Game Theory in Psychology

Game theory is a theoretical framework that is used for the optimal decision-making of players in a strategic setting. A key characteristic of game theory is that a player’s payoff is dependent on the strategy of other players.

Game theory applies to any situation with two or more players where the payoffs or consequences can be quantified. It helps predict the most likely outcome, because each player’s result depends on what the others choose. Every choice affects everyone else.

John von Neumann, a mathematician and physicist, founded the field with the economist Oskar Morgenstern.

Their 1944 book, Theory of Games and Economic Behavior, set out the formal framework. Its core claim was simple. Any economic situation could be defined as a game between two or more players (von Neumann & Morgenstern, 1944).

A white chess king standing beside a fallen black king on a chessboard, representing strategic competition
Game theory assumes that the players within a game are rational and will strive to maximize their payoffs in the game. As well as economics, game theory has a wide range of applications, including in psychology, evolution, war, politics, and business.

Key Takeaways

  • Strategic Interdependence: A player’s payoff depends on what the other players choose, so the best move depends on the moves they are expected to make.
  • Nash Equilibrium: A set of choices where no player can gain by changing strategy alone. It can leave everyone worse off than cooperation would.
  • Prisoner’s Dilemma: Each prisoner does best by confessing whatever the other does, so both confess and both do worse than if both had stayed silent.
  • Game Types: Games can be cooperative or non-cooperative, zero-sum or non-zero-sum, and simultaneous or sequential.
  • Repeated Play: When players meet again and again, cooperation can pay. Tit-for-tat, which copies the opponent’s last move, won Axelrod’s tournaments.
  • Real Behavior: People often depart from pure self-interest. They reject unfair offers and pay to punish free-riders, so fairness and reciprocity shape strategic choices.

What are the components of a game?

The components that are necessary to a game, according to game theory, are:

Players

A player is a strategic decision-maker within the game. Players can be individuals, firms, or even competing organisms.

A game needs at least two players, and they must be able to interact in some way. A lone decision-maker facing only nature is making an individual choice, so game theory would not apply.

In the Prisoner’s Dilemma, the players are the two prisoners.

Strategy

Strategies are the complete plans of action available to each player. A strategy specifies what a player will do in every circumstance that might arise in the game.

A strategy is chosen in light of personal self-interest and what the other players are expected to do. Each prisoner’s strategy is simple: confess or stay silent.

Payoffs

Payoffs are the quantifiable outcomes that each combination of strategies produces, such as money, years in prison, or evolutionary fitness.

What defines a game is that a player’s payoff depends on their own strategy and on everyone else’s. In the Prisoner’s Dilemma, the payoffs are prison sentences. In the Ultimatum Game, they are shares of money.

Every other element of the game, from strategy to equilibrium, is judged by the payoffs it produces.

Other elements of a game

In a game, players share ‘common’ knowledge of the rules, the strategies available, and the possible payoffs. Sequential games also have an ‘information set’: what a player knows at each decision point.

Classical game theory assumes players are rational and act in their own self-interest. Real people often break this assumption.

A game reaches equilibrium when every player has made a decision and an outcome is fixed.

Game Theory Examples: Classic Games

The Prisoner’s Dilemma

In 1950, RAND Corporation mathematicians Merrill Flood and Melvin Dresher ran an informal experiment in which two colleagues played a repeated game. The colleagues cooperated far more than equilibrium predicted (Flood, 1958). Albert Tucker later added the prisoner story that gave the game its name.

The game is one of the best-known examples of game theory. There are many variations, but one scenario runs as follows:

  • There are two criminals who are caught red-handed for committing a crime together.

  • They are taken to the police station and are placed in separate interrogation rooms for questioning, so neither can communicate with one another.

  • The prisoners are told that if they both confess to the crime, then they will each receive a 5-year jail sentence. If neither confesses, they will each serve a 2-year sentence.

  • However, if one prisoner confesses but the other does not, the prisoner who confesses goes free, whereas the one who does not confess serves nine years.

Your choiceOther prisoner stays silentOther prisoner confesses
You stay silent2 years eachYou: 9 years; other: free
You confessYou: free; other: 9 years5 years each
Prison sentences in the Prisoner’s Dilemma. Confessing is the better choice in both columns.

The dilemma is that each prisoner’s payoff depends on the other’s behavior. If they could confer, they might agree to stay silent and serve only two years each.

But they cannot confer. Confessing is the dominant strategy, because it gives a better result whatever the other prisoner does.

