Consider the following game in extensive form, involving the chance parameter p. A P[T] = P (0,0) 97 U P[H] = 1-p h B h d P[T] = P (-60,60) (20,-20) (40,-40) (0,0) n P[H]=1-P (0,0) Suppose that p = 0.75 and the strategy profile (u, h) is played. What expected payoff does player B receive? (Report your answer in decimal form, rounding if necessary to two places.

Suppose the following game is played infinite times in the future. Time discount is 0.90. What should be the value of x so that the equilibrium strategy is (Cooperate, Cooperate)?      Player 2 Player 1 Cooperate Defect Cooperate (x, x) (2, 14) Defect (14, 2) (5, 5)

Finding Nash Equilibria Consider the following two player, normal form game: Player 1 Player 2 C L (2,1) U M (-2,-2) D R (2, -1) (1,2) (-1, 1) (0,0) (3,1) (0,0) (-1,-1) Find all pure and mixed strategy Nash equilibria. Calculate each player's expected payoffs at each equilibrium.

Note: The answer should be typed.

John and Paul are walking in the woods one day when suddenly an angry bear emerges from the underbrush.  They each can do one of two things: run away or stand and fight.  If one of them runs away and the other fights, then the one who ran will get away unharmed (payoff of 0) while the one who fights will be killed (payoff -200).  If they both run, then the bear will chase down one of them and eat them to death but the other one will get away unharmed.  Assuming they don't know which one will escape we will call this a payoff of -100 for both.  If they BOTH fight, then they will successfully drive off the bear but they may be injured in the process (payoff -20).  Construct a payoff matrix for this game and identify the pure strategy Nash equilibrium.  (Indicate it with words not with a circle!)

In the table below are the values of the ordinal utility function. Find all Nash equilibria of the game determined by the matrix below? Which of these are strict Nash equilibria?

Determine all of the Nash equilibria (pure-strategy and mixed-strategy equilibria) of the following game:

Consider the following game:   Sarah R S T   Peter    X 9, 6 4, 4 6, -3 Y 6, 6 7, 6 2, 2 Z 9, 7 1, 5 6, 7   How many (pure strategy) Nash equilibria does this game have?