Key Concepts in Game Theory

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Why This Matters

Game theory isn't just abstract math—it's the analytical engine behind nearly every strategic business decision you'll encounter. Whether you're analyzing why competitors undercut prices, how to structure a negotiation, or why firms in an oligopoly behave the way they do, game theory provides the framework. You're being tested on your ability to identify equilibrium concepts, strategic interdependence, and the conditions that lead to cooperation versus competition.

The concepts here connect directly to market structure analysis, pricing strategy, and competitive dynamics. When you see a case about firms choosing output levels or bidders strategizing in an auction, you need to instantly recognize which game-theoretic model applies and what outcome it predicts. Don't just memorize definitions—know what strategic situation each concept explains and when to apply it.

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Equilibrium Concepts: Predicting Stable Outcomes

These concepts help you identify where strategic interactions "settle"—the outcomes that persist because no player wants to deviate unilaterally. Understanding equilibrium is essential for predicting market outcomes and competitor behavior.

Nash Equilibrium

• No player can improve by changing strategy alone—each player's choice is optimal given what others are doing
• Can exist in pure or mixed strategies—pure means specific actions, mixed means randomizing with probabilities
• Not always efficient—Nash outcomes can be suboptimal for everyone (see Prisoner's Dilemma), which is why regulation or coordination sometimes matters

Dominant Strategy

• Yields the highest payoff regardless of opponents' choices—simplifies analysis because you don't need to predict others' moves
• Not all games have one—when dominant strategies exist for all players, they converge to Nash Equilibrium automatically
• Key shortcut in problem-solving—always check for dominant strategies first before doing more complex equilibrium analysis

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Strategic Dilemmas: When Rationality Backfires

These situations reveal the tension between individual optimization and collective welfare. The core mechanism is that pursuing self-interest leads to outcomes worse than cooperation—a market failure that explains cartels, public goods problems, and regulatory interventions.

Prisoner's Dilemma

• Individual rationality leads to collective irrationality—both players defect even though mutual cooperation yields higher payoffs for both
• Dominant strategy is to defect—regardless of what the other player does, defecting always pays better individually
• Foundation for understanding cartels—explains why price-fixing agreements collapse without enforcement mechanisms

Coordination Games

• Players benefit from matching choices—unlike the Prisoner's Dilemma, interests are aligned but coordination is the challenge
• Multiple equilibria create uncertainty—without communication or signals, players may end up at inferior outcomes
• Critical for technology adoption and standards—explains network effects, platform competition, and why markets sometimes lock into inferior technologies

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Dynamic Strategy: Timing and Repetition

When games unfold over time—either through sequential moves or repeated interactions—strategy changes fundamentally. The ability to observe, react, and build reputation transforms the strategic landscape.

Sequential Games

• Order of moves matters—first-movers may gain advantage, or late-movers may benefit from observing and reacting
• Solved using backward induction—start from the final decision and work backward to determine optimal play at each stage
• Represented by game trees (extensive form)—essential for analyzing negotiations, market entry timing, and contract design

Repeated Games

• Future interactions change present incentives—the shadow of the future enables cooperation that wouldn't occur in one-shot games
• Reputation becomes strategic asset—players can punish defection and reward cooperation over time
• Tit-for-tat and similar strategies emerge—simple reciprocity rules often sustain cooperation in infinitely repeated games

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Strategy Under Uncertainty: Randomization

When predictability is a weakness, randomization becomes optimal. Mixed strategies prevent exploitation by keeping opponents unable to anticipate your moves.

Mixed Strategy

• Players randomize across actions with specific probabilities—not random guessing, but calculated probability distributions
• Necessary when no pure strategy Nash exists—ensures equilibrium in games like matching pennies or penalty kicks
• Probabilities are chosen to make opponents indifferent—you mix so that your opponent can't exploit any predictable pattern

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Market Applications: Competition and Negotiation

These concepts apply game theory directly to business contexts—how firms compete, how parties negotiate, and how auctions allocate resources. Mastering these models is essential for market structure analysis.

Oligopoly Models (Cournot and Bertrand)

• Cournot: firms compete on quantity—each firm chooses output level, market price emerges from total supply, Nash Equilibrium yields moderate prices and profits
• Bertrand: firms compete on price—with identical products, price competition drives profits to zero (Bertrand paradox)
• Model choice depends on industry characteristics—capacity-constrained industries fit Cournot; easily adjustable output fits Bertrand

Bargaining Theory

• Analyzes how surplus gets divided—outcomes depend on bargaining power, outside options (reservation prices), and information asymmetries
• Cooperative vs. non-cooperative approaches—Nash bargaining solution assumes efficient outcomes; strategic models allow for inefficiency and delay
• Information is power—the party with better information about valuations or alternatives typically captures more surplus

Auction Theory

• Format affects bidding behavior and revenue—English (ascending), Dutch (descending), and sealed-bid auctions produce different strategic incentives
• Winner's curse: winning may mean overpaying—especially in common-value auctions, the winner often has the most optimistic (possibly wrong) estimate
• Strategic underbidding is rational—sophisticated bidders shade bids below true valuations to avoid the winner's curse

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Quick Reference Table

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Self-Check Questions

1. A firm knows its best response regardless of competitor actions. Is this a Nash Equilibrium, a dominant strategy, or both? Explain the relationship between these concepts.

2. Two streaming platforms would both benefit from adopting the same video codec, but neither wants to switch first. Is this a Prisoner's Dilemma or a Coordination Game? What distinguishes them?

3. Compare Cournot and Bertrand competition: Why does the same market structure (oligopoly) produce such different profit outcomes depending on the competitive variable?

4. In a repeated game, how does the "shadow of the future" change strategic incentives compared to a one-shot game? Give a business example where this matters.

5. An FRQ describes a sealed-bid auction where bidders have similar estimates of an item's true value. What strategic concern should bidders have, and how should it affect their bids?