Problem 1: Game Theory.

Consider a game with the following payoff matrix:

Left Right

Up 1,1 0,0

Down 0,0 2,2

(a) How many players does this game have? What are the strategies of each player?

(b) What are the Nash equilibria of this game?

(c) What are the Pareto Efficient outcomes?

(d) Design the payoff matrix of a game with no Nash Equilibria. The game should have 2 players, 2 strategies for each player, and the payoffs for each player should be either 0or

Disclaimer. If you haven't had another game theory class, ignore this disclaimer.If you have had another game theory class, you may know that every game has a mixed (random-ized) Nash equilibrium.Part (d) of problem 2 wants you to design a game with no pure(deterministic) Nash equilibrium.