Questions: Game Theory Basics

Question 1

In the Prisoner's Dilemma, both players have defect as a dominant strategy. What happens when both players follow their dominant strategies?

• A. Both players achieve the best possible joint outcome
• B. Both players get their individually best possible payoff
• C. One player benefits at the other's expense
• D. Both players end up worse off than if they had both cooperated

Answer: (D)

This is the defining tragedy of the Prisoner's Dilemma: mutual defection (the dominant strategy outcome) is worse for both players than mutual cooperation would have been. It is not the worst absolute outcome (being the sole cooperator is worse), but it is worse than the cooperative outcome — illustrating how individually rational choices can be collectively self-defeating.

Question 2

If both players in a game act rationally and choose their dominant strategies, they are expected to reach the best possible collective outcome.

• T. True
• F. False

Answer: False

The Prisoner's Dilemma is a direct counterexample. Both players rationally choose to defect (their dominant strategy), yet the result is mutual defection — worse for both than mutual cooperation. Rational individual play can produce collective irrationality. This is one of the central insights of game theory and the foundation for understanding market failures, public goods problems, and arms races.

Question 3

Why is a 'dominant strategy' stronger than merely 'the best response to a specific opponent action'?

Model answer: A dominant strategy is optimal regardless of what the opponent does — it beats or ties every other strategy no matter the opponent's choice. A best response depends on the opponent's action and may differ across scenarios.

The key word is 'regardless.' A strategy that is best only when the opponent plays X is a conditional best response, not a dominant strategy. A dominant strategy must outperform (or at least match) every other strategy for every possible opponent action, making it robust to uncertainty. When one exists, rational players choose it without needing to predict the opponent at all.