Arthur and Bertha Are Asked by Their Boss to Vote

question 20

Multiple Choice

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?

• A)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
• B)Arthur votes for A with probability 3/4 and for B with probability 1/4.Bertha votes for A with probability 1/5 and for B with probability 4/5.
• C)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 3/4 and for B with probability 1/4.
• D)Arthur votes for A with probability 3/7 and for B with probability 4/7.Bertha votes for A with probability 4/7 and for B with probability 3/7.
• E)Arthur votes for A and Bertha votes for B.

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Definitions:

Compounded Forces

Forces that act together on an object, combining their effects to produce a single resultant force.

Mechanical Spring

A device made of elastic material designed to return to its original shape when a force is removed, often used to absorb shock or store potential energy.

Pneumatic Service

A type of service or system that utilizes compressed air or gas to operate machinery, tools, or control systems in various industrial, automotive, and manufacturing applications.