empirical work by Dluhosch and Horgos (Reference Dluhosch and Horgos2013) based on the WTO's dispute settlement process suggests that, on average, countries, which are more often involved in the WTO's dispute settlement's threat of TFT are eventually more open to trade than other countries. This is broadly consistent with the political-economy approach to institutions as presented here.

Because strategies affect trade flows and specialization, effects are far from straightforward. Rents of vested interests are subject to change, as are politically perceived payoffs. While TFT in this analysis shares some results known from self-enforcing institutional economics, there are also some twists and qualifications that emerge from our analysis: e.g., a higher political leverage does not necessarily cater to a ‘pure prisoner's dilemma’ – as one might think prima facie; and the stakes have quite different implications, depending on whether other parameters are above or below a particular threshold value (see Figure 4). These are just two examples among a set of results, which emerge from a more rigorous theoretic analysis of the evolution of institutions in trade, which stretch beyond the traditional abstract iterative reasoning.

Naturally, a free trade regime does not emerge under each and every constellation of domestic interest groups. As such, TFT is no panacea. Nor do the results imply that TFT is in any case considered a superior strategy over any other strategy that might be available, including possibly the linking of trade issues with other policies, side payments or other forms of implicit or explicit compensation that effectively ‘bribe’ protectionist interest groups or else tame their appetite and their vigorous effect. A complementary comparative institutional analysis might thus be an interesting extension.