Suppose that in the Hawk-Dove game the payoff to each player is 8 if both play Hawk.If both play Dove, the payoff to each player is 3, and if one plays Hawk and the other plays Dove, the one that plays Hawk gets a payoff of 8 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) .19.
B) .69.
C) .38.
D) .10.
E) 1

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sangit tiwari · Accepted Answer

Final Answer : C, Explanation :  In the Hawk-Dove game, the expected payoff for a player who chooses Hawk depends on the proportion of the opponent population that chooses Dove. Similarly, the expected payoff for a player who chooses Dove also depends on the proportion of the opponent population that chooses Dove.Let x be the proportion of the population that chooses Hawk, then (1-x) is the proportion of the population that chooses Dove. The expected payoff to a player who chooses Hawk is:(1-x)8 + x( - 8)The expected payoff to a player who chooses Dove is:(1-x)3 + x3In equilibrium, the expected payoffs to choosing Hawk and Dove must be equal. Setting the two equations above equal and solving for x, we get:(1-x)8 + x( - 8) = (1-x)3 + x3Simplifying and solving for x, we get:x = (5- )/5Substituting the given values for  , we get:x = (5-1)/(5) = 0.8So the proportion of the population that chooses Hawk is 0.8, which is equal to 80%. Therefore, the proportion of the population that chooses Dove is (1-0.8) = 0.2, which is equal to 20%. To find the percentage, we multiply by 100, which gives us:Hawk: 80%Dove: 20%Therefore, the answer is C) 38.

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