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Session Length
~17 min
Adaptive Checks
15 questions
Transfer Probes
8
Game theory is the mathematical study of strategic interaction among rational decision-makers. It provides a formal framework for analyzing situations in which the outcome of one participant's choices depends on the choices made by others. Originally developed to address problems in economics, game theory has become an essential tool across disciplines including political science, biology, computer science, and philosophy, wherever agents with potentially conflicting interests must make interdependent decisions.
The field was formally established by mathematician John von Neumann and economist Oskar Morgenstern in their 1944 landmark work, Theory of Games and Economic Behavior. John Nash later revolutionized the discipline by introducing the concept of Nash Equilibrium, a state in which no player can benefit by unilaterally changing their strategy. Nash's work, along with contributions from John Harsanyi and Reinhard Selten on incomplete information and subgame perfection, earned them the 1994 Nobel Prize in Economics and cemented game theory as one of the most influential analytical frameworks of the twentieth century.
Today, game theory underpins auction design, international diplomacy, evolutionary biology, artificial intelligence, and mechanism design. It explains why firms engage in price wars, how species evolve cooperative behaviors, and why arms races escalate. From the Prisoner's Dilemma that illuminates the tension between individual and collective rationality to the sophisticated signaling games used to model market competition, game theory provides the conceptual vocabulary and mathematical rigor needed to reason about strategic behavior in virtually any domain.
One step at a time.
A set of strategies, one for each player, such that no player can improve their payoff by unilaterally changing their own strategy while the other players keep theirs unchanged. It represents a stable state of mutual best responses.
Example: In a duopoly where two firms set prices, a Nash Equilibrium occurs when neither firm can increase profit by changing its price alone, often resulting in both firms pricing at the competitive level.
A canonical two-player game illustrating why two rational individuals might not cooperate, even when cooperation would yield a better outcome for both. Each player has an incentive to defect regardless of the other's choice.
Example: Two competing firms could both benefit from keeping prices high, but each has an incentive to undercut the other. Both end up lowering prices, leaving both worse off than if they had cooperated.
A strategy that yields a higher payoff for a player regardless of what strategies the other players choose. When a player has a dominant strategy, rational play dictates that they should always choose it.
Example: In the classic Prisoner's Dilemma, defecting is a dominant strategy: no matter what the other player does, defecting always yields a better individual outcome.
A game in which one player's gain is exactly equal to the other player's loss, so the total payoff across all players always sums to zero. These are purely competitive situations with no opportunity for mutual benefit.
Example: Chess and poker are zero-sum games: for one player to win, the other must lose. In contrast, trade negotiations are typically not zero-sum because both sides can benefit.
A strategy in which a player randomizes over two or more pure strategies according to specific probabilities, rather than choosing a single deterministic action. Mixed strategy equilibria exist even when no pure strategy equilibrium does.
Example: A soccer penalty kicker randomizes between shooting left and right to keep the goalkeeper guessing, rather than always kicking in the same direction.
A refinement of Nash Equilibrium for sequential games requiring that the strategy profile constitutes a Nash Equilibrium in every subgame of the original game. It eliminates non-credible threats.
Example: In an entry deterrence game, an incumbent's threat to start a price war if a competitor enters is not credible if the price war would also harm the incumbent. Subgame perfection rules out this empty threat.
Often called 'reverse game theory,' mechanism design involves designing game rules and incentive structures so that self-interested players, acting strategically, produce a desired outcome. It is used to design auctions, voting systems, and markets.
Example: The Vickrey auction (second-price sealed-bid auction) is designed so that each bidder's dominant strategy is to bid their true valuation, solving the problem of strategic underbidding.
A game in which players have incomplete information about other players' characteristics (types), such as their payoffs, strategies, or beliefs. Players form probabilistic beliefs about unknown information and maximize expected utility.
Example: In a sealed-bid auction, each bidder knows their own valuation but not the valuations of others, so they must form beliefs about competing bids when deciding how much to offer.
More terms are available in the glossary.
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