10. Game theory Player Rhas a $2, a $5, and a $10 bill. Player Chas a $1, a $5,and a $10 bill. Each player selects and shows (simultaneously)one of his or her three bills. If the total value of the two billsshown is even, R wins Cs bill; if the value is odd, C wins Rs bill.(Which player would you rather be?)(A) Set up the payoff matrix for the game.(B) Solve the game using the simplex method discussed in thissection. (Remove any recessive rows and columns, if present,before you start the simplex method.)

Answer a) According to the given situation below is a payoff matrix…

Answered: Player Rhas a $2, a $5, and a $10 bill.…

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

Chapter18: Auctions

Section: Chapter Questions

Problem 18.1IP

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10. Game theory

Player Rhas a $2, a $5, and a $10 bill. Player Chas a $1, a $5,
and a $10 bill. Each player selects and shows (simultaneously)
one of his or her three bills. If the total value of the two bills
shown is even, R wins Cs bill; if the value is odd, C wins Rs bill.
(Which player would you rather be?)
(A) Set up the payoff matrix for the game.
(B) Solve the game using the simplex method discussed in this
section. (Remove any recessive rows and columns, if present,
before you start the simplex method.)

Definition Definition Economic decision-making framework that analyzes how different players optimize their outcomes with given pay-offs corresponding to their available strategies. The assumptions of game theory are: The number of players or competitors are finite/limited; All participants are rational The rules of the game are known to every player; and Each participant has a finite set of actions. A common way in which game theory is presented as an ( m x n ) matrix in which m represents the strategies of row player and n represents the strategies of column player. There are several limitations of game theory: Many businesses have a large number of competitors, and selecting an optimal strategy in these circumstances is difficult; Real-life business operating environments are full of uncertainty and difficult to model as a game theory; and The assumption of rationality and utility maximization isn't always an accurate portrayal of human nature.

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