Dominant Strategy Examples

Why This Matters

In AP Microeconomics, game theory questions test whether you understand strategic decision-making—how rational actors choose when their outcomes depend on others' choices. You're not just being tested on definitions; you need to recognize when a dominant strategy exists, when it doesn't, and why following individual incentives sometimes leads to collectively terrible outcomes. These concepts connect directly to market failures, oligopoly behavior, public goods provision, and externalities.

The examples below demonstrate core principles you'll encounter on both multiple-choice and FRQ sections: the tension between Nash equilibrium and Pareto efficiency, why cooperation breaks down even among rational actors, and how payoff structures determine strategic behavior. Don't just memorize game names—know what concept each game illustrates and be ready to identify dominant strategies (or their absence) from a payoff matrix.

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Games Where Betrayal Is the Dominant Strategy

These games share a crucial feature: each player's best response is the same regardless of what the other player does. The result? Both players rationally choose strategies that leave everyone worse off than if they'd cooperated.

Prisoner's Dilemma

• Betrayal dominates for both players—confessing yields a better payoff whether your partner stays silent or also confesses
• Nash equilibrium is Pareto inefficient, meaning both players end up worse off than mutual cooperation would achieve
• Classic example of market failures—explains why firms in oligopolies struggle to maintain collusion without enforcement mechanisms

Traveler's Dilemma

• Undercutting is always rational—choosing a number one lower than your opponent guarantees a bonus, creating a race to the bottom
• Iterative reasoning leads to minimum claims, as each player anticipates the other's undercutting strategy
• Demonstrates how competition destroys surplus—both players receive far less than they would under simple cooperation

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Games Without Pure Dominant Strategies

Not every strategic situation has a clear "always do this" answer. These games require players to randomize their choices or adapt based on expectations about opponents—introducing the concept of mixed strategy equilibrium.

Matching Pennies

• No dominant strategy exists—choosing heads beats an opponent choosing heads, but loses to tails
• Mixed strategy equilibrium requires 50/50 randomization, making the opponent indifferent between choices
• Models zero-sum competition—one player's gain exactly equals the other's loss, like penalty kicks in soccer

Chicken Game

• Each player prefers to swerve if the other won't—but prefers to stay straight if the other swerves
• Multiple Nash equilibria exist, with outcomes depending on credible commitment and reputation
• Models brinksmanship situations—nuclear standoffs, labor negotiations, and firms competing for market dominance

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Games Where Coordination Beats Individual Optimization

These games show that dominant strategies don't always exist—and when they do, following them may not be optimal. Success depends on trust, communication, or social norms that align individual choices.

Stag Hunt

• Cooperation yields the highest payoff—hunting stag together dominates hunting hare, but only if both players coordinate
• Risk dominance vs. payoff dominance creates tension—hunting hare is safer but inferior
• Models network effects and technology adoption—everyone benefits from the same platform, but switching requires trust

Battle of the Sexes

• No dominant strategy for either player—each prefers their own activity but values coordination over going alone
• Two Nash equilibria exist, requiring negotiation or focal points to resolve
• Illustrates coordination problems in markets—standardization decisions, meeting locations, compatible technologies

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Games Revealing Social Preferences and Fairness

Standard game theory assumes players maximize material payoffs—but these games consistently show that real humans care about fairness, reciprocity, and social norms. They challenge the pure rationality assumption.

Ultimatum Game

• Rational proposers should offer the minimum—responders should accept any positive amount rather than get nothing
• Empirically, low offers get rejected, even though rejection is "irrational" in payoff terms
• Demonstrates fairness concerns override material incentives—critical for understanding wage negotiations and market behavior

Dictator Game

• Keeping everything is the dominant strategy—the recipient has no power to punish or reward
• Most dictators share anyway, revealing altruism, guilt, or social preference motivations
• Tests whether fairness requires strategic incentives—spoiler: it doesn't

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Games Modeling Resource Competition and Public Goods

These games explain why markets fail to provide public goods and how common resources get overexploited. The dominant strategy analysis reveals the logic behind free-riding and the tragedy of the commons.

Public Goods Game

• Free-riding is the dominant strategy—contributing costs you while benefits are shared equally
• Collective contributions maximize group welfare, but individual incentives undermine provision
• Directly models public goods problems—national defense, clean air, and public broadcasting all face this structure

Hawk-Dove Game

• No pure dominant strategy—being a hawk wins against doves but loses badly against other hawks
• Equilibrium depends on population composition, with mixed strategies emerging in evolutionary contexts
• Models common resource conflicts—territorial disputes, competitive advertising, and arms races

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Quick Reference Table

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Self-Check Questions

1. Which two games both have dominant strategies that lead to Pareto-inefficient outcomes, and what distinguishes their strategic structures?

2. If given a payoff matrix where Player A's best response is the same regardless of Player B's choice, what term describes Player A's strategy, and which classic game best illustrates this?

3. Compare and contrast the Ultimatum Game and Dictator Game: what does the difference in observed behavior tell us about the source of fairness in economic decisions?

4. An FRQ describes two firms deciding whether to advertise aggressively or maintain current spending, where aggressive advertising is costly but captures market share from passive competitors. Which game does this most closely resemble, and what outcome would you predict?

5. Why does the Stag Hunt have two Nash equilibria while the Prisoner's Dilemma has only one, and what does this difference imply about the role of trust in strategic situations?