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- a. Consider the following sequential game. Player 1 A B Player 2 Player 1 a a B Player 2 (4) () y i. Determine the subgame perfect Nash equilibria and their outcomes. ii. Determine the Nash equilibria of the game. For each of the Nash equilibria, argue why no player has a profitable deviation. ii. Determine which parts of the Nash equilibrium strategies involve uncredible threats.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.4. 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.
- Consider the following game : Stag Rabbit Stag 9, 9 0, 8 Rabbit 8, 0 7, 7 The first payoff is that of player 1 and the second that of player 2. a. ) Draw the extensive form of the simultaneous game. Find all the Nash equilibrium. p. Suppose player 1 moves first or we are in a sequential game now. Draw the extensive form in the sequential version. c. What is the subgame perfect Nash Equilibrium (SPNE) in the sequential version? d. ) Explain why it is an SPNE.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)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.
- 5. Consider a simultaneous game in which player A chooses one of two actions (Up or Down), and B chooses one of two actions (Left or Right). The game has the following payoff matrix, where the first payoff in each entry is for A and the second for B.(8 points) B Right Left 3,3 5,1 Down 2,2 4,4 a. Find the Nash equilibrium or equilibria. b. Which player, if any, has a dominant strategy? A UpExercise 6.8. Consider the following extensive-form game with cardinal payoffs: 1 R O player pay 000 2 1 M 3 b 010 O player 3's payoff 1 2 221 2 000 0 0 (a) Find all the pure-strategy Nash equilibria. Which ones are also subgame perfect? (b) [This is a more challenging question] Prove that there is no mixed-strategy Nash equilibrium where Player 1 plays Mwith probability strictly between 0 and 1.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 ہے 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.