Two people play the following game infinitely. If Player 1 uses a grim trigger strategy, how high must be the discount factor to sustain cooperation from Player 2? Discuss the intuition of the grim trigger strategy and calculated discount factor. Player 2 L R U 5,5 1, 2 0,7 Player 1 2,2 2,3 0,4 D 8,0 3,1 2, 3

INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. b1 b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of 5 such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)

Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).

the Consider a simultaneous-move integer game between two players: Marilyn and Noah. Each of player is required to announce a positive integer between 1 to 4. In other words, a player can announce 1, 2, 3, or 4. Two players announce their integers simultaneously. Notice that this game is different from the games we learned in class in that each player has four actions to take. The payoffs of the players in the game are specified as follows: (1) when the two announced integers are different, whoever reports the lower number pays $1 to the other player, so that the loser of the game has payoff -1 and the winner of the game has payoff 1; (2) when the two players announce the same integer, their payoffs are both O. What is Marilyn's maximin strategy? 01 02 03 O