Economics 405/505 Game Theory Spring 2017 Prof. Rui Zhao Homework 1. Due on Thursday 02/09 at the beginning of class. 1. (Hawk-Dove) Two animals are fighting over some prey. Each can choose one of two stances: passive or aggressive. Moreover, (1) Each prefers to be aggressive if its opponent is passive, and prefers to be passive if its opponent is aggressive; (2) Given its own choice, each animal prefers the outcome when its opponent is passive to the outcome in which its opponent is aggressive. Choose your own payoff numbers to formulate the interaction as a matrix game and find its Nash equilibria. Are the equilibria efficient? (You are free to assign payoffs for the players, but the numbers you choose should reflect the players' preferences as described in the above two conditions.)