driver chooses simultaneously between going straight (S), swerving left (L), and swerving right (R). If one driver goes straight while the other swerves, either right or left, the one who goes straight gets payoff 3 while the other gets -1. If each driver swerves to his left, or each swerve to his right, then each gets 0 (remember, they are going in opposite directions). If both go straight, or if one swerves to his left while the other swerves to his right, then the cars crash and each gets payoff -4. Write the payoff matrix for this game а. b. Find all of the game's Nash equilibria in pure strategies.

driver chooses simultaneously between going straight (S), swerving left (L), and swerving right (R). If one driver goes straight while the other swerves, either right or left, the one who goes straight gets payoff 3 while the other gets -1. If each driver swerves to his left, or each swerve to his right, then each gets 0 (remember, they are going in opposite directions). If both go straight, or if one swerves to his left while the other swerves to his right, then the cars crash and each gets payoff -4. Write the payoff matrix for this game а. b. Find all of the game's Nash equilibria in pure strategies.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Cameron and Luke are playing a game called ”Race to 10”. Cameron goes first, and the players take turns choosing either 1 or 2. In each turn, they add the new number to a running total. The player who brings the total to exactly 10 wins the game. a) If both Cameron and Luke play optimally, who will win the game? Does the game have a first-mover advantage or a second-mover advantage? b) Suppose the game is modified to ”Race to 11” (i.e, the player who reaches 11 first wins). Who will win the game if both players play their optimal strategies? What if the game is ”Race to 12”? Does the result change? c) Consider the general version of the game called ”Race to n,” where n is a positive integer greater than 0. What are the conditions on n such that the game has a first mover advantage? What are the conditions on n such that the game has a second mover advantage?
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