Arthur and Bertha Are Asked by Their Boss to Vote

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.