3. Find the Nash equilibria of the following normal form game (Gibbons, 1992, pgs. 9-10). Player 2 Save Use Delay Save 5,5 -2,10 0,0 Player 1 Use 3,2 1,-1 0,0 Delay 0,0 0,0 0,0

B block allow 5,9 3, 11 high A 6,2 4,4 low In this normal form game, there is a Nash equilibrium where A chooses high; block high; allow low; block low; allow and B chooses

Consider the following simultaneous move game: Player 1 U M D Player 2 L 2,10 2,5 8,7 C 5,2 11,8 8,4 R 5,4 2,9 8,3 In the Nash equilibrium of this game, player 1 receives a payoff of ✓ and player 2 receives a payoff of

Hi this is from a textbook. Thank you.   Consider the following game in which Sally can play T or B and John chooses between L or R. Each player makes their choice simultaneously. If Sally chooses T and John chooses L, Sally gets a payoff of 5 and John has a payoff of 4. If Sally plays T and John R, Sally’s payoff is 8 and John gets 3. If Sally Chooses B and John L, the payoffs are 3 to Sally and 2 to John. Finally, if Sally chooses B and John R, the payoffs are 7 to Sally and 0 to John. Which statement is true?   a) The Nash equilibrium is (B,R); this is a prisoners’ dilemma b) The Nash equilibrium is (T,R); this is a prisoners’ dilemma c) The Nash equilibrium is (T,R); this is not dominant strategy equilibrium d) The Nash equilibrium is (T,L); this is a dominant strategy equilibrium e) None of the above

Consider a sequential game where there are two players, Jake and Sydney. Jake really likes Sydney and is hoping to run in to her at a party this weekend. Sydney can't stand Jake. There are two parties going on this weekend and each player's payoffs are a function of whether they see one another at the party. The payoff matrix is as follows: Sydney Party 1 Party 2 Party 1 6, 18 18, 6 Jake Party 2 24,8 0,24 a) Does this game have a pure strategy Nash Equilibrium? b) What is the mixed strategy Nash Equilibrium? c) Now suppose Sydney decides what party she is going to first. Her roommate is friends with Jake and will call him to tell him which party they go to. Write the extensive form of this game (game tree). d) What is the subgame perfect Nash equilibrium from part c?

Can you help me with the question below? What is [are] the Nash Equilibrium [Equilibria] of this game? A) (10;10) and (20;20) B) (30;30) C) (10;20) and (20;10) D) (20;20) E) (30;30)

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3. How many extensive forms are there that are equivalent to the following normal form game (pay attention to the payoffs in the matrix)? You may rename strategies, if necessary. Show the extensive forms. II ti t2 t3 t4 ts to si 7,1 2,2 | 1,5 7,1 I 2,2 1,5 S2 3,3 3,3 | 3,3 2,1 2,1 2,1

Up ооооо Down Player 1 Up No EFFICIENT equilibrium exists Down Up Down Player 2 P1 gets $120 P2 gets $5 P1 gets $100 P2 gets $10 P1 gets $95 P2 gets $95 In the game above, what is/are the EFFICIENT sub-game perfect Nash equilibrium? (up,up) (up,down) (down, up) (down, down) P1 gets $15 P2 gets $25

The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff of