What Is Game Theory? Principles and Applications in Economics

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Game theory is the study of strategic decision-making: how rational decision-makers choose actions when the outcome for each of them depends on what the others choose. It turns a situation such as two firms setting prices, a buyer and seller negotiating, or bidders competing in an auction into a formal model with players, available strategies and payoffs. It then asks which combinations of choices are stable and why. In economics, game theory is the standard tool for analyzing markets with a few interdependent competitors, bargaining, auctions and any setting where “what should I do?” depends on “what will they do?”

Key takeaways

• Game theory models interactions in which each participant’s payoff depends on the choices of all participants, not on their own choice alone.
• A game is defined by its players, the strategies available to them, the information they have and the payoffs attached to each outcome.
• The Nash equilibrium is the central solution concept: a set of strategies in which no player can do better by changing only their own strategy.
• Games are classified as cooperative or non-cooperative, zero-sum or non-zero-sum, simultaneous or sequential, and one-shot or repeated. Each classification changes the predicted outcome.
• Economists use game theory to explain oligopoly pricing, collusion, entry deterrence, auctions and negotiation. Its main weakness is its reliance on assumptions about rationality and information that real people often violate.

What Is Game Theory?

A “game” here is not a pastime but any situation with two or more decision-makers whose results are linked. Chess fits, but so do an airline price war, a wage negotiation, a merger decision and a sealed-bid auction for drilling rights.

What separates game theory from ordinary decision analysis is interdependence. A farmer deciding how much fertilizer to buy faces uncertainty about weather, but the weather does not respond to the farmer’s choice. A gas station deciding whether to cut its price faces a rival who is making the same calculation and who will react. Game theory is built for that second kind of problem, where each side must reason about the reasoning of others.

The framework is used across economics, business, political science, military strategy, evolutionary biology and computer science. In economics, it is a core part of microeconomics, especially the study of imperfect competition.

The Building Blocks of a Game

• Players: The decision-makers: individuals, firms, governments or even genes in evolutionary models.
• Actions: The individual moves available at a given point, such as “raise price” or “hold price.”
• Strategy: A complete plan specifying what a player will do in every situation that could arise, including situations that never occur. In a one-move game, a strategy and an action are the same thing.
• Payoff: The value a player receives from an outcome, measured in dollars, profit, market share, years in prison or utility. What matters is that players can rank outcomes.
• Information set: What a player knows when it is their turn to move, which matters most in sequential games where earlier moves may be hidden.
• Equilibrium: A combination of strategies that is stable under a stated solution concept, typically meaning no player has a reason to change course given what the others are doing.

Standard models assume players are rational (they pursue the highest payoff available) and that the rules and payoffs are common knowledge: each player knows them, knows that the others know them, and so on. Much of the field’s progress since the 1950s has come from relaxing these assumptions to allow private information, limited reasoning or learning over time.

How Game Theory Works

Representing a Game

The normal form (or strategic form) is a table, often called a payoff matrix. Each row is a strategy for one player, each column is a strategy for the other, and each cell shows the payoffs for both. The normal form suits simultaneous games, where players choose without seeing each other’s choice.

The extensive form is a game tree. It starts at a single decision point, branches for each available action, and continues through each later decision until it reaches the payoffs at the end. The extensive form shows the order of moves and what each player knows at each point, which makes it the natural choice for sequential games such as negotiations or market entry.

Interpreting a Game: A Worked Example

Consider a hypothetical example. Two airlines, A and B, fly the same route and must each choose a High or Low fare for the coming season. The numbers are invented quarterly profits in millions of dollars, with A’s payoff listed first.

Airline A reasons through B’s two possible choices:

1. If B charges High, A earns 10 with a High fare and 14 with a Low fare. Low is better.
2. If B charges Low, A earns 4 with a High fare and 6 with a Low fare. Low is still better.

Whatever B does, a Low fare pays A more, so Low is a dominant strategy for A. The payoffs are symmetric, so the same holds for B: both charge Low and each earns 6. Many games have no dominant strategy, and players must then reason about what others are likely to do. The opposite, a dominated strategy, is always beaten by another; rational players can eliminate such strategies, which often simplifies a game.

This is the central tension of many economic games. Both airlines would be better off at High/High (10 each), but each gains by undercutting the other, so the stable outcome, Low/Low, is worse for both firms (and better for passengers). The structure is a version of the prisoner’s dilemma.

