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- Find all Nash equilibria for the player 1 and player 2 of the following game with vNM preferences:if Y =4 (b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?Two players play the following game for infinite times. For the player to continue to cooperate what would be the ranges of their discount factor, δ_1 and δ_2, respectively? cooperate betray cooperate (10,20) (-25,30) betray (15, -22) (-12, -18)
- E3 Bayesian Game]. Consider a Bayesian game described by a following payoff matrix. Please solve (show your solution). 1. Enumerate all pure strategies for each player. 2. Suppose that player 1 observes his type ?1 = 3. How does player 1 think of the probability of ?2? 3. Find a (pure strategy) Bayesian Nash equilibrium.In equilibrium, what is the probability that player 1 will use the pure strategy E in this game?Consider the following game in strategic or normal form. A2 B2 C2 A1 1,0 1,2 -2,1 B1 6,2 0,3 2,3 C1 2,2 -2,1 2,3 Use the iterative elimination of strictly dominated strategies to reduce the game as much as possible. What is the set of rationalizable strategies for each player? What is/are Nash equilibrium(s) in this game?
- Paramter y = 0 What is the highest payoff any player can receive in any subgame perfect Nashequilibrium of the repeated game?Country A is rich and country B is poor. Consequently, residents of country B want to immigrate to country A. The trouble is that there is no legal way to do. So they attempt to cross the border Illegally. There are 3 border crossings at which a resident of B may attempt to cross the border. An attempt is successful if there is no border guard at the crossing, and unsuccessful if there is a guard at the crossing. Country A has only 1 border guard. Model the game in which a resident of country B attempts to enter country A at one of the 3 border crossings, and the government of country A chooses to post its border guard at one of the 3 border crossings. In this game, each player has 3 pure strategies. A) What are the ultimate outcomes in this game? B) What are the player's Bernoulli Payoffs? C) Find a mixed strategy equilibrium of the game.Consider the game in the table below. Is the Nash Equilibrium efficient? Enter 111 for YES and 222 for NO. firm a left right firm b up 9,5 10,6 down 6,10 7,9
- on 8.1 Consider the following game: Player 1 A C D 7,6 5,8 0,0 Player 2 E 5,8 7,6 1, 1 F 0,0 1,1 4,4 a. Find the pure-strategy Nash equilibria (if any). b. Find the mixed-strategy Nash equilibrium in which each player randomizes over just the first two actions. c. Compute players' expected payoffs in the equilibria found in parts (a) and (b). d. Draw the extensive form for this game.Determine the optimum strategies and the value of the game with the followingpayoff matrix of player A where A1, A2 are the strategies for player A and B1, B2 are for player B.B1 B2A1 5 1A2 3 4Consider a game with two players (Alice and Bob) and payoffffs Bob Bob s1 s2 Alice, s1 3, 3 0, 0 Alice, s2 0, 0 2, 2 In the equilibrium in the above game, Alice should (A) always choose the fifirst strategy s1; (B) choose the fifirst strategy s1 with probability 40% ; (C) choose the fifirst strategy s1 with probability 50% ; (D) choose the fifirst strategy s1 with probability 60% .
