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Matsumura, S., & Kobayashi, T. (1998). A game model for dominance relations among group-living animals. Behav. Ecol. Sociobiol., 42(2), 77–84.
Abstract: Abstract We present here an attempt to understand behaviors of dominant individuals and of subordinate individuals as behavior strategies in an asymmetric “hawk-dove” game. We assume that contestants have perfect information about relative fighting ability and the value of the resource. Any type of asymmetry, both relevant to and irrelevant to the fighting ability, can be considered. It is concluded that evolutionarily stable strategies (ESSs) depend on the resource value (V), the cost of injury (D), and the probability that the individual in one role will win (x). Different ESSs can exist even when values of V, D, and x are the same. The characteristics of dominance relations detected by observers may result from the ESSs that the individuals are adopting. The model explains some characteristics of dominance relations, for example, the consistent outcome of contests, the rare occurrence of escalated fights, and the discrepancy between resource holding potential (RHP) and dominance relations, from the viewpoint of individual selection.
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Nakamaru, M., & Sasaki, A. (2003). Can transitive inference evolve in animals playing the hawk-dove game? J. Theor. Biol., 222(4), 461–470.
Abstract: What should an individual do if there are no reliable cues to the strength of a competitor when fighting with it for resources? We herein examine the evolutionarily stable strategy (ESS) in the hawk-dove game, if the opponent's resource-holding potential (RHP) can only indirectly be inferred from the outcome of past interactions in the population. The strategies we examined include the classical mixed strategy in which no information on past games is utilized, the `imprinting' strategy in which a player increases/decreases its aggressiveness if it wins/loses a game, the `immediate inference' strategy in which a player can infer the strength of those opponents it fought before, and the `transitive inference' strategy in which a player can infer the strength of a new opponent through a third party with which both players have fought before. Invasibility analysis for each pair of strategies revealed that (i) the transitive-inference strategy can always invade the mixed strategy and the imprinting strategy, and itself refuses invasion by these strategies; (ii) the largest advantage for transitive inference is achieved when the number of games played per individual in one generation is small and when the cost of losing an escalated game is large; (iii) the immediate inference, rather than the transitive inference, can be an ESS if the cost of fighting is small; (iv) a strong linear ranking is established in the population of transitive-inference strategists, though it does not perfectly correlate to the ranking by actual RHPs. We found that the advantage of the transitive inference is not in its ability to correct a misassessment (it is actually the worst in doing so), but in the ability of quickly lining up either incorrect or correct assessments to form a linear dominance hierarchy.
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