*Goals:*

- Students will demonstrate an understanding of how to use a Payoff Matrix and the background of the Prisoner’s Dilemma game.
- Students will demonstrate an understanding of Nash Equilibrium.
- Students will participate in a Prisoner’s Dilemma game of their own.

**Time needed:** 30-40 minutes

**Materials Required:** A lot of smaller candies (similar to what is often distributed at Halloween)

**Overview:**

An understanding of the Prisoner’s Dilemma game allows students to understand several Game Theory concepts, such as the Payoff Matrix, Nash Equilibrium, Dominant Strategies, and the Pareto Efficient Outcome.

- The Payoff Matrix is a table that displays the strategies of one player in a column and the decisions of another player in a row along with a matrix of the different outcomes given every combination of strategies. There is an example of a Payoff Matrix in the demonstration section, below.
- The Nash Equilibrium is a stable point in a game where no player can gain by switching their choice, given all other players’ choices remain the same; no player wishes to deviate from the Nash Equilibrium. Nash Equilibrium may be identified by determining the dominant strategies for each party.
- A dominant strategy is where one strategy always provides a player with a better outcome, no matter what other players do.
- A Pareto Efficient Outcome is one in which no individual can be better off from deviating without making another party worse off.

A Prisoner’s Dilemma is a situation in which the players may not cooperate even though it is in their best collective interest to do so, settling on a Nash Equilibrium that may not be Pareto Efficient.

In the clip “Jyn Speaks To Saw,” Jyn must speak to Saw to talk him into cooperating with the other rebels. These strategies can be mapped on a Payoff Matrix to demonstrate the Prisoner’s Dilemma and thus show students why Saw does not cooperate.

**Demonstration:**

- Show the clip “Jyn Speaks With Rebels” to students.
- After showing the clip and explaining the concepts discussed in the overview section, the scenario we see in the clip can be mapped with a 2×2 Payoff Matrix between The Rebels and Saw:

This payoff matrix shows the Prisoner’s Dilemma scenario between The Rebels and Saw. Each party has the choice to Cooperate or Defect and be an extremist. From the clip, we can tell that the Rebels and Jyn would like to cooperate with Saw; however, Saw is an extremist and refuses to cooperate.

The class can discuss the Nash Equilibrium and Pareto Efficient Outcome to explain why Saw does not cooperate and why the Rebels wish that he would.

Once the students fully understand each of the player’s decisions, they will be placed in their own Prisoner’s Dilemma situation…“Prisoner’s Dilemma In-Class” worksheet

**Discussion:**

Now that the students have participated in their own Prisoner’s Dilemma situation, they should be better able to understand the decisions made by both parties in the clip. Here are some questions you could ask:

- For the students who Cooperated:
- Why did you Cooperate?
- Would your payout have been higher or lower had you Defected?

- For the students who Defected:
- Why did you Defect?
- Would your payout have been higher or lower had you Cooperated?

- Questions for all:
- How would your strategy have changed if you were able to communicate with your counterpart? Would this have made it easier or harder to cooperate?
- How would you feel if you knew who your counterpart was but they refused to communicate with you (just as Saw refused to communicate with the other Rebels)?

Here are links to additional Game Theory-related games that can be used to explain rational decision making: