Games People Play

1. Game Theory is the Study of Strategic Interaction

Simply put, game theory is the study of strategic, interactive decision making among rational individuals.

Understanding interactions. Game theory provides a framework for analyzing situations where individuals make decisions that affect others, or in response to others' actions. It's a powerful tool for navigating the "sea of games" that constitutes much of our lives, from trivial choices like where to meet for lunch to profound ones like international conflict. The field gained prominence with John von Neumann and Oskar Morgenstern's 1944 book, Theory of Games and Economic Behavior, which aimed to place neoclassical economics on a more scientific footing.

Core components. Every game, regardless of its complexity, is built upon three fundamental elements: players, strategies, and payoffs.

• Players: The decision-makers involved in the game.
• Strategies: A complete plan specifying a player's decision for every possible situation they might encounter. These can be "pure" (deterministic) or "mixed" (involving randomness).
• Payoffs: The rewards or losses a player experiences based on the combined strategies of all players, reflecting their true preferences.

Practical utility. Game theory helps us not only understand the game we're in but also how to change it to better suit our interests. Its applications are vast, spanning business, economics, military strategy, politics, and even biology. For instance, game theorists designed the multi-objective auction system for government licensing of the radio spectrum, which raised $400 billion for the U.S. treasury and efficiently distributed licenses.

2. Games Unfold Sequentially or Simultaneously

As the name suggests, sequential games have events unfolding over time. … Most of the encounters you think of as interaction with other people are sequential games.

Timing matters. Games are broadly categorized by the timing of players' decisions: sequential or simultaneous. In sequential games, players have some knowledge of previous actions, influencing subsequent choices. These are best represented by a "game tree," where decisions branch out over time. A powerful solution method for sequential games is "rollback," which involves working backward from the end of the game to determine optimal moves.

Concurrent decisions. Simultaneous games, conversely, involve players making decisions without knowing the others' choices, even if they don't literally move at the exact same moment. These are typically represented by a "matrix form," where rows and columns correspond to player strategies and cells contain payoffs. A key solution concept for both types of games is the "Nash equilibrium," a strategy profile where no player can unilaterally improve their payoff by changing their strategy.

Dominance and elimination. For simultaneous games, simplifying the matrix often involves identifying "dominated strategies"—choices that are always worse than another, regardless of what other players do. The "iterated elimination of dominated strategies" (IEDS) can reduce complex games, sometimes revealing a unique Nash equilibrium. The "best-response method" can systematically find all Nash equilibria by highlighting optimal responses for each player to every possible strategy of their opponent.

3. Classic 2x2 Games Reveal Fundamental Dilemmas

Because of their tininess … they appear again and again at the heart of many other games, and knowing them gives you a place to start in evaluating such games.

Atomic interactions. Four fundamental 2x2 simultaneous games serve as building blocks for understanding more complex interactions: the coordination game, the battle of the sexes, chicken, and the prisoner's dilemma. These "atomic" games illustrate recurring strategic challenges and their potential solutions.

Common archetypes:

• Coordination Game: Players prefer to match choices, with one matching outcome being mutually preferred (e.g., both dress formally).
• Battle of the Sexes: Players prefer to match, but each has a different preferred matching outcome (e.g., one prefers formal, the other casual, but both want to match). These often require a "Schelling point" or focal point for resolution.
• Chicken: Players want to avoid a disastrous mutual outcome, but each prefers the other to "chicken out" (e.g., two cars speeding towards each other).
• Prisoner's Dilemma: Each player has a dominant strategy to "defect," leading to a mutually worse outcome than if they had both "cooperated." This equilibrium is not "Pareto-optimal," meaning a better outcome for all exists.

Paradox of cooperation. The Prisoner's Dilemma is particularly maddening because rational individual choices lead to a collectively suboptimal result. Achieving cooperation in such scenarios is a central problem in game theory, highlighting the tension between individual self-interest and collective well-being. These classic games demonstrate how understanding underlying structures can inform decision-making in diverse real-world contexts.

