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(See Problem 2

question 17

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(See Problem 2.) Arthur and Bertha are asked by their boss to vote on a company policy. Each of them will be allowed to vote for one of three possible policies, A, B, and C. Arthur likes A best, B second best, and C least. Bertha likes B best, A second best, and C least. The money value to Arthur of outcome C is $0, outcome B is $1, and outcome A is $4. The money value to Bertha of outcome C is $0, outcome B is $4, and outcome A is $1. The boss likes outcome C best, but if Arthur and Bertha both vote for one of the other outcomes, he will pick the outcome they voted for. If Arthur and Bertha vote for different outcomes, the boss will pick C. Arthur and Bertha know this is the case. They are not allowed to communicate with each other, and each decides to use a mixed strategy in which each randomizes between voting for A or for B. What is the mixed strategy equilibrium for Arthur and Bertha in this game?


Definitions:

Degrees of Freedom

The number of independent values or quantities that can be assigned to a statistical distribution without violating any constraints.

Dependent Variable

A variable in an experiment or model that is expected to change as a result of manipulations or changes in the independent variable(s).

Independent Variables

Variables that are manipulated or categorized to determine their effect on other variables.

Quantity Minimized

Refers to the outcome of an optimization problem where the goal is to find the smallest possible value of a certain quantity.

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