Answered: Consider the following Bayesian game.…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the following Bayesian game. There are two players 1 and 2. Both players choose whether to play A or B. Two states are possible, L and R. In the former, players play a stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player 2 knows the state, while Player 1 thinks that the state is L with probability q and R with probability 1 ! q. Payo§s in each state respectively satisfy:

Player 1 is the row player, and their payo§ is the first to appear in each entry. Player 2 is the
column player and their payo§ is the second to appear in each entry.

(a) What is the set of possible strategies for the two players in this game?

(b) Find all the pure strategy Bayes Nash equilibria for any value of q 2 (0, 1).

2. Consider the following Bayesian game. There are two players 1 and 2. Both players choose
whether to play A or B. Two states are possible, L and R. In the former, players play a
stag-hunt game, and in the latter, players play a matching pennies game. Suppose that Player
2 knows the state, while Player 1 thinks that the state is L with probability q and R with
probability 1– q. Payoffs in each state respectively satisfy:
1\2| A
5, 5 0,1
1\2
2,0 0,2
0, 2 2,0
B
B
State L:
A
State R:
A
B
1,0 1,1
B
Player 1 is the row player, and their payoff is the first to appear in each entry. Player 2 is the
column player and their payoff is the second to appear in each entry.
(a) What is the set of possible strategies for the two players in this game? (4 marks)
(b) Find all the pure strategy Bayes Nash equilibria for any value of q E (0, 1). (16 marks)

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