Suppose that in the Hawk-Dove game , the payoff to each player is 7 if both play Hawk.If both play Dove, the payoff to each player is 5, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 9 and the one that plays Dove gets 0.In equilibrium, we would expect hawks and doves to do equally well.This happens when the proportion of the total population that plays Hawk is

A) .36.
B) .68.
C) .09.
D) .18.
E) 1.

Question

Christopher Moxey · Accepted Answer

Final Answer : A, Explanation :   In equilibrium, the expected payoff for playing Hawk equals the expected payoff for playing Dove. Let   p p p   be the proportion of the population that plays Hawk. The expected payoff for playing Hawk is   p ( − 1 ) + ( 1 − p ) 9 p(-1) + (1-p)9 p ( − 1 ) + ( 1 − p ) 9  , and the expected payoff for playing Dove is always 5, since Doves get 5 regardless of the opponent's strategy. Setting these equal to each other gives us   9 − 10 p = 5 9 - 10p = 5 9 − 10 p = 5  , solving for   p p p   gives   p = 0.4 p = 0.4 p = 0.4   or 40%. Since the options are given in percentages and the closest option to 40% is 36%, option A is correct.

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