If the other stays silent, confessing means going free instead of serving two years. If the other confesses, it means five years instead of nine.

So both prisoners confess, and both serve five years. Mutual silence would have cost them only two. Individual rationality and the collective good pull in opposite directions.

The Iterated Prisoner’s Dilemma and Tit-for-Tat

The one-shot dilemma is bleak. Most real interactions repeat, though. In the iterated prisoner’s dilemma, the same players meet again and again, so defection can be punished and cooperation rewarded.

That makes conditional cooperation rational even for self-interested players. The question becomes which strategy performs best over the long run.

Robert Axelrod answered it with computer tournaments (Axelrod, 1984; Axelrod & Hamilton, 1981).

  • Aim: To find which strategy performs best in the iterated prisoner’s dilemma, and how cooperation can emerge without an authority to enforce it.
  • Method: Axelrod invited game theorists, economists, psychologists, and others to submit programs that played every other program in a round-robin, 200 rounds per pairing. The first tournament drew 14 entries, and a second drew 62 from six countries.
  • Results: Tit-for-tat, entered by the psychologist Anatol Rapoport, won both tournaments. It cooperates on the first move, then copies the opponent’s previous move.
  • Conclusion: Cooperation can arise and last among self-interested players if they are likely to meet again and use reciprocity: be nice, retaliate, forgive.

Axelrod identified four traits of successful strategies. Nice strategies never defected first. Retaliatory ones punished a defection at once. Forgiving ones returned to cooperation as soon as the opponent did. Clear ones were simple enough to recognize.

Nice strategies took the top eight places in the second tournament. In an evolutionary simulation, tit-for-tat grew to dominate the population, because reciprocators cooperated with each other and outscored exploiters. Axelrod and Hamilton (1981) extended this logic to biology, showing how reciprocity can be evolutionarily stable.

Tit-for-tat is fragile to noise. If one move is misperceived, two tit-for-tat players can fall into a chain of alternating defections.

Later work showed that more forgiving variants, and the win-stay, lose-shift rule, do better in noisy settings because they recover from error. The results also depend on the pool of strategies submitted.

The Ultimatum Game

This game is a simple take-it-or-leave-it bargaining game involving two players. One player is assigned as the proposer, while the other is the responder.

The proposer is allocated a sum of money, for instance, $4. They then must decide how much of this $4 to give the responder. The responder decides whether to accept or reject the offer.

If the responder accepts, the players split the money in the way the proposer suggested. If the responder rejects the offer, neither player gets any money.

A self-interested proposer might offer a low amount. But the responder may reject it, and then both players get nothing.

Under rational choice theory, a responder should accept any offer, even $1, because something is better than nothing. A rational proposer should therefore offer the smallest amount and keep the rest.

Real players do not behave this way. Güth et al. (1982) tested the prediction with real money.

  • Aim: To test whether real players bargain as game theory predicts.
  • Method: Forty-two economics students in Cologne played the game for real money, taking both proposer and responder roles. It was anonymous and one-shot, so reputation could not explain any generosity.
  • Results: Proposers did not offer the minimum: the modal offer was close to an even split. Responders often rejected low but positive offers, giving up real money.
  • Conclusion: Fairness norms, and a willingness to pay a personal cost to punish unfairness, shape bargaining more than narrow payoff-maximizing does.

Few findings in social science have replicated more often. Interpreting it needs care, though. Rejections may reflect inequity aversion, spite, anger, or a wish to uphold a social norm. The original sample was small and made up of economics students.

Fairness is also not universal. Offers and rejection thresholds vary substantially across societies (Henrich et al., 2001). A meta-analysis found that responder behavior differs more across cultures than proposer behavior (Oosterbeek et al., 2004).

The Public Goods Game

The public goods game scales the dilemma up from two players to a group. Each member receives an endowment and privately chooses how much to put into a common pool. The pool is multiplied, then split equally among all members, whatever each contributed.

Everyone gains most if all contribute everything. Yet each individual does best by contributing nothing and free-riding on the others. Zero contribution is therefore the Nash Equilibrium, a miniature version of the tragedy of the commons (Hardin, 1968).

In practice, groups start by contributing about half their endowment. Contributions then decay toward zero over repeated rounds as cooperators, seeing themselves exploited, withdraw their own cooperation.

Free-riding in groups also appears as social loafing, where people put in less effort when working together.