4. Uncertainty is Modeled Through Chance and Information Asymmetry

There are really three main ways that unpredictability or chance works its way into game theory: as uncertainty about the outcome of an event within the game, as an uncertainty about the structure of the game itself, or as an uncertainty about the pure strategy that a player will choose.

Embracing unpredictability. Game theory incorporates uncertainty in several ways. First, chance events can occur within a game, modeled by adding "Nature" as a player making random "decisions" with given probabilities. Second, players might be uncertain about the game's structure itself, leading to "incomplete information" (e.g., not knowing an opponent's payoffs). Third, players might use "mixed strategies," randomly selecting their pure strategy with specific probabilities, which requires "cardinal payoffs" (measuring preference intensity) rather than just "ordinal payoffs" (rankings).

Asymmetric knowledge. "Incomplete information" often manifests as "asymmetric information," where one player knows something another doesn't. John Harsanyi's Nobel Prize-winning "Harsanyi transformation" converts these into "imperfect information" games, where players know the game structure but not their exact position within it. This allows for analysis using expected values, which are calculated by multiplying each payoff by its probability of occurring and summing the results.

Signaling and screening. In asymmetric information games, players engage in "signaling" (conveying private information) and "screening" (trying to discover private information). For example, in the "market for lemons" scenario, where only the seller knows a car's quality, asymmetric information can cause the market for good cars to collapse. Credible signals, like a hazardous waste company offering to buy back homes at pre-plant values, can overcome information asymmetry. Conversely, "moral hazard" arises when a party doesn't bear the full consequences of their actions, leading to riskier behavior (e.g., insured drivers being less careful).

5. Strategic Moves Shape Outcomes by Altering Credibility

A threat, promise, or commitment always involves … saying … in at least one circumstance, you’re going to take an action that is not in your best interest at the time.

Beyond simple choices. Strategic moves—threats, promises, and commitments—are powerful tools that can dramatically alter game outcomes by changing the perceived future actions of players. Unlike "assurances" (promises you want to keep) or "warnings" (threats you want to follow through on), strategic moves involve declaring an intention to act against one's immediate self-interest under specific conditions.

The credibility challenge. The effectiveness of any strategic move hinges entirely on its "credibility." If a player's declared intention isn't believed, it has no impact. Credibility problems arise because rational players are expected to act in their best interest at the time of decision, not necessarily according to prior declarations. For example, a promise to go to Disneyland if a child gets an A in math is not credible if the family was going anyway.

Achieving believability. Players can establish credibility by:

• Altering payoffs: Changing the game's structure so that following through on the strategic move becomes the best option (e.g., signing a contract with penalties, or the "Ultimatum Game" where a third party is paid to punish low offers).
• Restricting strategies: Limiting future choices, often called "burning bridges" (e.g., a doomsday device, or appointing an agent with limited authority).
• Building reputation: A history of adhering to commitments (e.g., Israel's stance on not negotiating with terrorists).
• Rational irrationality: Convincing others you don't play rationally or value payoffs as expected (e.g., President Kennedy's "brinkmanship" in the Cuban Missile Crisis).

Strategic moves are generally aimed at "deterrence" (maintaining status quo, often with threats) or "compellence" (changing status quo, often with promises).

6. Repeated Interactions Foster Cooperation and Complex Strategies

If the duration of the game is unknown but likely to be suf¿ciently long, rational players may adopt strategies resulting in sustained mutual cooperation.

The supergame effect. Many real-world interactions are not one-shot events but "repeated games" or "supergames," consisting of multiple rounds of a "stage game." This history of past interactions and anticipation of future ones profoundly influences strategic choices, often leading to more complex "closed-loop" strategies that depend on prior moves.

