Suppose on a committee of three people Kim (the chair), Chris, and Terry each have one vote, but Kim breaks any tie. In attempting to elect someone to host the summer picnic, each person has a priority list: $\begin{array}{clll}
&\mid& \text { Kim's Priorities}&\text { Chris's Priorities}&\text { Terry's Priorities}\
\hline \text { 1st choice } &\mid& \text { Kim } & \text { Chris } & \text { Terry } \
\text { 2nd choice }&\mid & \text { Terry } & \text { Kim } & \text { Chris } \
\text { 3rd choice } &\mid& \text { Chris } & \text { Terry } & \text { Kim }
\end{array}$ Which of the following are Nash equilibria?
I: Every person votes for Kim.
II: Every person votes for Chris.

Question

Suppose on a committee of three people Kim (the chair), Chris, and Terry each have one vote, but Kim breaks any tie. In attempting to elect someone to host the summer picnic, each person has a priority list: $\begin{array}{clll}
&\mid& \text { Kim's Priorities}&\text { Chris's Priorities}&\text { Terry's Priorities}\
\hline \text { 1st choice } &\mid& \text { Kim } & \text { Chris } & \text { Terry } \
\text { 2nd choice }&\mid & \text { Terry } & \text { Kim } & \text { Chris } \
\text { 3rd choice } &\mid& \text { Chris } & \text { Terry } & \text { Kim }
\end{array}$ Which of the following are Nash equilibria? 
I: Every person votes for Kim.
II: Every person votes for Chris.

Quizplus · Accepted Answer

In this scenario, if any one person switches their vote, it will still result in a tie, which Kim will break in favor of herself. Therefore, each person voting for their first choice is a Nash equilibrium. Both options I and II satisfy this condition.

Suppose on a Committee of Three People Kim (The Chair)