Imagine a population of falcons and pigeons . When they meet an opponent, the falcons fight until they either win or are seriously hurt. The pigeons only threaten their opponents but withdraw if the other wants to fight. Let us suppose also that the long-term survival of the two types of bird depends on the results obtained in these fights and that the winnings of each possible fight are as follows: 50 points for winning, -100 points for being seriously hurt and -10 for wasting time making threats. In other words, (1) if a falcon meets a pigeon, the pigeon withdraws and obtains a zero result and the falcon gets 50 points; (2) if a falcon meets another falcon, they fight to the bitter end when one wins 50 points and the other loses -100; and (3) if a pigeon meets another pigeon, both make threats for a long time until one of them gives in with a probability of 0.50, so that both win on average 15 points (= [50 - 10] 0.50 + [-10] 0.50).
a) Let us suppose, first, that there is no way of knowing in advance if an individual is a falcon or a pigeon until the fight begins. Start with a population of pigeons. What result is obtained? Imagine that a mutant falcon appears. What would the result be? Suppose that, with their better results, the mutant falcons proliferate and the population is now made up of falcons, what result would they obtain and what result would a mutant pigeon obtain? What would the composition of an equilibrium population be? Why would it be an equilibrium population? Show graphically the results of the falcons and pigeons in terms of the proportion of pigeons.
b) Let us now suppose that it is possible to distinguish whether an individual is a falcon or pigeon before the fight starts, that both types of animals can choose before fighting whether to undertake or not the detection, and that the costs of detection amount to 5 units.
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Based on Dawkins (1986, pp. 104-109) following a model by Maynard Smith