Consider a normal form game in which player 1 has three strategies, A1, B1, C1 and player 2 has three strategies, A2, B2, C2. Suppose that A1 is a best response to B2, B1 is a best response to A2, A2 is a best response to B1, and B2 is a best response to A1. Do we know with certainty whether A1 is rationalizable or not?
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- Consider a normal form game in which player 1 has two strategies, A1,B1 and player 2 has two strategies, A2,B2. Suppose that A1 is a best response to A2 and A2 is a best response to A1. Do we know whether A1 is rationalizable?Consider the following simultaneous move game where player 1 has two types. Player 2 does not know if he is playing with type a player 1 or type b player 1. Player 2 C D Player 1 A 12,9 3,6 B 6,0 6,9 C D A 0,9 3,6 B 6,0 6,9 Type a Player 1 Prob = 2/3 Type b Player 1 Prob = 1/3 Find the all the possible Bayesian Nash Equilibriums (BNE) of this game.i. ii. QUESTION ONE A. A Nash equilibrium is a strategy profile such that every player's strategy is the best response to all the other players. It requires that each player makes a best response and that expectations regarding the play of other players are correct. Below is the table showing strategies and payoff for Player 1 and Player 2. PLAYER 1 R1 R2 R3 R4 C1 0,7 5,2 7,0 6,6 C2 2,5 3,3 2,5 2,2 PLAYER 2 C3 7,0 5,2 0,7 4,4 CA 6,6 2,2 4,4 10,4 REQUIRED; Transform the normal form game above into an imperfect extensive game form Find the Nash equilibrium for the game above using iterative deletion of strictly dominated strategies. Find the Nash equilibrium using brute force or cell by cell inspection.
- Consider the following two-player game.First, player 1 selects a number x≥0. Player 2 observes x. Then, simultaneously andindependently, player 1 selects a number y1 and player 2 selects a number y2, at which pointthe game ends.Player 1’s payoff is: u1(x; y1) = −3y21 + 6y1y2 −13x2 + 8xPlayer 2’s payoff is: u2(y2) = 6y1y2 −6y22 + 12xy2Draw the game tree of this game and identify its Subgame Perfect Nash Equilibrium.Game Theory and Strategic Choices – End of Chapter Problem The Old Familiar and The Beehive are the only two bistros in town. Each is trying to decide whether or not it should advertise in the local newspaper. The accompanying payoff table gives their weekly profits under each possible outcome. The Beehive The Beehive does advertise does not advertise The Old Familiar The Old Familiar earns $X in profits. earns $3,500 in profits. The Old Familiar does advertise The Beehive The Beehive earns $Y in profits. earns $2,250 in profits. The Old Familiar The Old Familiar earns $2,000 in profits. earns $2,500 in profits. The Old Familiar does not advertise The Beehive The Beehive earns $4,000 in profits. earns $3,500 in profits. a. Which combination or combinations of X and Y would make a situation in which The Old Familiar does not advertise and The Beehive advertises a Nash equilibrium?Game theory Consider a simultaneous move game with two players. Player 1 has three possible actions (A, B, or C) and Player 2 has two possible actions (D or E.) In the payoff matrix below, each cell contains the payoff for Player 1 followed by the payoff for Player 2. Player 2 7. Player 1 A B C D -3, -3 0, -11 -4, 3 -11, E 0 -7, -7 -12, 0 (a) Identify any dominated strategies in this game. If there are none, state this clearly. (b) Identify any pure strategy Nash Equilibria in this game. If there are none, state this clearly
- Consider the game of Chicken in which each player has the option to “get out of the way” and “hang tough” with payoffs: Get out of the way Hang tough Get out of the way 2,2 1,3 Hang tough 3,1 00 a. Find all pure strategy Nash equilibria, if they exist b. Let k be the probability that player 1 chooses “hang tough” and u be the probability that player two chooses “hang tough.” Find the mixed stragety Nash equilibria, if they existSuppose that you are a manager. You are considering whether or not to monitor employees with the payoffs in the normal-form accompanying game. Worker Work Shirk Manager Monitor -1,1 1,-1 Don't Monitor 1,-1 -1,1 Which of the following pairs of strategies constitutes a Nash equilibrium? Multiple Choice Manager monitors and worker shirks. Manager does not monitor and worker works. Manager monitors and worker works. O None of the answers is correct.Consider the following coordination game: Player 2P1 Comedy Show Concert Comedy Show 11,5 0,0 Concert 0,0 2,2 a. Find the Nash equilibrium(s) for this game.b. Now assume Player 1 and Player 2 have distributional preferences. Specifically, both people greatly care about the utility of the other person. In fact, they place equal weight on their outcome and the other person’soutcome, ρ = σ = ½. Find the Nash equilibrium(s) with these utilitarianpreferences.c. Now consider the case where Player1 and Player2 do not like each other. Specifically, any positive outcome for the other person is viewed as anegative outcome for the individual, ρ = σ = -1. Find the Nashequilibrium(s) with these envious preferences.
- Person A English Chinese English 10,10 5,0 Person B Chinese 0,5 5,5 A) Find the Nash equilibria of this two-person game in mixed strategies. B) Is there an equilibrium in which everybody prefers speaking English? If yes, is it stable? C) Is there an equilibrium in where everybody prefers speaking Chinese? If yes, is it stable? D) Is there an equilibrium where some people prefer speaking English, and some prefer speaking Chinese? What is the equilibrium value of p, and is this equilibrium stable?Consider the following game tree. The players are P1 and P2. The strategies available to P1 are L, M, R. The strategies available to P2 are A and B. P1 L R M P2 (1,10) A В A B (0,0) (2,1) (0,0) (2,1)Consider the game with the payoffs below. Which of the possible outcomes are MORE efficient than the Nash Equilibrium (NE)? Note, they do NOT need to be Nash equilibria themselves, they just need to be more efficient than the NE. Multiple answers are possible, but not necessary. You need to check ALL correct answers for full credit. JILL High Medium LowMAGGIE Left 3,4 2,3 2,2Center 4,8 9,7 8,7Right 7,6 8,5 9,4Group of answer choices (Left, Low) There is no strategy combination that is more efficient than the Nash equilibrium for this game. (Right, Medium) (Left, High) (Center, Medium) (Center, High) (Center, Low) (Left, Medium) (Right, Low) (Right, High)