Abstract Can selection based on individual advantage result in limits to the magnitude of the damage animals may inflict on conspecifics in agonistic encounters? A formulation of intraspecific conflict in terms of game theory introduced by Maynard Smith (Journal of Theoretical Biology, 1974 , 47, 209–221) is used to examine this question. Maynard Smith put forward the concept of an evolutionarily stable strategy (ESS), one which it will never be to an individual's advantage to depart from, and the resulting analysis is used here to determine the behaviors that will evolve when aggression is modeled as a game between two contestants, each of which has two options, “Attack” or “Display.” It is assumed that the opponents may be of two types which differ in the destruction they are capable of inflicting but that prior to a contest a contestant cannot recognize the type its opponent belongs to. The Weak inflict damage DI when victorious in a contest but the Strong inflict damage DK > DI and the Strong always defeat the Weak when both attack. It is shown that under selection the Strong will wholly replace the Weak when DK ≤ V, V being the value of the prize, but that when DK > V an equilibrium between the two types results. Such a heterogeneous group gives a greater return to its members than a homogeneous group with D ≤ V, and the value of DK will tend to become large, the probability of an attack decreasing inversely. A population in which two types are initially present but recognizably different will evolve toward indistinguishability. If a third type is introduced the intermediate strain will disappear, restoring a bimodal distribution of destructive capacity. In a group whose members are related there will be a higher proportion of the Weak type at equilibrium and the overall probability of attack will be reduced. Such a group will offer a greater return to its members than association with randomly selected conspecifics, assuming that the ESS is played in each case. Under such conditions evolution should favor association with kin. In all cases V constitutes an upper limit to the expected level of damage in encounters. This defines an intrinsic restriction to the magnitude or the frequency of aggressive damage.
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