Each player simultaneously chooses a number from {1, 2,..., 10} and writes it down on a piece of paper; then the players compare the two numbers. If the numbers differ by one, the player with the higher number pays the other player £2. If the players' choices differ by two, the player with the lower number pays £1 to the other player. If the numbers differ by 3 or more then the player with the highest number pays £2 to the other player. In the event of a tie, no money changes hands. Construct a game matrix which describes this game, and evaluate what each player's optimum strategies would be.

Each player simultaneously chooses a number from {1, 2,..., 10} and writes it down on a piece of paper; then the players compare the two numbers. If the numbers differ by one, the player with the higher number pays the other player £2. If the players' choices differ by two, the player with the lower number pays £1 to the other player. If the numbers differ by 3 or more then the player with the highest number pays £2 to the other player. In the event of a tie, no money changes hands. Construct a game matrix which describes this game, and evaluate what each player's optimum strategies would be.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter8: Game Theory

Section: Chapter Questions

Problem 8.9P

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