Module 2 / Lesson 5.2
Strategic Interactions, Prisoner's Dilemma and Game Theory
Lesson guide
Learning: Learn the material presented below and watch the video below. In the last lesson (6.1) on Public Goods, we learned about why free-riding and externalities might lead to undesirable outcomes for society when individuals do what is best for themselves. In this lesson, we will learn about another setting: strategic interactions, where we may get to undesirable outcomes for society when individuals do what is best for themselves.
Thinking Tasks: While completing the learning tasks for this lesson, think about the followig:
- Game Theory and its application to strategic decision-making.
- Understand and diagram the Prisoner's Dilemma payoff matrix.
- Difference between a Dominant Strategy, Nash Equilibrium, and Pareto Optimum.
- Why rational self-interest often leads to collectively poor outcomes.
- The "Prisoner's Dilemma" is the classic example for this.
- It explains dilemmas in arms races, pollution, business competition, and technology development.
1. What is Game Theory?
Game theory is a branch of applied mathematics that provides tools for analyzing situations in which parties, called players, make decisions that are interdependent. This interdependence causes each player to consider the other player’s possible decisions, or strategies, in formulating strategy.
Cite: Britannica, Game TheoryExample: The Schelling Point (Coordinated Game)
Let's imagine you and your friend want to meet up in Manhattan at noon but have lost communication. You could meet at the top of the Empire State Building or Grand Central Station main hall.
Your action depends entirely on what you think your friend will do, and vice versa. It would be optimal if you could coordinate on both going to the same place. This is called a Focal Point or Schelling Point, a solution that people will tend to choose by default in the absence of communication, because it seems natural, special, or relevant to them.
However, not all games have aligned incentives, as we will see next.
2. Prisoner's Dilemma
The Prisoner's Dilemma (PD) is the most famous example of a non-cooperative game. In a PD game:
- The game involves two players who are arrested, held separately, accused of committing a crime together, and then asked by the police to betray the other player by testifying against them.
- Two players must each choose cooperate (don't testify, don't betray your partner) or defect (testify, betray your partner) without knowing what the other will do.
- Payoffs are structured so that defecting is always the better individual choice (the Dominant Strategy).
- This creates a classic social dilemma: rational choices don't lead to the best collective outcome. It would be better for both people if both cooperate instead of both defect, but each player defects because they benefit from defection at the expense of the other person.
Payoff Matrix Example (Years in Prison)
The numbers represent the sentence length (negative values are bad outcomes):
| Partner Cooperates (Don't Testify) | Partner Defects (Testify) | |
|---|---|---|
| You Cooperate (Don't Testify) | Both get -1 Year (Best Joint Outcome) |
You: -8 Years Partner: 0 Years |
| You Defect (Testify) | You: 0 Years Partner: -8 Years |
Both get -3 Years (Nash Equilibrium) |
3. Key Game Theory Concepts
The best choice for a player, no matter what the other player does. In the Prisoner's Dilemma, Defecting is the Dominant Strategy.
An outcome where each player picks the best reply to the other’s strategy. The "Both Defect" outcome is the Nash Equilibrium, neither player can do better by switching their strategy alone.
An outcome where no player can be made better off without making the other player worse off. The "Both Cooperate" outcome is Pareto optimal (but NOT the Nash equilibrium), but rarely chosen due to self-interest.
Why Don’t Players Cooperate?
There is no guarantee the other player won't defect for a better individual payoff.
In a one-shot game, there is no punishment mechanism for the defector.
Rational self-interest dictates taking the short-term personal gain (defecting).
It might be optimal for each individual to move forward with actions for which it would be better if all of us held back. The pursuit of individual rationality often leads to collective harm.