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In an iterated two-person game, for instance prisoner's dilemma or thesnowdrift game, there exist strategies that force the payoffs of the opponentsto be equal. These equalizer strategies form a subset of the more generalzero-determinant strategies that unilaterally set the payoff of an opponent. Achallenge in the attempts to understand the role of these strategies in theevolution of animal behavior is the lack of iterations in the fights for matingopportunities or territory control. We show that an arbitrary two-parameterstrategy may possess a corresponding equalizer strategy which produces the sameresult: statistics of the fight outcomes in the contests with mutants are thesame for each of these two strategies. Therefore, analyzing only the equalizerstrategy space may be sufficient to predict animal behavior if nature, indeed,reduces (marginalizes) complex strategies to equalizer strategy space. Thework's main finding is that there is a unique equalizer strategy that predictsfight outcomes without mutual cooperation. The lack of mutual cooperation is acommon trait in conflict escalation contests that generally require a clearwinner. In addition this unique strategy does not assess information of theopponent's state. The method bypasses the standard analysis of evolutionarystability. The results fit well the observations of combat between male bowland doily spiders and support an empirical assumption of the war of attritionmodel that the species use only information regarding their own state duringconflict escalation.

Single Equalizer Strategy with no Information Transfer for Conflict Escalation