a. Suppose players announce simultaneously whether they want to ex- change their houses. If both players agree to an exchange, the exchange takes place. Otherwise no exchange takes place. Find a Bayesian Nash equilibrium of this game in pure strategies in which each player i ac- cepts an exchange if and only if the value v, does not exceed some threshold 0₁. b. How would your answer to (a) change if player j's valuation of player i's house were v? c. Try to explain why any Bayesian Nash equilibrium of the game de- scribed in (a) must involve threshold strategies of the type postulated in (a)

a. Suppose players announce simultaneously whether they want to ex- change their houses. If both players agree to an exchange, the exchange takes place. Otherwise no exchange takes place. Find a Bayesian Nash equilibrium of this game in pure strategies in which each player i ac- cepts an exchange if and only if the value v, does not exceed some threshold 0₁. b. How would your answer to (a) change if player j's valuation of player i's house were v? c. Try to explain why any Bayesian Nash equilibrium of the game de- scribed in (a) must involve threshold strategies of the type postulated in (a)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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How would this exercise be solved step by step?

12.7 Trading Places: Two players, 1 and 2, each own a house. Each player i values
his own house at vi. The value of player i's house to the other player, i.e., to
player j i, is 3v₁. Each player i knows the value v; of his own house to
himself, but not the value of the other player's house. The values v; are drawn
independently from the interval [0, 1] with uniform distribution.
a. Suppose players announce simultaneously whether they want to ex-
change their houses. If both players agree to an exchange, the exchange
takes place. Otherwise no exchange takes place. Find a Bayesian Nash
equilibrium of this game in pure strategies in which each player i ac-
cepts an exchange if and only if the value v; does not exceed some
threshold 0;.
b.
How would your answer to (a) change if player j's valuation of player
i's house were {v;?
c.
Try to explain why any Bayesian Nash equilibrium of the game de-
scribed in (a) must involve threshold strategies of the type postulated
in (a).

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