# 4: Non-Zero-Sum Games


In the previous chapters, we concentrated on zero-sum games. We know how to solve any zero-sum game. If it has a pure strategy equilibrium, then we know the players should play the equilibrium strategies. If it doesn't have an equilibrium point, then we have seen methods for finding a mixed strategy equilibrium. Assuming both players are our model rational players, then we know they should always play an equilibrium strategy. In this chapter we turn our attention to non-zero-sum games.

• 4.1: Introduction to Two-Player Non-Zero-Sum Games
In this section, we introduce non-zero-sum games. In a non-zero-sum game the players' payoffs no longer need to sum to a constant value. Now it is possible for both players to gain or both players to lose.
• 4.2: Prisoner's Dilemma and Chicken
Both Prisoner's Dilemma and Chicken are models of games where we describe the choice of strategy as “Cooperate” and “Defect”. In Prisoner's Dilemma, we think of “cooperating” as cooperating with the other player, and “defecting” as turning against the other player. In Chicken, players cooperate by swerving and defect by driving straight. Using these examples, think about how these games can model other everyday interactions where you could describe your choices as cooperating and defecting.
• 4.3: A Class-Wide Experiment
We are going to look at a class-wide game. Each member of the class secretly chooses a single letter: “C” or “D,” standing for “cooperate” or “defect.” This will be used as your strategy choice in the following game with each of the other players in the class. Here is how it works for each pair of players: if they both cooperate, they get each get 3 points. If they both defect, they each get 1 point. If one cooperates and one defects, the cooperator gets nothing, but the defector gets 5 points.
• 4.4: What Makes a Prisoner's Dilemma?
In this section, we give a mathematical description of Prisoner's Dilemma and compare it to some similar games.
• 4.5: Another Multiplayer Experiment
This activity needs to be played as a class. All players need to be able to respond without being able to see the responses of others. Answers may be revealed before moving on to the next question. Without sharing your answers with others, select your answer to the following questions. Try to be as honest about your answer as possible. Make sure you have a reason for each answer.
• 4.6: Volunteer's Dilemma
In Section 4.5 we played a game called Volunteer's Dilemma. In this section, we will compare Class-wide Prisoner's Dilemma with Volunteer's Dilemma. In particular, we want to think about the effect cooperating and defecting have on the group of players. How does one player's choice affect everyone else? What happens to the group if there is a single cooperator or a single defector? What happens if everyone cooperates or everyone defects?
• 4.7: Repeated Prisoner's Dilemma
In this section, we look at two players playing Prisoner's Dilemma repeatedly. We call this game an iterated Prisoner's Dilemma. Before playing the iterated version, think about how you would play the above game if you only play it once with an opponent.
• 4.8: Popular Culture: Prisoner's Dilemma and Chicken
In this section, we will look at applications of Prisoner's Dilemma and Chicken in popular culture.

This page titled 4: Non-Zero-Sum Games is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Jennifer A. Firkins Nordstrom via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.