The Nash Equilibrium

A Nash equilibrium is a combination of strategies, one per player, in which each strategy is a best response to the others: no player can increase their payoff by changing only their own strategy. It is a “no regrets” outcome: given what everyone else did, nobody wishes they had acted differently.

In the airline example, Low/Low is the Nash equilibrium. If A switched alone to High, its profit would fall from 6 to 4. The same is true for B. High/High is not an equilibrium because either airline could raise its profit from 10 to 14 by switching alone.

The concept is named after mathematician John Nash, who showed in work published in 1950 and 1951 that every game with a finite number of players and strategies has at least one equilibrium of this kind, provided players are allowed to randomize. Nash shared the 1994 Nobel Memorial Prize in Economic Sciences with John Harsanyi and Reinhard Selten for their contributions to non-cooperative game theory.

Three properties of the Nash equilibrium are easy to misread.

It is stable, not necessarily good. Low/Low is an equilibrium even though both firms prefer High/High. Equilibrium describes where self-interested choices settle, not what is best for the group.

A game can have more than one, and the theory alone may not say which one players will reach.

It may require randomizing. Some games have no equilibrium in which players pick a single action with certainty, so the equilibrium involves mixed strategies.

Games With Multiple Equilibria

Coordination games have several stable outcomes. Suppose two companies must each choose a technical standard for a new device. If both choose the same standard, their products are compatible and both profit. If they choose different standards, both lose. “Both choose Standard 1” and “both choose Standard 2” are each Nash equilibria, and neither firm wants to deviate once the other has committed.

In a variant called the Battle of the Sexes, or Bach or Stravinsky, two people want to spend the evening together but prefer different concerts, so there are two equilibria, each favoring a different player. Which one is reached can depend on conventions, history, who moves first or communication beforehand, which is why economists study focal points and commitments.

The Hawk-Dove game (also called Chicken) models conflict over a resource. If both players act aggressively (Hawk), both suffer the worst outcome, so the pure-strategy equilibria have one Hawk and one Dove: the game is about who yields. It is used to analyze price wars, labor disputes and diplomatic brinkmanship.

Mixed-Strategy Equilibrium: A Worked Calculation

When predictability is a weakness, players randomize. A mixed strategy assigns a probability to each action. The key insight for finding a mixed-strategy equilibrium is that each player randomizes in a way that makes the other player indifferent between their options; otherwise the other player would exploit the imbalance.

Take a hypothetical penalty kick in soccer. The kicker aims Left or Right; the goalkeeper dives Left or Right at the same moment. The table shows assumed probabilities that the kick scores:

Let p be the probability the keeper dives Left. The kicker is indifferent when both kicks have the same expected scoring rate:

• Kick Left: 0.60p + 0.95(1 − p) = 0.95 − 0.35p
• Kick Right: 0.90p + 0.70(1 − p) = 0.70 + 0.20p

Setting them equal gives 0.25 = 0.55p, so p ≈ 0.45. The keeper dives Left about 45% of the time.

Let q be the probability the kicker aims Left. The keeper is indifferent when both dives allow the same scoring rate:

• Dive Left: 0.60q + 0.90(1 − q) = 0.90 − 0.30q
• Dive Right: 0.95q + 0.70(1 − q) = 0.70 + 0.25q

Setting them equal gives 0.20 = 0.55q, so q ≈ 0.36. The kicker aims Left about 36% of the time and Right about 64%. At these probabilities, the kick scores about 79% of the time whatever either player does. Any predictable pattern, such as always aiming at the kicker’s stronger side, would let the keeper lower that rate.

The same logic applies to tax audits, security inspections and a baseball pitcher varying pitches.

Types of Games

Cooperative vs. Non-Cooperative Games

Non-cooperative game theory studies players who act independently to pursue their own goals and cannot make binding agreements. Any cooperation must be self-enforcing. Most applications in economics, including oligopoly, auctions and the Nash equilibrium itself, belong here. Rock-paper-scissors is a simple non-cooperative game.

Cooperative game theory assumes players can form coalitions and make enforceable agreements, and asks which coalitions will form and how the joint payoff is divided. Solution concepts include the core (allocations no subgroup could improve on by breaking away) and the Shapley value (developed by Lloyd Shapley in 1953), which pays each player their average contribution to every possible coalition. Uses include cost-sharing among utilities, voting power analysis and dividing joint-venture profits.

The labels can mislead: a non-cooperative game can produce cooperation, as in repeated games. The distinction is whether agreements are binding, not how friendly the players are.