Overcoming the Prisoner's Dilemma. In a fixed-length repeated Prisoner's Dilemma, the "rollback" logic dictates that rational players will defect in every round, as there's no incentive to cooperate in the final round, which then makes the penultimate round the "real" last round, and so on. However, if the game's duration is unknown, cooperation becomes possible. If the probability of continuing the game (˜) is sufficiently high, the long-term benefits of cooperation outweigh the short-term gain of defection, making strategies like "grim trigger" (cooperate until betrayed, then defect forever) viable Nash equilibria.

Tit for Tat's success. Robert Axelrod's famous computer tournaments for the iterated Prisoner's Dilemma revealed the surprising effectiveness of the simple "tit for tat" strategy: cooperate on the first round, then mirror the opponent's previous move.

• Nice: Never the first to betray.
• Provocable: Quickly punishes defection.
• Forgiving: Returns to cooperation after punishment.
• Straightforward: Easy for others to understand and predict.
  This strategy's success suggests that cooperation can emerge and persist in environments where interactions are ongoing and the future is uncertain.

7. Evolutionary Game Theory Explains Population-Level Behavior

This version of game theory rests on a different foundation than the one that we’ve developed so far. … And in spite of this, we’re going to see that many of the results that we’ve seen already are results that can be paralleled in the ¿eld of evolutionary game theory.

Beyond individual rationality. Evolutionary game theory applies game-theoretic concepts to populations, often within a species, where individual behaviors ("phenotypes") are "hardwired" and cannot change. Instead, successful phenotypes (strategies) propagate through generations based on their "fitness"—their expected payoff from interacting with the population. This field explores how the distribution of phenotypes evolves over time and which strategies are "evolutionarily stable."

Evolutionarily Stable Strategies (ESS). A population exhibiting an ESS is one that cannot be successfully invaded by a small number of individuals with a different phenotype. For example, in a "hawk/dove" game (where hawks fight and doves display), neither an all-hawk nor an all-dove population might be an ESS. Instead, a "polymorphic ESS" (a stable mix of phenotypes) or a "monomorphic ESS" (a single phenotype playing a mixed strategy) might emerge.

Parallels with traditional game theory. Remarkably, many results from evolutionary game theory, such as the existence of ESSs, parallel the Nash equilibria found in traditional game theory, even though evolutionary models do not assume individual rationality or knowledge of payoff matrices. This suggests that the underlying logic of strategic interaction can lead to similar stable outcomes whether driven by conscious rational choice or by natural selection. The "War of Attrition," where players pay increasing costs until all but one gives up, is an example of a game with a polymorphic ESS, where a mixed strategy of buzzing in at random times proves optimal.

8. Game Theory Explains Economic Behavior and Market Structures

When you strip a situation down to its essentials, it’s surprising how often you’ll be looking at a game.

Market dynamics. Game theory is a cornerstone of modern microeconomics, particularly in analyzing market structures beyond perfect competition or monopoly. It illuminates how firms make strategic decisions regarding production, pricing, and market entry, especially in "oligopolies"—markets with a small number of competitors.

Oligopoly models:

• Monopoly: A single firm maximizes profit by setting quantity where marginal revenue equals marginal cost.
• Von Stackelberg Duopoly: A sequential game where one firm (the leader) chooses its production level first, and the other (the follower) responds. This often grants a significant first-mover advantage to the leader.
• Cournot Duopoly: A simultaneous game where firms independently choose production quantities. The equilibrium is found where each firm's output is its best response to the other's output. This often leads to lower profits for both firms compared to a monopoly, but higher than perfect competition.

Auctions and the Winner's Curse. Auctions are pervasive economic games, from spectrum licenses to online sales. They are used when there's uncertainty about an item's value.

• Private-value auctions: Each bidder has a different, known valuation.
• Common-value auctions: The item has the same value to all, but bidders only have estimates.
  The "winner's curse" is a common phenomenon in common-value auctions where the winner tends to overpay because the highest estimate is often too optimistic. Bidders learn to "shade" their bids (bid less than their estimate) to mitigate this. The "revenue equivalence theorem" suggests that under certain conditions, different auction formats (English, Dutch, first-price, second-price) yield the same expected revenue.

