Consider the following simultaneous game.a.b.C.d.Player 1UPlayer 2L8,83,0R3,38,3What are the pure-strategy Nash equilibria? Identify.Find whether there are any mixed-strategy equilibria.Assume now the game above is being modified as a sequential game whereplayer 1 would move first and player 2 second. Find all Nash and subgameperfect equilibria for the game.Would a Nash equilibrium always be Pareto efficient? Use your answer in (a) toexplain.

There are two players : Player 1 & 2 Strategy Set of Player 2 : {L , R } Strategy Set of Player…

Answered: Consider the following simultaneous…

Consider the following simultaneous game. Player 1 U D Player 2 L 8,8 3,0 R 3,3 8,3 What are the pure-strategy Nash equilibria? Identify.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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The following table contains the possible actions and payoffs of players 1 and 2. Player 1 U M D L 2,10 2,5 8,7 Player 2 C 5,2 11,8 8,4 R 5,4 2,9 8,3 This is a simultaneous move game. In a pure strategy Nash equilibrium of this game, Player 1 receives a payoff of ✓and player 2 receives a payoff of If, instead of playing simultaneously, player 2 moves first, then in the Nash equilibrium player 1 receives a payoff of ✓and player 2 receives a payoff of
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Consider the extensive form game portrayed below. The top number at aterminal node is player 1’s payoff, the middle number is player 2’s payoff,and the bottom number is player 3’s payoff.a. Derive the strategy set for each player. (Note: If you do not want to listall of the strategies, you can provide a general description of a player’sstrategy, give an example, and state how many strategies are in thestrategy set.)b. Derive all subgame perfect Nash equilibria. c. Derive a Nash equilibrium that is not a SPNE, and explain why it isnot a SPNE.
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.
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