Zero-Sum vs. Non-Zero-Sum Games

In a zero-sum game, one player’s gain is exactly another’s loss, so the total payoff is fixed. Chess, poker among players (before the house’s cut) and most sports matches are zero-sum: one side’s win is the other’s defeat. Pure conflict games like these were the first to be solved mathematically, through John von Neumann’s minimax theorem.

In a non-zero-sum game, the total payoff changes with the players’ choices, so both sides can gain or both can lose, as in trade, partnerships and most negotiations. When all parties can come out ahead, the game is positive-sum or “win-win.” The airline example is non-zero-sum: total profit is 20 at High/High and 12 at Low/Low.

Financial markets are a common source of confusion. A futures or options contract is zero-sum between the two counterparties before costs, and fees make it slightly negative-sum for traders collectively. Owning stocks can be positive-sum, because company earnings and dividends can raise the value of all shares at once. Even a single trade can benefit both parties, such as a retiree selling shares for income and a younger investor buying for growth.

Simultaneous vs. Sequential Games

In simultaneous games, no player observes the others’ moves before deciding, even if they do not move at the same instant. Firms drawing up annual pricing plans at the same time are an example, modeled with normal-form tables.

In sequential games, players move in turn and later players see earlier moves, as in negotiations where one side offers and the other responds. They are solved by backward induction: determine what the last mover will do, then work back to the first move.

In a hypothetical market-entry game, a potential entrant decides whether to Enter a market or Stay Out. If it enters, the incumbent chooses to Fight (start a price war) or Accommodate (share the market).

• Enter, then Fight: entrant −3, incumbent 5
• Enter, then Accommodate: entrant 5, incumbent 10
• Stay Out: entrant 0, incumbent 20

Working backward: after entry, the incumbent earns 10 by accommodating and 5 by fighting, so it accommodates. Anticipating that, the entrant compares 5 (enter) with 0 (stay out) and enters. A threat to fight any entrant is not credible, because carrying it out costs the incumbent money. An outcome that survives this test at every stage is called a subgame perfect equilibrium, a refinement developed by Reinhard Selten. “Stay Out, and Fight if entry occurs” is also a Nash equilibrium, but it rests on a threat the incumbent would not carry out, which is why the refinement matters.

The example also shows what would make the threat credible: a commitment that changes the incumbent’s payoffs, such as investing in excess production capacity in advance so that fighting becomes cheaper than accommodating.

One-Shot vs. Repeated Games

A one-shot game is played once, so there is no future in which to reward or punish behavior and little reason to cooperate.

A repeated game is played many times by the same players, each of whom can see what happened before. Repetition can change the outcome substantially. In the airline game played once, both firms charge Low. Played indefinitely, with no known final round and with firms that value future profits enough, both can sustain High fares by following a rule such as “charge High as long as the rival does; if the rival ever undercuts, charge Low from then on.” Undercutting gains 4 in one period but forfeits 4 in every later period, so it no longer pays.

This logic, formalized in the folk theorems, explains how tacit cooperation can emerge among rivals without any agreement, and why it can unravel from the end if the game has a known final round. In the United States, explicit price-fixing agreements are illegal under the Sherman Act, so competition authorities watch markets where repeated interaction makes coordination easier.

Information: Perfect, Imperfect, Complete and Incomplete

• Perfect vs. imperfect information: With perfect information, every player sees all previous moves when it is their turn, as in chess. With imperfect information, some moves are hidden, as in poker or any simultaneous game.
• Complete vs. incomplete information: With complete information, every player knows everyone’s payoffs. With incomplete information, some players hold private information about their costs, valuations or type. John Harsanyi showed how to analyze these as Bayesian games, in which players hold and update beliefs about each other. Auctions, insurance, used-car sales and job-market signaling are examples.

Classic Games and What They Teach

The Prisoner’s Dilemma

In the best-known game in the field, two suspects are questioned in separate rooms with no way to communicate, and prosecutors, lacking evidence for a full conviction, offer each a deal. In a common version:

1. If both confess, each serves 3 years.
2. If one confesses and the other stays silent, the confessor serves 1 year and the silent one serves 5.
3. If both stay silent, each serves 2 years.

Confessing is a dominant strategy: it cuts your sentence from 2 years to 1 if the other stays silent, and from 5 years to 3 if the other confesses. Both confess and serve 3 years, even though mutual silence would give each 2.

The structure was framed by Merrill Flood and Melvin Dresher at the RAND Corporation in 1950 and named by Albert Tucker. It describes price wars, advertising arms races (where rival firms’ heavy spending largely cancels out), overfishing of shared waters and arms races between countries.

