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If the cost of fighting is great enough, the game thus yields a mixed equilibrium featuring both strategies.In this context, it seems likely that selection will favor eavesdroppers who attend to the outcome of contests between others, because the information they have gathered may allow them to determine whether they face an aggressive or cautious opponent (and thereby avoid a costly, escalated fight).Fights between pairs of animals frequently take place within a wider social context.The displays exchanged during conflict, and the outcome of an encounter, are often detectable by individuals who are not immediately involved.Eavesdropping, as this behavior has been called (4), allows an animal to assess the aggression and fighting ability of potential opponents before any direct contest.In this way, an eavesdropper may avoid escalated conflict with a dangerous enemy (3–5, 8, 11, 12).

In every round, members of the population are paired at random, and each pair plays a single bout of the Hawk–Dove game: each individual must choose to play hawk (i.e., to escalate) or to play dove (i.e., to rely on ritualized display, and back down in the face of escalated aggression). An individual who plays hawk always defeats an opponent who plays dove, whereas contestants who adopt the same course of action are both equally likely to win (or to lose) the fight.

I will assume that 0 I consider three possible strategies or types of player: hawks and doves always adopt the tactic for which they are named; eavesdroppers, by contrast, play hawk when facing an opponent who lost in the previous round and dove when facing an opponent who won (I thus assume that eavesdroppers have a “memory” of only one round and do not track the success of others over a longer time period).

Let Each difference equation is obtained by summing the probabilities of victory for an individual of the relevant type when facing all possible types of opponent, weighted according to the probability with which each is encountered (note that having obtained victory probabilities for any two of the three types in this way, the probability of victory for the remaining type may be derived from the requirement that the overall proportion of winners in any one round equals 0.5). 1 a–c, it follows that the proportions of the three types that were victorious in their last encounter rapidly converge to as the fitness of each of the three strategies. 3 a–c, one can thus investigate the evolution of the frequencies of the three types under the influence of selection.

However, the analysis can be extended easily to consider imperfect eavesdropping. Thus the model upholds suggestions that eavesdropping is most likely when the costs of fighting are relatively high (3, 8, 11), although the less reliable eavesdroppers are, the lower the cost of fighting at which they reach peak frequency.

Why is it that eavesdropping does not spread to fixation?

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