What stops the unravelling is punishment. Fehr and Gächter (2002) tested whether people would pay to punish free-riders even when it gains them nothing.

  • Aim: To test whether people punish free-riders at a personal cost, and whether that punishment can sustain cooperation that would otherwise collapse.
  • Method: Small groups played a public goods game, with or without the option to pay one unit to remove three from a free-rider. Groups were reshuffled each round, so partners never met again.
  • Results: Without punishment, cooperation decayed toward free-riding; with it, cooperation stayed high and rose. High contributors punished low contributors, driven by anger at norm violators.
  • Conclusion: People engage in altruistic punishment, paying a personal cost to punish norm violators for no material gain, and this helps sustain large-scale cooperation.

The stranger design makes this a particularly clean demonstration. With no future interaction and full anonymity, no self-interested motive can explain the punishment.

The finding has proved robust, but its scope has limits. The classic experiments used modest stakes and mostly Western, educated samples.

In some societies, people also punish high contributors, which can remove the benefit of punishment (Herrmann et al., 2008). Punishment can also waste resources, since the cost of punishing may exceed the cooperation gained.

The Volunteer’s Dilemma

In a volunteer’s dilemma, someone must do a chore or job for the good of everyone. The task is usually unpleasant. Everyone presumably has the skills to do it, but no one wants to.

Examples include cleaning up, repairing a broken item, or completing a group project. If nobody steps forward, the task goes undone. The whole group suffers.

Each member must decide whether to be the one who steps forward. The volunteer gains no extra benefit, because everyone else benefits too. So there is little incentive to act. The bystander effect has the same structure: each witness expects someone else to help.

The Centipede Game

This is an extensive-form game, meaning the players take turns. Two players alternately choose whether to take a larger share of a slowly growing pot of money.

The pot is arranged so that passing it is risky. If a player passes and the other player takes the money, the passer receives less than if they had taken the pot themselves.

The game ends when a player takes the pot. That player gets the larger portion and the other gets the smaller share. There are 100 rounds in total, but the game can end at any point, even after the first round.

Cooperative vs. non-cooperative game theories

Cooperative and non-cooperative game theories are the most common types of game theory.

Cooperative game theory studies how groups, or coalitions, interact. Players can make binding agreements, and the analysis concerns how the group divides the known payoffs. It is a game between groups rather than between individuals.

Non-cooperative game theory is the dominant strand. Players cannot make binding agreements, so each pursues personal goals given only the available strategies and the outcomes of each combination of choices. Rock-paper-scissors is a real-world example.

Zero-Sum, Non-Zero-Sum, and Sequential Games

In a zero-sum game, one player’s gain is exactly another’s loss, as in poker among friends. There is no scope for mutual benefit.

Non-zero-sum games allow outcomes where all players gain or all lose. Most social life works this way, which is why these games can model cooperation and its failures.

Games can also be simultaneous or sequential. In a simultaneous game, players move at once without knowing each other’s current choices. In a sequential game, players move in turns and see what came before, which brings in threats and reputation.

Types of game strategy

Below are some of the game strategies that players can use according to game theory:

Maximax strategy

A maximax strategy aims for the maximum possible payoff. The player takes a chance on the best outcome, even if a highly unfavorable outcome is possible.

In the Prisoner’s Dilemma, a maximax player confesses, hoping the other stays silent so that they go free.

This strategy is often viewed as naïve and overly optimistic since it assumes there will be a highly favorable environment for the player, which may not always be the case.

Maximin strategy

A maximin strategy is where a player chooses the best of the worst payoff. This is commonly chosen when a player cannot fully rely on the other players to keep to any prior agreement.

In the Prisoner’s Dilemma, confessing risks five years at worst, if the other player confesses. Denying risks nine years in the same case.

Thus, the best of the worst payoff, the maximin strategy, is to confess.

Dominant strategy

A dominant strategy gives a player the best payoff whatever the other players do. In the Prisoner’s Dilemma, confessing is dominant for each player.

That makes the choice simple, but not the result: when both follow it, both end up worse off than if they had stayed silent.

What is Nash Equilibrium?

The Nash Equilibrium is named after the mathematician John Nash. He proved that every finite game has at least one equilibrium, though sometimes only in mixed, or randomized, strategies (Nash, 1950).

In a Nash Equilibrium, no player can improve their own payoff by changing strategy alone, given what everyone else is doing. Each player’s choice is a best response to the others’. So nobody has a reason to move.

