Game theory problem Exercise 1.12. Consider the following game. There is a club with three members:Ann, Bob and Carla. They have to choose which of the three is going to bepresident next year. Currently Ann is the president. Each member is both acandidate and a voter. Voting is as follows: each member votes for one candidate(voting for oneself is allowed); if two or more people vote for the same candidatethen that person is chosen as the next president; if there is complete disagreement,in the sense that there is exactly one vote for each candidate, then the person fromwhom Ann voted is selected as the next president.(a) Represent this voting procedure as a game frame, indicating inside each cell ofeach table which candidate is elected.(b) Assume that the players' preferences are as follows: Ann > CarlaAnnCarla BobBob>Bob Ann, Bob Carla Ann Carla Carla.Using utility values 0, 1 and 2, convert the game frame into a game.AnnBob.(c) Apply the IDWDS to the game of part (b). Is there a weak iterated dominant-strategy equilibrium?(d) Does the extra power given to Ann (in the form of tie-breaking in case ofcomplete disagreement) benefit Ann?

Game theory is a mathematical discipline commonly applied to the analysis of interactive strategic…

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Game theory problem

Exercise 1.12. Consider the following game. There is a club with three members:
Ann, Bob and Carla. They have to choose which of the three is going to be
president next year. Currently Ann is the president. Each member is both a
candidate and a voter. Voting is as follows: each member votes for one candidate
(voting for oneself is allowed); if two or more people vote for the same candidate
then that person is chosen as the next president; if there is complete disagreement,
in the sense that there is exactly one vote for each candidate, then the person from
whom Ann voted is selected as the next president.
(a) Represent this voting procedure as a game frame, indicating inside each cell of
each table which candidate is elected.
(b) Assume that the players' preferences are as follows: Ann > Carla
Ann
Carla Bob
Bob>Bob Ann, Bob Carla Ann Carla Carla.
Using utility values 0, 1 and 2, convert the game frame into a game.
Ann
Bob.
(c) Apply the IDWDS to the game of part (b). Is there a weak iterated dominant-
strategy equilibrium?
(d) Does the extra power given to Ann (in the form of tie-breaking in case of
complete disagreement) benefit Ann?

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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