Arthur and Bertha Are Asked by Their Boss to Vote

question 9

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 $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?

• A)Arthur votes for A with probability 4/5 and for B with probability 1/5.Bertha votes for A with probability 1/5 and for B with probability 4/5.
• B)Arthur and Bertha each votes for A with probability 1/2 and for B with probability 1/2.
• C)Arthur votes for A with probability 1/5 and for B with probability 4/5.Bertha votes for A with probability 4/5 and for B with probability 1/5.
• D)Arthur votes for A with probability 4/8 and for B with probability 4/8.Bertha votes for A with probability 4/8 and for B with probability 4/8.
• E)Arthur votes for A and Bertha votes for B.

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Definitions:

Cephalocaudal

A pattern of growth and development in which areas of the body develop from head (cephalo) to tail (caudal) direction.

Proximodistal

A pattern of physical and motor development that progresses from the center of the body outward toward the extremities.

Upper-Arm Movement

The action or range of motion associated with the segment of the arm located between the shoulder and the elbow.

Fine Finger Movements

The ability to make small, precise movements with the fingers, often necessary for tasks such as writing or manipulating small objects.