Suppose there exists a large population of people in which there exists people who choose to live in a valley and people who choose to live on a mountain. People are matched in a pair at random to play the following game. If two Valley people meet, they live together in a Valley with plentiful resources and each earns a payoff of 2. If two Mountain people meet, they live together on a Mountain with scarce resources and a harsh terrain and each earns a payoff of 1. If a Valley person and a Mountain person meet, they do not coordinate on a place to live, and so each earns a payoff of 0. 

a. Formulate a normal-form representation of the game described above. A complete normal-form representation will clearly and accurately identify players, strategies, and payoffs. 

 

b. Study the normal-form representation you wrote in part a. above and find all of the game's Nash equilibria. Please list the game's pure strategy and mixed strategy Nash equilibria.

c. Suppose that the population proportion of Valley people is # and that the population proportion of Mountain people is 1 #. Use the normal-form representation you wrote in part a. above to derive expressions for the expected payoffs of the Valley people and of as Mountain people. On a single pair of axes, graph the Valley people and the Mountain people expected payoff functions and then use your graph to identify and explain which strategy configurations are evolutionary stable strategies according to the dynamics of evolution and selection.