Consider a new card game between 2 players: Jim (player 1) and Kelly (player 2) Jim is dealt two cards : 09 and 9. Kelly is also dealt two cards: 6 and 4. Now, each of the players will play 1 card both at the same time. The payoff of Jim is 1 points if he plays a card of opposite color (red/black) than Kelly, and otherwise his payoff is 7 points. The payoff of Kelly is 5 points if the difference of the already played card numbers is greater than 6, otherwise her payoff is 8 points. 1. Find the action sets of each player and the action profile of the game. 2. Represent the game in the Normal form. 3. Find the Best Responses for Jim. 4. Find the Best Responses for Kelly. 5. Find all the Nash Equilibriums of the game (if any).
Consider a new card game between 2 players: Jim (player 1) and Kelly (player 2) Jim is dealt two cards : 09 and 9. Kelly is also dealt two cards: 6 and 4. Now, each of the players will play 1 card both at the same time. The payoff of Jim is 1 points if he plays a card of opposite color (red/black) than Kelly, and otherwise his payoff is 7 points. The payoff of Kelly is 5 points if the difference of the already played card numbers is greater than 6, otherwise her payoff is 8 points. 1. Find the action sets of each player and the action profile of the game. 2. Represent the game in the Normal form. 3. Find the Best Responses for Jim. 4. Find the Best Responses for Kelly. 5. Find all the Nash Equilibriums of the game (if any).
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter15: Strategic Games
Section: Chapter Questions
Problem 9MC
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Transcribed Image Text:Consider a new card game between 2 players: Jim (player 1) and Kelly (player 2)
Jim is dealt two cards : 09 and 49. Kelly is also dealt two cards: 06 and 4. Now, each of the players will play 1 card both at the same time.
The payoff of Jim is 1 points if he plays a card of opposite color (red/black) than Kelly, and otherwise his payoff is 7 points.
The payoff of Kelly is 5 points if the difference of the already played card numbers is greater than 6, otherwise her payoff is 8 points.
1. Find the action sets of each player and the action profile of the game.
2. Represent the game in the Normal form.
3. Find the Best Responses for Jim.
4. Find the Best Responses for Kelly.
5. Find all the Nash Equilibriums of the game (if any).
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