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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 $3. 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:

Belt Restraint

A device used to restrict the movement of patients to prevent them from harming themselves or others, typically in a healthcare setting.

Abdomen

The part of the body between the chest and pelvis, containing most of the digestive organs among other structures.

Apply

This term refers to the act of putting into service or action, often related to techniques, methods, or requesting for positions or roles.

Restraint-Free Environment

A care setting that avoids the use of physical restraints or restrictive interventions, promoting freedom of movement and respect for patient autonomy.

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