Arthur and Bertha Are Asked by Their Boss to Vote

question 4

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 $5.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 5/6 and for B with probability 1/6.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 5/6 and for B with probability 1/6.
• D)Arthur votes for A with probability 5/9 and for B with probability 4/9.Bertha votes for A with probability 4/9 and for B with probability 5/9.
• E)Arthur votes for A and Bertha votes for B.

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Definitions:

Ida B. Wells

An African American journalist, abolitionist, and feminist who led an anti-lynching crusade in the United States during the late 19th century.

Anti-Discrimination

Policies, laws, and principles designed to prevent unfair treatment of individuals based on race, gender, religion, age, sexual orientation, nationality, or any other characteristic.

Fourteenth Amendment

An amendment to the United States Constitution, granting citizenship to former slaves and providing all citizens with "equal protection under the laws," ratified in 1868.

Supreme Court

The highest federal court in the United States, endowed with the judicial power of the government and hence functions as the ultimate authority on constitutional interpretation.