The following game is played by 2 playerse Jacke Right 2,1e 3,0e 0,2- Lefte Middlee Up 3,5 1,2 0,4 -1,1 Adame Middlee 2,1 Downe 4,3 L. a) Determine all dominant strategies for Adam and Jack. b) Solve the equilibrium for this game.

Player 1 Cooperate (C) Defect (D) Cooperate (C) 3,3 8,0 Player 2 Defect (D) 0,8 1,1 In general, a combination of strategies is a Nash equilibrium if ... Every player is choosing a best response against the other players' strategies. Every player has a positive payoff. The players maximize the sum of their payoffs. The players choose identical strategies. If the game is repeated, which cooperative actions could benefit both players? O Both players choose C. Player 1 chooses C, Player 2 chooses D. O Player 1 chooses D, Player 2 chooses C. Both players choose D.

(The Beckhams' dilemma) Victoria and David are husband and wife. They both prefer ciean to dirty house but neither likes to clean the house. Their payoffs are given in the table below. Victoria Clean Don't clean 0,8 Clean 5,5 David Don't clean 8,0 1,1 a) Let say they play the clean house game only once, what is the Nash equilibrium? b) Let say Victoria and David has to decide whether to clean or not every day for indefinite number of days. How grim-trigger strategy will be our subgame perfect Nash equilibrium? In other words, what is the patience rate that ensure Victoria and David maintain the cleanliness of the house?

Player 1 Up Down [Select] Left 2,4 6,5 Player 2 In the above game, player 1 would play [Select] Right 1,0 4,2 , player 2 would play resulting in a Nash Equilibrium of [Select]

Consider the following sequential game: 1 O D,L U.L U,R U D,R D (0,2) 2 L What is the subgame perfect Nash equilibrium of this game? R. (-1,-1) (1,1)

Image attched

acsdk xbnxnw edjqbs snxq