Game Theory

Core concepts in this department

• Nash Equilibrium

  A Nash equilibrium is a strategy profile in which no player can improve their payoff by unilaterally changing strategy, given what everyone else is doing. Nash (1950) proved every finite game has at least one, possibly in mixed strategies. In pricing and platform competition it predicts where rivalry settles absent coordination, not where firms would like it to settle.

• Dominant Strategy

  A dominant strategy yields at least as high a payoff as every alternative regardless of what other players do. When each player has one, the outcome is a dominant-strategy equilibrium, the most robust prediction in game theory because it requires no beliefs about rivals. Second-price auctions are prized precisely because truthful bidding is dominant.

• Prisoner's Dilemma

  The prisoner's dilemma is a two-player game in which defection is each player's dominant strategy, yet mutual defection leaves both worse off than mutual cooperation. Devised at RAND in 1950 by Flood and Dresher and named by Albert Tucker, it is the canonical model of price wars, promotional escalation, and any arms race where individual rationality produces collective loss.

• Folk Theorem (Repeated Games)

  The folk theorem states that in an infinitely repeated game with sufficiently patient players, any feasible payoff profile giving each player at least their minmax value can be sustained as an equilibrium through credible punishment strategies. It is why tacit price discipline and promotional truces persist without any agreement, and why they collapse when discount rates rise.

• Costly Signaling

  Costly signaling is the transmission of private information through an action that is cheaper for a high-quality sender than for a low-quality one, so that imitation does not pay. Spence (1973) formalized it for education; Nelson (1974) and Milgrom and Roberts (1986) applied it to advertising, where visible spend tells buyers a firm expects the repeat purchases only a good product earns.

• Mechanism Design

  Mechanism design is game theory run in reverse: instead of predicting behaviour inside a given set of rules, it designs the rules so that self-interested participants produce the outcome the designer wants. Hurwicz, Maskin, and Myerson shared the 2007 Nobel for the field. Auctions, reputation systems, and matching markets are its applied surface in digital products.

• Incentive Compatibility

  A mechanism is incentive compatible when each participant's best response is to reveal their private information truthfully. The revelation principle (Myerson 1979) shows any equilibrium outcome of any mechanism can be reproduced by a direct, truthful one, which is why marketplace design can restrict attention to rules under which honesty is the dominant or the Bayesian best strategy.

• Vickrey Auction

  A Vickrey auction is a sealed-bid auction in which the highest bidder wins but pays the second-highest bid, which makes bidding one's true value a dominant strategy. Vickrey (1961) introduced it; the generalized second-price auction that ran search advertising for roughly two decades is its multi-slot descendant, although not truthful in the same way.

• Commitment Device

  A commitment device is an action that deliberately removes a player's own future options in order to make a threat or a promise credible. Schelling (1960) showed that limiting oneself can strengthen a bargaining position: capacity investments, price-match guarantees, most-favoured-customer clauses, and public launch dates all work by making retreat expensive enough that rivals believe it will not happen.

• Focal Point (Schelling Point)

  A focal point, or Schelling point, is the equilibrium players converge on in a coordination game without communicating, because something about it stands out: salience, precedent, or convention. Schelling (1960) documented the effect experimentally; in markets it explains why standards wars, default settings, and round-number prices resolve the way they do rather than the way the theory alone would predict.

• Bayesian Persuasion

  Bayesian persuasion is the design of an information structure by a sender who commits to a signal before observing the state, in order to move a rational receiver's actions. Kamenica and Gentzkow (2011) characterized the optimum through concavification of the sender's value function. It formalizes when partial disclosure of reviews, ratings, or prices beats full transparency.

• Principal-Agent Problem

  The principal-agent problem arises when one party delegates work to another whose actions are imperfectly observable and whose interests differ. Jensen and Meckling (1976) and Holmström (1979) formalized the resulting trade-off between risk sharing and incentives; sales compensation, agency fee structures, and attribution disputes are its everyday forms inside a growth organization.

• Nash Bargaining Solution

  The Nash bargaining solution is the division of surplus that maximizes the product of the two parties' gains over their outside options. Nash (1950) derived it from four axioms; Rubinstein (1982) showed alternating-offer bargaining converges to it as offers become frequent. Its lesson for negotiators: payoff is set by outside options and relative patience, not by splitting the difference.

• Evolutionarily Stable Strategy

  An evolutionarily stable strategy is one that, once adopted by a population, cannot be invaded by any rare alternative. Maynard Smith and Price (1973) introduced it to explain restraint in animal conflict; applied to markets it explains why competitors converge on identical positioning and why a deviant strategy pays only if it reaches critical mass before it is copied.