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 Chris.
II: Every person votes for his/her second choice.

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 Chris.
II: Every person votes for his/her second choice.

Quizplus · Accepted Answer

In scenario I, every person voting for Chris is a Nash equilibrium because no single voter has an incentive to change their vote, as doing so would not change the outcome in their favor. In scenario II, every person voting for their second choice also results in a Nash equilibrium. Kim and Terry voting for their second choice (Chris) would lead to Chris winning, which is the best outcome they can achieve given the others' votes. Chris voting for Kim (his second choice) does not change the outcome in his favor, as voting for himself would still result in a tie that Kim would break in favor of Chris. Thus, both scenarios are stable and no one has an incentive to unilaterally change their strategy, making both I and II Nash equilibria.

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