Suppose a game is being played with monetary payoffs:

Suppose that x is the Column players payoff and y is Row players payoff

a) Suppose that players are selfish, such that uc(x,y) = x and ur(x,y) = y. What are the pure Nash Equilibria of the game above?

b) Again, assuming both players are selfish, determine if there is Mixed Strategy Nash Equilibrium. If there is, compute the MSNE.

c) Which strategies are Pareto optimal? Show your work.

d) Suppose that both players are utilitarian (want to maximize the total amount of money earned by each player), so that uc(x, y) = x + y and ur(x, y) = x + y. Compute all Nash Equilibria (pure and mixed).

e) Do utilitarian players achieve the Pareto optimal outcome?

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