Question

1. What's the payoff of each situation?

A three-person committee has to choose a winner for a national art prize. After some debate, there are three candidates still under consideration: a woman who draws antelope in urban settings, a man who makes rectangular lead boxes, and a woman who sculpts charcoal. Lets call these candidates a, b and c and call the committee members 1, 2 and 3. The preferences of the committee members are as follows Member 1: a b>c Member 2: c>a b Member 3 b>c>a, where"" should be interpreted as "is preferred" The rules of the competition say that, if they disagree, they should vote (secret ballot, one member one vote) and that, if and only if the vote is tied, the winner will be the candidate for whom member 1 voted. Suppose that each committee member gets a payoff of 1 if her most preferred candidate is elected, 0 if her second most preferred candidate is elected, and -1 if her least preferred candidate is elected. Suppose each committee member votes for her most preferred candidate, the payoff for member 1 is for member 2 is and for member 3 is Now suppose that member 3 votes for candidate c while members 1 and two vote as before. Then, the payoff for member 1 is for member 2 is and for member 3 is (Please, enter numerical values like -2, -1, 0, 1 etc).

2. How many strategies does each player A and B have?

Answer 1

1.

Given the preferences relations, we can see that

$a \succ b$ for 2 members - 1 and 2.

$b \succ c$ for 2 members - 1 and 3.

$c \succ a$ for 2 members - 2 and 3.

Since there is intransitivity among the relations, there arises a disagreement and members will vote.

If each member votes for her most preferred candidate. the result will be inconclusive and would be resolved by the preferred choice of member 1.Thus "a" wins the election.

Payoff for member 1 = +1

Payoff for member 2 = 0

Payoff for member 3 = -1

If member 3 votes for c, and the other two vote as before (1 for a and 2 for c), "c" wins the election. Thus payoff to member 1 is -1, member 2 is +1 and member 3 is 0.