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:

Isolated Type

Denotes a classification or category typically used in psychology or psychiatry to describe individuals who prefer solitude and show little interest in social interactions.

Chronic Alcoholic

An individual suffering from alcoholism for a long duration, showing a consistent pattern of excessive drinking despite negative consequences.

Anxious Attachment

An anxious, uncertain, and clingy style of attachment; in some models, includes a negative view of the self.

Harry Harlow

An American psychologist best known for his research on social isolation, maternal-separation, and dependency needs of rhesus monkeys, which played a significant role in understanding human emotional and social development.