Origins of behavioural variability: Categorical and discriminative assessment in serial contests

Can social behaviour be probabilistic? Classical results in evolutionary game theory seem to suggest that recognizable asymmetries between individuals in the likelihood of winning fights (i.e. in resource holding power, RHP) rule out the stable probabilistic behaviour associated with mixed strategies. Here, using a variant of the hawk-dove game, I show that these mixed strategies can be common in asymmetric contests, because opponents of similar RHP benefit by ignoring discernable differences to form RHP equivalence categories. This process of categorizing (i.e. opting not to distinguish an opponent's discernably different RHP from one's own) can be adaptive when assessment is imprecise or expensive and mistakes can lead to dangerous combat. For large RHP differences between opponents, discriminating by acting on the discernable RHP difference is evolutionarily stable. For moderate RHP differences, typically neither categorizing nor discriminating is stable, but categorizing predominates if social interactions are frequent. More frequent interactions imply that the social status ultimately achieved is more important in accumulating fitness; this reduces the probability that a loser in combat will accept the submissive role without additional fighting, where this probability of 'surrender' expresses another mixed strategy. These patterns appear to fit the establishment of social relationships in some species for which combat is dangerous, and the analysis represents a step towards understanding the emergence of dominance hierarchies.