In the repeated version, Anatol Rapoport’s tit for tat cooperates on the first round and then copies the opponent’s previous move, rewarding cooperation and retaliating against defection. It won Robert Axelrod’s computer tournaments around 1980, but it is not optimal in every setting: its performance depends on the strategies it faces and on whether moves can be misread.

The Dictator Game and the Ultimatum Game

In the dictator game, Player A receives a sum of money and decides how much, if any, to give Player B, who has no say. A purely self-interested player would keep everything, yet in experiments many participants give some away, making the game a standard tool for studying fairness, altruism and charitable giving.

The ultimatum game adds a veto: if B rejects A’s proposed split, both get nothing. Backward induction says B should accept any positive amount, so A should offer the smallest possible sum. Experiments repeatedly find low offers rejected: people give up money to punish what they see as unfair treatment, a result central to behavioral economics.

The Volunteer’s Dilemma

In a volunteer’s dilemma, one person must bear a cost for the group to benefit, and the worst outcome arises if no one does. Junior accountants who discover fraud take a personal risk by reporting it, but if no one reports it, the fraud may bankrupt the company and cost everyone their jobs. The game helps explain why larger groups sometimes respond more slowly: each member can more easily assume someone else will act.

The Centipede Game

In the centipede game, two players take turns either taking the larger share of a growing pot or passing it; if you pass and your opponent takes on the next turn, you get less than if you had taken. The number of rounds is fixed and known. Backward induction says the last mover takes, so the previous mover takes earlier, and the reasoning unwinds until the first player should take immediately, when the pot is smallest. In experiments, people typically pass for several rounds and earn more than the theory predicts, a standard illustration of the gap between strict rationality and actual behavior.

The Stag Hunt

In the stag hunt, two hunters can cooperate to catch a stag, which requires both, or each can hunt a smaller but guaranteed hare alone. “Both hunt stag” and “both hunt hare” are both equilibria. Unlike the prisoner’s dilemma, where defecting always pays, this is a trust problem: cooperating pays as long as the other side does too. Investment projects that succeed only if several firms commit fit this structure.

Types of Game Theory Strategies

Maximax Strategy

A maximax strategy picks the option with the best possible outcome, ignoring how bad the alternatives could be. A startup staking its entire capital on one product launch, which could multiply its value or leave it insolvent, is playing maximax. The rule suits players who can absorb the downside.

Maximin Strategy

A maximin strategy picks the option whose worst outcome is the least bad, giving up upside for protection against disaster. A company that settles a lawsuit out of court accepts a certain loss to avoid a larger judgment at trial. In zero-sum games, von Neumann’s minimax theorem shows that maximin play by both sides leads to a stable outcome.

Game Theory in Economics and Business

Economics

The model of perfect competition assumes so many firms that none affects the price, and the monopoly model assumes a single seller with no rival. Most real industries sit in between, where each firm’s best decision depends on its rivals. Game theory gave economics the tools to analyze how that strategic interaction shapes prices, output and market structure.

Its main economic applications include:

• Oligopoly: Markets with a few large sellers, such as airlines, wireless carriers or soft drinks. The Cournot model (from Cournot’s 1838 duopoly analysis) has firms choose quantities; the Bertrand model has them choose prices. Their very different predictions show how much the choice of strategic variable matters.
• Collusion and cartels: The prisoner’s dilemma explains why cartel members cheat on agreed output limits; repeated-game analysis explains when coordination can still persist.
• Auctions: Auction theory studies bidding under different formats (English, Dutch, sealed-bid first-price, second-price) and how sellers should design them. Governments use it to sell wireless spectrum licenses, and Paul Milgrom and Robert Wilson received the 2020 Nobel Memorial Prize for improvements to auction theory and new formats.
• Market design and matching: Matching theory, recognized by the 2012 prize to Lloyd Shapley and Alvin Roth, assigns medical residents to hospitals, students to schools and kidney donors to patients.
• Monetary and trade policy: Central bank commitments work only if the public believes them, and tariff retaliation is a repeated game between governments.
• Information economics: Signaling and screening models explain why education can act as a signal to employers, why warranties signal quality and how insurers sort low-risk from high-risk customers.

