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If a strategy profile is a Nash equilibrium, there is at least one player that could achieve higher payoffs by deviating.
(a) True. (b) False.
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- Two students, X and Y, are given blank cards. Each student is to write a number between 0 and 100. The cards are then collected and the numbers on them averaged. The student whose choice is closest to half of the average is the winner. (a) Write down the best response for each player. (b) What is the Nash equilibrium of this game?in every Nash equilibrium, the strategy of every player is a best response to the strategies chosen by the other players. (a) True. (b) False.Asap
- Player 2 Cooperate (1,000, 1,000) Cheat Player 1 (400, 2,000) Cooperate Cheat (2,000, 400) (500, 500) The above payoff matrix is for two players, each with two strategies. What is the Nash equilibrium of this game? Cheat and Cooperate Cheat and Cheat Cooperate and Cooperate Cooperate and CheatA game can have more than one Nash equilibria.(a) True. (b) False.Suppose there are two players playing a game with east or west and south and nerth ways. Find the expected Nash equilibrium by using the concept of probabilities. Player X Left[L) Right|R) Player Y Up(U) (5,6) (0,8) (4,6) Down[D) (0,9)
- Parameter z = 1 How many pure strategy profiles exist in this game?Find the mixed strategy Nash equilibrium by using the concept of probabilities. Player X West{W} East{E} Player Y (0,10) South{S} (7,8) (4,8) (0,12) North{N}Profits for two competing firms depend on the decisions to advertise or not to advertise as follows: If neither firm advertises, each makes a weekly profit of $100. If one firm advertises while the other does not, the firm that advertises makes $120 while the firm that doesn’t advertise makes $60. If both firms advertise, each firm makes $80. (a) What is the Nash equilibrium? Is this outcome efficient, from the perspective of the two firms? (b) How does the outcome of the game change if the parties can make a binding agreement in advance about advertising practices? (c) How does the game change if it is repeated over the course of many weeks (but the firms cannot make a binding agreement about how much advertising they will do)?
- We have two cable TV companies, Astounding Cable and Broadcast Cable, each simultaneously deciding on a high, medium, or low advertising budget. Their payoffs (in millions) are as follows in the image. True or false? (i) Astounding should play High if Broadcast plays Medium. (ii) This game has a dominant strategies equilibrium. (iii) Astounding playing Medium and Broadcast playing High is a Nash equilibrium.Consider the following game. Firm 1 can implement one of two actions, A or B. Firm 2 observes the action chosen by Firm 1 and then decides whether to fight it or not. (-10, 20) F2 Fight A Don't fight -(30, 10) Firm 1 (-10, 0) Fight B Don't fight -(20, 15) (a) Consider the following strategy profile: Firm 1 chooses A; Firm 2 chooses fight if A, and fight if B. • this strategy profile is [Select] (b) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses fight if A, and don't fight if B. • this strategy profile is [Select] O (c) Consider the following strategy profile: Firm 1 chooses B; Firm 2 chooses don't fight if A and don't fight if B. • this strategy profile is [Select] 00 F2 ()Player 2 1 2 3 1 (0,2) (1,0) (0,2) (0,2) Player 1 2 (1,0) (1,0) 3 (0,2) (1,0) (0,2) 1. Find all pure. strategy Nash equilibria 2. Does the game have a mixed strategy equilibrium? If so, find one. Otherwise, provide an explanation
