3. Consider the following degenerate game. Please find all the pure and mixed strategy Nash Equilibria. egge n Player 2 a b. L 1 3 Player 1 -3 -2 R 1 -1 6. -3 2. 2. 3.
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- Player 1 X Y Player 2 1 2 1 3,2 2 Wo 1 1,3 -0,1 hich of the following is the Subgame Perfect Nash Equilbrium in this4. Correlated EquilibriaConstruct an example (not one from class or the reading) of a Normal form game with a correlated equilibrium that is not a Nash equilibrium.Find the Subgame Perfect Nash Equilibrium of this game using backward induction. Please write down the calculations to show why a player prefers one action over another. (N represents nature)
- Answer all questions, show all working. 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? Explain the differences between cooperative and non- cooperative games. What are the fundamental hypotheses about the behavior of the persons in Game theory?parameter z= 1 In the unique subgame perfect Nash equilibrium, what is the sum of the payoffs tothe two players?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.
- 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 7,9Suppose that the following prisoner's dilemma game (stage game) is played repeatedly and players discount future payoffs with the common discount factor δ <1. a) Carefully specify the strategy spaces for both players, draw the extensive form game and find a subgame perfect Nash equilibrium when the stage game is played twice, and both players observe the outcome of the first play.. Find the Nash equilibrium of the following modified Rock-Paper-Scissors game: • When rock (R) beats scissors (S), the winner’s payoff is 10 and the loser’s payoff is −10. • When paper (P) beats rock, the winner’s payoff is 5 and the loser’s payoff is −5. • When scissors beats paper, the winner’s payoff is 2 and the loser’s payoff is −2. • In case of ties, both players receive 0 payoff. You are suposed to create a system of equations and then solve for them and find 3 probabilities- please show how to do that
- 1. Assume this game is played 2 times and there is no discounting. The whole payoff for two periods is the sum of payoffs of each period. Draw a tree of the game and solve it with subgame prefect Nash equilibrium. Explain clearly, handwritten is preferable.2 firms are engaged in Cournot competition; firm A faces the cost curveCA(yA)=40yAand firm Bfaces the cost curveCB(yB)=40yB. The inverse market demand curve isP(y)=100y, whereyrepresents market level of output. a)Define the Cournot game. b)In 1 or 2 sentences explain why a firm has no incentive to deviate from the Cournot Nash equilibrium(holding their opponent’s strategy constant). c)Find the Cournot Nash Equilibrium. d)Now suppose instead of playing their strategies at the same time, firm A moves first and then firm B moves second(sequentialgame).Does firm A earn higher profits in this game or the game in part c)?Are the following true or false (justify answer: just T or F will not suffice): A) In a sequential game, the leader always receives a higher payoff due to his/her knowledge of the rationality of the second player. B) Games of complete information are a sub-type of games of perfect information. C) If a game with a more than one unique Nash Equilibrium is played finitely many times, the only type of sub-game perfect equilibriums is some sequence of Nash equilibriums played at every stage.