Business and Marketing

In business, game theory means mapping what competitors can do, estimating what each outcome is worth to them and predicting their response before committing. Typical uses include:

• Pricing: A price cut that rivals match immediately may simply lower every firm’s profit.
• Product launches and capacity: Expanding capacity or launching a product can deter rivals or provoke a race.
• Entry deterrence: Threats deter only when credible, which is why firms make commitments that are costly to reverse.
• Negotiation: Bargaining models highlight each side’s alternative if talks fail (the BATNA, best alternative to a negotiated agreement) and the value of patience and commitment.

Many business decisions unfold like a game tree, with a series of choices whose final payoff is unknown until all moves are made. Every strategic option also carries an opportunity cost: the payoff of the best alternative strategy given up.

Finance

In finance, game-theoretic reasoning appears in Treasury auctions, in takeover battles between bidders and target boards, in bank runs (a coordination game with two equilibria, since depositors withdraw if they expect others to) and in market microstructure models of how informed and uninformed traders interact. Game theory explains incentives and strategic behavior; statistics measures what actually happened in the data.

Limitations of Game Theory

Rationality. Standard models assume players consistently maximize their payoffs. Real people make mistakes, rely on rules of thumb, act on emotion and sometimes cooperate when strict self-interest says they should not, as the ultimatum and centipede experiments show. Behavioral game theory tries to address this by building limited reasoning and social preferences into the models.

Information and values. Many models assume players know the rules, the payoffs and each other’s options, but firms rarely know rivals’ costs or intentions precisely. Loyalty, reputation and spite can be included as payoffs, but choosing how much weight to give them is a judgment, not a calculation.

Multiple equilibria. When a game has several stable outcomes, the theory may say what is possible without saying what will happen; the result can depend on social context, history and who the players are.

Model sensitivity. Small changes in assumptions, such as whether moves are sequential or simultaneous, or whether the game ends at a known date, can reverse a prediction. Results that hold in a tidy two-player model may not carry over to a market with many players, uncertain payoffs and changing rules.

For these reasons, game theory is best used to structure thinking about incentives and responses rather than to forecast precise outcomes.

Game Theory vs. Related Concepts

Several terms are often confused with game theory or with each other.

Game theory vs. decision theory. Decision theory covers a single decision-maker facing uncertainty from nature, such as weather or random events. Game theory covers several decision-makers who respond to each other. The maximin and maximax rules come from decision theory and are applied within games.

Game theory vs. probability or gambling theory. Probability theory calculates the odds of random events. Game theory deals with opponents who choose deliberately. Roulette is a probability problem; poker is a game-theory problem because opponents bluff and adapt.

Nash equilibrium vs. Pareto efficiency. An outcome is Pareto efficient if no one can be made better off without making someone worse off. A Nash equilibrium can be Pareto inefficient, as in the prisoner’s dilemma, where mutual confession is the equilibrium but mutual silence leaves both better off.

Dominant strategy vs. Nash equilibrium. Every combination of dominant strategies is a Nash equilibrium, but many Nash equilibria involve no dominant strategies. In coordination games, each player’s best choice depends entirely on what the other does.

Game theory vs. “game theory optimal” (GTO). In poker, GTO play is an equilibrium strategy no opponent strategy can exploit. It is an application of mixed-strategy equilibrium, not a separate theory, and the best response against a weak opponent may differ from it.

A Brief History of Game Theory

• 1838: Antoine Augustin Cournot’s duopoly analysis anticipated what would later be recognized as a Nash equilibrium.
• 1913: Ernst Zermelo showed that a finite game of perfect information, such as chess, can be analyzed by working backward.
• 1920s: Émile Borel wrote on strategic games, and in 1928 John von Neumann proved the minimax theorem for two-person zero-sum games.
• 1944: Von Neumann and economist Oskar Morgenstern published Theory of Games and Economic Behavior, generally regarded as the founding work of the field and its link to economics.
• 1950s and 1960s: Nash’s equilibrium and the RAND prisoner’s dilemma were followed by the Shapley value (1953), Selten’s subgame perfection and Harsanyi’s theory of incomplete information.
• 1994 onward: Nobel Memorial Prizes went to Nash, Harsanyi and Selten (1994); Robert Aumann and Thomas Schelling (2005); Shapley and Roth (2012); and Milgrom and Wilson (2020).

FAQs

The Bottom Line

Game theory matters to economists, business strategists and investors who face rivals, bargaining partners or bidders whose choices shape their results. Its models show why stable outcomes can leave everyone worse off and why only credible commitments deter. Because real people break its assumptions about rationality and information, it works best as a way to structure thinking about incentives and responses, not as a tool for forecasting precise outcomes.