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 drive the van, each person has a priority list: $\begin{array}{clll}
&\mid& \text { Kim's Priorities}&\text { Chris's Priorities}&\text { Terry's Priorities}\
\hline \text { 1st choice } &\mid&\text { Chris } & \text { Kim } & \text { Terry } \
\text { 2nd choice }&\mid &\text { Kim } & \text { Chris } & \text { Chris } \
\text { 3rd choice } &\mid& \text { Terry } & \text { Terry } & \text { Kim }
\end{array}$ Which of the following are Nash equilibria?
I: Every person votes for his/her first choice.
II: Kim and Chris vote for Chris; Terry votes for Terry.

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 drive the van, each person has a priority list: $\begin{array}{clll}
&\mid& \text { Kim's Priorities}&\text { Chris's Priorities}&\text { Terry's Priorities}\
\hline \text { 1st choice } &\mid&\text { Chris } & \text { Kim } & \text { Terry } \
\text { 2nd choice }&\mid &\text { Kim } & \text { Chris } & \text { Chris } \
\text { 3rd choice } &\mid& \text { Terry } & \text { Terry } & \text { Kim }
\end{array}$ Which of the following are Nash equilibria? 
I: Every person votes for his/her first choice.
II: Kim and Chris vote for Chris; Terry votes for Terry.

Quizplus · Accepted Answer

For choice I, every person voting for their first choice is not a Nash equilibrium as one person can deviate and vote for their second choice, which would result in that person's preferred outcome. 
For choice II, if Kim and Chris vote for Chris and Terry votes for Terry, this is a Nash equilibrium. If any person deviates and votes for their second choice, the outcome would not change since Kim breaks the tie. Therefore, both choices I and II are not Nash equilibria, and the only Nash equilibrium is choice II.

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