Considering the Prisoner’s Dilemma game theory, we can work out the Nash Equilibrium of the choices both prisoners make:

  • The best option for prisoner one, if prisoner 2 confesses, is to also confess because if they deny the crimes, prisoner one will receive a 9-year sentence.

  • The best option for prisoner one if prisoner 2 denies the crimes is to confess, because prisoner one then goes free instead of serving 2 years.

Thus, confessing is the best choice whatever the other prisoner does, so the only Nash Equilibrium is for both prisoners to confess.

Yet this equilibrium is not the best outcome. Both prisoners serve five years, when mutual silence would have cost them only two. A Nash Equilibrium can leave everyone worse off, because no single player can gain by moving away from it alone.

A game can have one Nash Equilibrium, several, or none in pure strategies. The Prisoner’s Dilemma has just one: both prisoners confess.

In simultaneous games that are repeated over time, one of the multiple equilibria is often reached through convention, communication, or trial and error.

The Nash Equilibrium is also a ‘no regrets’ outcome. Once a player has decided, they would not change their choice, given what the others did. Equilibrium is usually reached over time, and once found, it is not deviated from.

To test for one, imagine taking a different move. If it would not help, you have found a Nash Equilibrium.

What is game theory used for?

Game theory can be applied to many aspects of life outside of the dilemma games. Some examples of everyday life applications include:

  • Rock, paper, scissors game

  • Chess

  • Poker

  • War strategies and conflict analysis

  • Market shares and stockholders

  • Business strategy

When applying game theory to business, for instance, there are a number of strategic choices which govern their ability to achieve a desired payoff.

Business can:

  • Make decisions on price and output

  • Make decisions on products as to whether to keep existing products or develop new ones.

  • Make decisions on promoting products, such as whether to spend more on advertising, spend less, or keep things constant.

  • Derive a range of payoffs from their strategy choices, such as making profits, improved chances of survival, and getting rid of rivals.

Psychologists use game theory to study trust, cooperation, and collective action. Overfishing, climate change, and vaccination all share the structure of the prisoner’s dilemma.

Communication matters. In a meta-analysis of decades of prisoner’s dilemma experiments, Sally (1995) found that letting players talk substantially raises cooperation, even when the talk is non-binding.

Game theory also shaped Cold War deterrence analysis.

It informs the study of bargaining, coalition formation, and voting too. There, the chance of meeting again and credible commitments decide whether cooperation holds.

Biology uses game theory too. The players are competing organisms and the payoffs are reproductive fitness. Maynard Smith and Price (1973) introduced the evolutionarily stable strategy, one that, once adopted by most of a population, no rare alternative can invade.

It is the biological counterpart of the Nash Equilibrium. Natural selection reaches it, not rational deliberation. That helps explain how a readiness to cooperate, retaliate, or share fairly could be built into human nature.

How does game theory relate to psychology?

Game theory also applies to human psychology. It predicts what a purely rational, self-interested player should do, so any departure from that prediction becomes a measurable psychological finding.

By using methods such as eye trackers, electroencephalography (EEG), and galvanic skin response (GSR), researchers can understand the decision-making process within games.

Emotion and Mood

Galvanic skin response (GSR), the skin’s electrical conductance, rises with emotional arousal. One study measured it while 30 undergraduates played the Ultimatum game (van ’t Wout et al., 2006).

Arousal was higher for unfair offers and linked to rejecting them. This held only for offers from human partners, not computers.

That matters because rejecting an offer is the ‘irrational’ move, since any money beats none. Emotion may override the calculation.

Mood matters too. Harlé and Sanfey (2007) induced sadness with short movie clips before participants played the Ultimatum game.

Sadness interacted with offer fairness: the sadder the participant, the fewer unfair offers they accepted.

Emotions carried into a game shift behavior, even when they are irrelevant to the transaction. Even subtle moods can bias decisions.

Brain Activity

Babiloni et al. (2007) used EEG to record brain activity while pairs played the Prisoner’s Dilemma. This hyperscanning records both players’ brains at the same time. Activity in the anterior cingulate cortex, an area linked to emotional control, was associated with the likelihood of betrayal.

Sanfey et al. (2003) scanned players during the Ultimatum game. Unfair offers activated the anterior insula, a region associated with negative emotions such as disgust and anger. The stronger the activation, the more likely the player was to reject the offer.

Unfair offers also engaged the dorsolateral prefrontal cortex, which supports deliberate goals such as keeping the money.

