Consider the following two-player game:P2LRU4,11,3P1D0, 01,2⚫ The game is REPEATED ONCE. Identify all the subgame perfect Nash equi-libria of this game (in pure strategies).⚫ If the game was INFINITELY repeated, and players had a discount factor of0<< 1, can there be a SPNE in which players always play (U, R)?

Part 1: Subgame Perfect Nash Equilibria (SPNE) for the game repeated onceStage game analysis:The…

Answered: Consider the following two-player game:…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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• (1,0) (1,1) Player 2 G D H (2,0) Action Player 1 Player 1 Action B Player 1 (3,-1) E Player 2 (0,1) (-1,-1) (a) Find all the Subgame Perfect Nash equilibria in this game. (b) Find all the Nash equilibria in this game. (Hint: write the game in strategic form.)
Problem 2. Consider the partnership-game we discussed in Lecture 3 (pages 81-87 of the textbook). Now change the setup of the game so that player 1 chooses x = [0, 4], and after observing the choice of x, player 2 chooses y ≤ [0, 4]. The payoffs are the same as before. (a) Find all SPNE (subgame perfect Nash equilibria) in pure strategies. (b) Can you find a Nash equilibrium, with player 1 choosing x = 1, that is not subgame perfect? Explain.
Consider the payoff matrix below, which describes a symmetric A B A 17,17 0,14 B 14,0 8,8 (a) Find all Nash equilibria of this game, including any mixed strategy equilibria. (b) Draw the expected payoff difference diagram for this game, including all the Nash equilibria you found in (a). is (c) What would you expect to occur most frequently when this game played as a lab experiment? Justify your answer using your answers from (a) and (b).
9 00 3 -2 -8 A = ( ) and B = 03 -5 -2 Let I be the bimatrix game whose payoffs are described by A for the row-player and B for the column- player. 1. Compute all mixed Nash equilibria of T. 9
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q60c- Is the Nash equilibrium the best outcome for this problem? Explain
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QS. Consider the following stage game B. C A (4, 4) (1, 5) (0, 3) B (7, 1) (3, 4) (0, 1) C (3, 0) (2, 0) (1, 1) (a). Find all Nash equilibria of the stage game (b). Suppose that the stage game is played two times and with agents discount factor given by 0<6 <1. Is there a subgame perfeet equilibrium equilibrium strategy profile in which (A, A) is played in the first round? If not explain whv. (Hint: Think of o 1)
Consider a Vickery auction. There are N bidders, each of them values the object £vi, with i = 1…N. Each bidder can submit a bid in a sealed envelope. Once all the bids have been made, the envelopes are opened. The winner of the auction is the bidder who made the highest bid, however, s/he pays the second-highest bid. What are the weakly dominant strategies in this game? Is there only one?
INFINITE REPETITION Consider the infinitely repeated game constructed from the following stage game. bị b2 a1 8,8 3,13 a2 13,3 0,0 Suppose that both players use the discount factor d to evaluate future payoff streams. What is the smallest value of d such that there exists a subgame perfect Nash equilibrium in which the action profile is played in all periods? (Please report your answer in decimal form, rounded if necessary to the nearest 0.01.)

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