Social eavesdropping: a game-theoretic analysis.

Here we extend the classic Hawk-Dove model of animal conflict to allow for continuous variation in fighting strengths. Whereas the winner of a fight is chosen at random in the discrete game, in our continuous game, the winner of any fight is the stronger individual, and costs are higher for more evenly matched opponents. We identify the evolutionary stable strength threshold beyond which an animal should be prepared to engage in aggressive behaviour and show that this threshold increases with variance in fighting strength when the costs of aggression are insensitive to the level of strength asymmetry, but decreases with variance when the costs are sensitive to the level of asymmetry. In contrast to the classic discrete game, population-wide aggressive behaviour occurs only when the costs of fighting are zero. It is now known that animals can eavesdrop on the outcome of contests between neighbours and modify their behaviour towards observed winners and losers. We therefore further extend our model to allow for social eavesdropping within networks comprising three individuals. Whereas earlier work showed that eavesdropping increases the frequency of mutually aggressive contests in the discrete game by enhancing the value of victory, here we show that aggression thresholds in the continuous game are always higher with eavesdropping than without it: for sufficiently weak animals, avoiding the costs of challenging an observed winner over-rides the potential benefit of winning, so that eavesdropping reduces the frequency of aggressive encounters. Thus, even though strength is not directly observable, information is extracted from the variation in fighting ability that the classic Hawk-Dove game ignores.