Distinguishing between defensive and offensive roles is key to understanding human behavior in conflict. De Dreu and Gross argue that differences in neurobiological responses between attackers and defenders indicate differences in motives and point to the need to model conflict as a game with asymmetric payoffs. This approach leaves a key question on the table: Why would humans evolve distinct neurobiological systems for attack and defense? A compelling explanation for role-contingent responses would derive differences in optimal behavior for attackers and defenders from symmetric initial conditions. Below I sketch a theory in which role-contingent behavioral differences arise from cumulative differences in the strategic environments of attackers and defenders that, themselves, are the result of equilibrium behavior in symmetric initial conditions.
To give a brief intuition: The process of gaining entry to a desirable group has predictable effects on the population characteristics of both those in and outside of the group. Thus, group membership is a noisy signal of relevant, unobservable individual traits (Spence Reference Spence1973) and a strategically relevant difference between otherwise identical individuals. Conceiving of the possession of an asset as a kind of group membership, otherwise identical attackers and defenders will exhibit different behaviors in equilibrium, consistent with the empirical patterns summarized by De Dreu and Gross.
To see the underlying mechanism, begin by considering a classic, symmetric incomplete information war of attrition. Two individuals compete for a prize, such as a territory, by trying to outlast the other; when one of them quits, the other immediately claims the prize. Suppose for simplicity that both face identical costs of waiting but have potentially different valuations of the prize – whether because they possess different abilities to exploit it, or different alternative opportunities, or simply different preferences. Although each individual knows only her or his own value of the prize, both are drawn from the same population with a commonly known distribution of prize valuations, so they have identical suppositions about each other. Thus, they are in ex ante identical strategic situations, and in equilibrium, their optimal strategies will be identical, monotonically increasing functions of their own values of the prize (Bishop et al. Reference Bishop, Cannings and Maynard Smith1978). It follows that the winner is always the contestant with the higher prize valuation.
Now suppose that this contest occurs in a larger environment in which many such contests, between many such (randomly chosen) pairs of contestants, are occurring simultaneously, and that after these contests are over, winners and losers can be readily distinguished by their possession of the prize. A loser may wish to try a second time to obtain a prize, against a different opponent. This second contest, however, is importantly different than the first one. The contestants are not in identical circumstances; the one who possesses the prize (the defender) is known to have won a previous contest, whereas the one who does not (the attacker) is known to have lost. Thus, each attacker knows that she or he faces an opponent who proved to be a higher type than some randomly selected individual faced previously; and each defender knows she or he faces an opponent who proved to be a lower type. Formally, the distribution of defenders first-order stochastically dominates the initial distribution, which first-order stochastically dominates the distribution of attackers.
This difference in the distributions of opponents affects the optimal strategic choices of contestants, relative to the initial fight, through two channels, both of which increase the optimal strategy for defenders and decrease it for attackers. First, suppose the defenders’ strategies are the same as their optimal behavior in the first fight. The direct effect of the difference between the distribution of defenders (who have all won the first fight) and the initial distribution is that a randomly selected defender quits later than before. Thus, an attacker's expected cost of winning is higher than it was in the first round of fighting, and so her or his optimal strategy is lower. By the symmetric argument, the defender's optimal strategy is higher relative to the initial contest.
Second, consider the indirect effects via the changes in opponents’ strategies just described. The decrease in the attacker's optimal quitting time decreases the defender's expected cost of winning, which increases the defender's optimal quitting time. By the symmetric argument, the attacker's optimal quitting time decreases. Thus, the direct and indirect effects reinforce one another. After just one round of conflict, it is optimal in equilibrium for an individual to expend greater resources to defend possession of a prize than to obtain it, holding constant her or his individual traits.
The previous example supposes the conflict is a war of attrition, but the fundamental causal argument is the same regardless of the mode of conflict: When entry into the group must be won, membership in the group becomes a signal of traits promoting victory, and non-membership becomes a signal of traits promoting defeat. A trait or combination of traits that is not readily observed but that affects the individual's investment into winning (an example of the private-information “type” in the previous analysis) creates differences in the cost of competing or in the ability to exploit the prize.
This drives a wedge between the optimal strategies of fully rational and far-sighted defenders and attackers in every subsequent round of conflict, holding constant the individual's traits. Hafer (2005) shows that a closed system obtains a finite-time reachable steady-state in which strategies of defenders and (potential) attackers diverge so much that no conflict actually occurs. It is straightforward to extend the results to a case in which frequent shocks to the populations (such as those that would occur with birth and death) would result in some conflict in the steady-state, in which individuals with identical traits fight harder and are more likely to win when defending than when attacking. These results provide a rationale for the advantageousness of developing neurobiological responses not merely to conflict, but to developing role-contingent, distinct responses to being the attacker or defender.
