Arthur and Bertha Are Asked by Their Boss to Vote

question 5

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

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Definitions:

Visual Cortex

The part of the cerebral cortex responsible for processing visual information, located in the occipital lobe of the brain.

Occipital Lobes

The rearmost lobe in each cerebral hemisphere of the brain, primarily responsible for processing visual information.

Split Brain

A condition resulting from surgery that isolates the brain’s two hemispheres by cutting the fibers (mainly those of the corpus callosum) connecting them.

Conscious Awareness

The state of being fully alert and aware of one’s thoughts, feelings, and environment.