Question 2 (Subgame-Perfect Nash Equilibrium Consider the following sequential game of imperfect information. E 5,5 P2 (c) soning. T 0,6 P1 L P2 B ( 6,0 R 2,0 P2 I P1 T e 1,1 5,1 b 0,2 P2 P2 A' R 0,0 P1 B' { 0,0 P2 1,5 (a) How many information sets does this game have? What constitutes a strategy in a sequential game of imperfect information? (b) Find all the pure strategy subgame-perfect Nash equilibria of this game. Remember to write them down properly. Could this game support a SPNE in mixed strategies? Explain your rea- (d) Suppose this game were a game of perfect information. What would the game tree look like? What would be the SPNE outcome?

Question 2 (Subgame-Perfect Nash Equilibrium Consider the following sequential game of imperfect information. E 5,5 P2 (c) soning. T 0,6 P1 L P2 B ( 6,0 R 2,0 P2 I P1 T e 1,1 5,1 b 0,2 P2 P2 A' R 0,0 P1 B' { 0,0 P2 1,5 (a) How many information sets does this game have? What constitutes a strategy in a sequential game of imperfect information? (b) Find all the pure strategy subgame-perfect Nash equilibria of this game. Remember to write them down properly. Could this game support a SPNE in mixed strategies? Explain your rea- (d) Suppose this game were a game of perfect information. What would the game tree look like? What would be the SPNE outcome?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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QUESTION 1: Game theory a) What is the pure strategy Nash equilibrium outcome if there is one? b) Is this a socially optimal outcome? If not, which outcome is preferred? c) Do all three solution approaches for simultaneous games work independently (not together)? If not, which do not? d) Draw the game as a game tree (extensive form). e) Switch the payoffs in cells (A, A) and (D, D). What is the pure strategy Nash equilibrium outcome if there is one?
Required a. Identify three Nash equilibria of this game. b. Explain in words which strategy pair is likely to be played in this game and why. Please give a detailed answer. Thanks!
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33. When neither player has a dominant strategy, A) game theory will not provide information.B) no Nash-Equilibrium exists.C) at least one Nash-Equilibrium exists.D) the game cannot be analyzed.
5 WHILE USING GAME THEORY METHOD EXPLAİN CLİMATE CHANGE STRATEGIES PLAYERS PAYOFFS AND OUTCOMES IN 200 WORDS
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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.
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