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Distinguishing between defensive and offensive roles is key to understanding human behavior in conflict. De Dreu and Gross argue that differences in neurobiological responses between attackers and defenders indicate differences in motives and point to the need to model conflict as a game with asymmetric payoffs. This approach leaves a key question on the table: Why would humans evolve distinct neurobiological systems for attack and defense? A compelling explanation for role-contingent responses would derive differences in optimal behavior for attackers and defenders from symmetric initial conditions. Below I sketch a theory in which role-contingent behavioral differences arise from cumulative differences in the strategic environments of attackers and defenders that, themselves, are the result of equilibrium behavior in symmetric initial conditions.
To give a brief intuition: The process of gaining entry to a desirable group has predictable effects on the population characteristics of both those in and outside of the group. Thus, group membership is a noisy signal of relevant, unobservable individual traits (Spence Reference Spence1973) and a strategically relevant difference between otherwise identical individuals. Conceiving of the possession of an asset as a kind of group membership, otherwise identical attackers and defenders will exhibit different behaviors in equilibrium, consistent with the empirical patterns summarized by De Dreu and Gross.
To see the underlying mechanism, begin by considering a classic, symmetric incomplete information war of attrition. Two individuals compete for a prize, such as a territory, by trying to outlast the other; when one of them quits, the other immediately claims the prize. Suppose for simplicity that both face identical costs of waiting but have potentially different valuations of the prize – whether because they possess different abilities to exploit it, or different alternative opportunities, or simply different preferences. Although each individual knows only her or his own value of the prize, both are drawn from the same population with a commonly known distribution of prize valuations, so they have identical suppositions about each other. Thus, they are in ex ante identical strategic situations, and in equilibrium, their optimal strategies will be identical, monotonically increasing functions of their own values of the prize (Bishop et al. Reference Bishop, Cannings and Maynard Smith1978). It follows that the winner is always the contestant with the higher prize valuation.
Now suppose that this contest occurs in a larger environment in which many such contests, between many such (randomly chosen) pairs of contestants, are occurring simultaneously, and that after these contests are over, winners and losers can be readily distinguished by their possession of the prize. A loser may wish to try a second time to obtain a prize, against a different opponent. This second contest, however, is importantly different than the first one. The contestants are not in identical circumstances; the one who possesses the prize (the defender) is known to have won a previous contest, whereas the one who does not (the attacker) is known to have lost. Thus, each attacker knows that she or he faces an opponent who proved to be a higher type than some randomly selected individual faced previously; and each defender knows she or he faces an opponent who proved to be a lower type. Formally, the distribution of defenders first-order stochastically dominates the initial distribution, which first-order stochastically dominates the distribution of attackers.
This difference in the distributions of opponents affects the optimal strategic choices of contestants, relative to the initial fight, through two channels, both of which increase the optimal strategy for defenders and decrease it for attackers. First, suppose the defenders’ strategies are the same as their optimal behavior in the first fight. The direct effect of the difference between the distribution of defenders (who have all won the first fight) and the initial distribution is that a randomly selected defender quits later than before. Thus, an attacker's expected cost of winning is higher than it was in the first round of fighting, and so her or his optimal strategy is lower. By the symmetric argument, the defender's optimal strategy is higher relative to the initial contest.
Second, consider the indirect effects via the changes in opponents’ strategies just described. The decrease in the attacker's optimal quitting time decreases the defender's expected cost of winning, which increases the defender's optimal quitting time. By the symmetric argument, the attacker's optimal quitting time decreases. Thus, the direct and indirect effects reinforce one another. After just one round of conflict, it is optimal in equilibrium for an individual to expend greater resources to defend possession of a prize than to obtain it, holding constant her or his individual traits.
The previous example supposes the conflict is a war of attrition, but the fundamental causal argument is the same regardless of the mode of conflict: When entry into the group must be won, membership in the group becomes a signal of traits promoting victory, and non-membership becomes a signal of traits promoting defeat. A trait or combination of traits that is not readily observed but that affects the individual's investment into winning (an example of the private-information “type” in the previous analysis) creates differences in the cost of competing or in the ability to exploit the prize.
This drives a wedge between the optimal strategies of fully rational and far-sighted defenders and attackers in every subsequent round of conflict, holding constant the individual's traits. Hafer (2005) shows that a closed system obtains a finite-time reachable steady-state in which strategies of defenders and (potential) attackers diverge so much that no conflict actually occurs. It is straightforward to extend the results to a case in which frequent shocks to the populations (such as those that would occur with birth and death) would result in some conflict in the steady-state, in which individuals with identical traits fight harder and are more likely to win when defending than when attacking. These results provide a rationale for the advantageousness of developing neurobiological responses not merely to conflict, but to developing role-contingent, distinct responses to being the attacker or defender.