5. Find all the Bayesian-Nash equilibria in pure strategies. Consider the following normal form game 1 A B 2 A B -1,-1 1,0 0,1 0,0 Now introduce a bit of incomplete information in the following way. In the incomplete information version player i gets (1+t) when it plays A and its rival plays B. Here t, is private information for player i. Each player j believes that t; (ij) is uniformly distributed over [- +e]. Everything else is the same as in the original game. Show that when e converges to zero the pure strategy Bayesian- Nash equilibrium converges to the mixed strategy Nash equilibrium of the complete information game.

5. Find all the Bayesian-Nash equilibria in pure strategies. Consider the following normal form game 1 A B 2 A B -1,-1 1,0 0,1 0,0 Now introduce a bit of incomplete information in the following way. In the incomplete information version player i gets (1+t) when it plays A and its rival plays B. Here t, is private information for player i. Each player j believes that t; (ij) is uniformly distributed over [- +e]. Everything else is the same as in the original game. Show that when e converges to zero the pure strategy Bayesian- Nash equilibrium converges to the mixed strategy Nash equilibrium of the complete information game.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.1P

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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.
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