So rejection is not a simple error. It can be read as the emotional fairness signal winning out over the cognitive self-interest signal.

Visual Attention

Peshkovskaya et al. (2017) used eye-tracking glasses to study visual perception during the Prisoner’s Dilemma. Total viewing time and fixation time on the non-cooperative option related to each player’s level of cooperation.

Greater attention to the non-cooperative option went with more defection. Where people look predicts how they choose.

Across all these methods, emotion and attention shape strategic choices continuously, and a purely rational model leaves out both.

Critical Evaluation of Game Theory

Game theory gives psychology a precise yardstick, but the people it studies often fail to meet it. Strengths and limitations follow from that gap.

Strengths of Game Theory

Game theory is a rigorous, general language for strategic interdependence. It unites economics, biology, political science, and psychology, and yields precise, testable predictions.

Its greatest gift is a benchmark of pure self-interest. By specifying what a rational egoist would do, game theory turns every human departure into a discovery. Fairness, reciprocity, costly punishment, and default cooperation have all become foundational findings this way (Güth et al., 1982; Fehr & Gächter, 2002).

The simple games also travel well. The same prisoner’s dilemma and ultimatum structures now organize brain-imaging studies of fairness (Sanfey et al., 2003) and multi-society surveys of bargaining norms (Henrich et al., 2001).

The same games work in the scanner, in the field, and in cross-cultural fieldwork. They give researchers a shared experimental currency across laboratories and societies.

Limitations of Game Theory

People break its core assumptions most often. Classical theory assumes rational, self-interested players. Real players are moved by fairness, emotion, trust, and social norms.

Players are also boundedly rational. Simon (1955) argued that decision-makers face limits of information, time, and processing capacity. They usually satisfice: they accept an outcome that is good enough rather than computing the best one.

Predictions are also sensitive to specification. Framing, whether a game is one-shot or repeated, and which equilibrium is selected can all change the result.

It names stable points, but not which one players reach. It also treats payoffs as given, rather than asking where preferences come from.

Behavioral economics, including prospect theory, likewise documents systematic departures from rational choice. Behavioral and evolutionary game theory fill these gaps. They treat fairness and reciprocity as psychological and evolved facts about the players, grafting the missing motives onto the rational-choice skeleton.

Contemporary Research

Modern evidence suggests that fairness and cooperation are defaults of human strategic thinking, not mere exceptions to rationality.

Fairness Across Societies

Henrich et al. (2001) ran standardized bargaining games in 15 small-scale societies. Offers and rejections tracked each community’s market integration and cooperative production. There was no single human constant.

A larger follow-up linked greater market integration and participation in world religions to stronger fairness and punishment (Henrich et al., 2010).

A meta-analysis of ultimatum experiments confirmed systematic cross-cultural variation, especially in responders’ willingness to reject (Oosterbeek et al., 2004).

The pattern is clear. A fairness-and-reciprocity system looks universal, but its settings are shaped by the social world.

Is Cooperation Intuitive?

The social heuristics hypothesis proposes that people carry cooperative habits from everyday life, where interactions repeat and are observed, into the laboratory. Deliberation then nudges them toward self-interest (Rand et al., 2012).

Early studies found that promoting intuition raised cooperation (Rand et al., 2014). A large registered replication found no effect of time pressure specifically (Bouwmeester et al., 2017).

A meta-analysis helps settle the debate.

  • Aim: To test whether cooperation is an intuitive default that deliberation restrains, as the social heuristics hypothesis predicts.
  • Method: Rand (2016) meta-analyzed 67 studies of cognitive-processing manipulations in economic cooperation games, with 17,647 participants in total. He found no sign of publication bias.
  • Results: Promoting intuition over deliberation produced 17.3% more pure cooperation, where cooperating carries no future benefit. It made no significant difference to strategic cooperation, where cooperating can pay off.
  • Conclusion: Cooperation looks like an intuitive default generalized from a social world that usually rewards it, while deliberation applies the cold self-interest classical game theory assumes.

Because it pools many studies and found no publication bias, this result is more reliable than any single experiment, including the contested replication. The rational actor is not wrong so much as partial: it describes what one deliberative system computes, not what the whole mind does.

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Saul McLeod, PhD

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Chartered Psychologist (CPsychol)

Saul McLeod, PhD, is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.


Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology, where she contributes accessible content on psychological topics. She is also an autistic PhD student at the University of Birmingham, researching autistic camouflaging in higher education.