Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
9th Edition
ISBN: 9781259290619
Author: Michael Baye, Jeff Prince
Publisher: McGraw-Hill Education
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Question
Chapter 10, Problem 10CACQ
To determine
The trigger strategy that allows player 1 to earn payoff of 140 and player 2 to earn payoff of 180.
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Using the payoff matrix, suppose this game is infinitely repeated and that the interest rate is sufficiently “low.” Identify trigger strategies that permit players 1 and 2 to earn equilibrium payoffs of 140 and 180, respectively, in each period
a) Find the Nash equilibria in the game (in pure and mixed strategies) and the associated payoffs for the players.
b) Now assume that the game is extended in the following way: in the beginning Player 1 can decide whether to opt out (this choice is denoted by O) or whether to play the simultaneous-move game in a) (this choice is denoted by G). If Player 1 opts out (plays O) then both Player 1 and Player 2 get a payoff of 4 each and the game ends. If Player 1 decides to play G, then the simultaneous-move game is played. Find the pure-strategy Nash equilibria in this extended version of the game. (Hint: note that Player 1 now has 4 strategies and write the game up in a 4x2 matrix.)
c) Write the game in (b) up in extensive form (a game tree). Identify the subgames of this game.
if Y =4
(b) What is the highest payoff any player can receive in any subgame perfect Nash equilibrium of the repeated game?
Chapter 10 Solutions
Managerial Economics & Business Strategy (Mcgraw-hill Series Economics)
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