9. Cooperative Games Address Value Distribution in Coalitions

The question then becomes: How much of that value does each player receive?

Collective action. Cooperative games focus on situations where players can form "coalitions" and make "binding agreements" to achieve a greater collective payoff than they could individually. The central challenge in these games is how to fairly distribute the "extra payoff" or "surplus" generated by cooperation among the members of a "grand coalition" (all players cooperating).

Fair division concepts:

• The Core: A set of allocations where no subgroup of players can do better by leaving the grand coalition and forming their own. Sometimes, the core can be empty (e.g., in a three-person majority vote to split money, any division can be outvoted by two players forming a new coalition).
• Shapley Value: A solution concept that assigns each player a payoff based on their average marginal contribution to all possible coalitions they could join. It's "efficient" (total payoffs equal total pie), "symmetric" (equal contributors get equal payoffs), and ensures players get at least what they'd get independently. It's often used as a "power index" in legislative bodies.
• Nash Cooperative Bargaining Solution: For two-player games, this solution suggests that players should receive their "BATNAs" (Best Alternatives To Negotiated Agreements—what they get if negotiations fail) plus an equal share of the remaining "surplus," assuming equal bargaining power. If bargaining powers are unequal, the surplus is divided proportionally.

Bargaining dynamics. Bargaining can also be modeled as a noncooperative sequential game, where delays in agreement carry costs. Impatience plays a crucial role; players with higher discount rates (less patience) are at a disadvantage, as they are more willing to concede to reach an immediate agreement.

10. Real-World Behavior Often Deviates from Pure Rationality

To heck with what people should do if they’re rational decision makers. If they don’t actually do what game theory says, then the theory has no predictive power.

Limits of rationality. While traditional game theory assumes players are perfectly rational—always making choices that maximize their expected payoff—real-world behavior frequently deviates from these predictions. This raises questions about game theory's "predictive power" (what people will do) and "prescriptive power" (what people should do).

Experimental evidence:

• Ultimatum Game: Game theory predicts the proposer offers a minimal amount, and the responder accepts. In reality, proposers offer around 40% of the pot, and responders often reject offers below 20-30%, suggesting a "visceral" rejection driven by fairness, as shown by brain activity in the insula.
• Dictator Game: A dictator simply divides money. While game theory predicts keeping all, about 80% share some, indicating a preference for fairness, though this diminishes with increased social distance or anonymity.
• "Guess 70% of the average" game: Rationality dictates everyone picks 0, but real players typically stop reasoning after a few steps, demonstrating "bounded rationality."

Behavioral game theory. This emerging field seeks to explain these disparities by incorporating psychological and cognitive factors into game theory. It acknowledges that humans have "finite powers of computation, memory, and information processing." Concepts like "fairness" and "altruistic punishment" (willingness to incur a cost to punish defectors) are recognized as powerful incentives that shape behavior, even if they complicate simple payoff structures.

11. "Co-opetition" Integrates Cooperation and Competition in Business

Brandenburger and Nalebuff outline an integrated, step-by-step approach for applying game theory to business. They take particular care to point out that businesses have to cooperate to create the pie before competing for the pieces.

Strategic business framework. Adam Brandenburger and Barry Nalebuff's "Co-opetition" offers a practical, game-theoretic approach to business strategy, emphasizing that firms must both cooperate to "create the pie" (expand the market) and compete to "divide the pie" (capture market share). Their "PARTS" framework provides a structured way to analyze business opportunities:

• Players: Customers, suppliers, competitors, and "complementors" (businesses whose products make yours more valuable).
• Added Value: The increase in the total value of the game when your business is included. This determines your bargaining power.
• Rules: The contracts, laws, and customs that govern interactions. Minor changes can have significant impacts (e.g., "most-favored customer" clauses can reduce price competition).
• Tactics: Actions taken to shape perceptions, including signaling, screening, and "signal-jamming" (preserving uncertainty).
• Scope: Recognizing that individual games are often linked to larger, interconnected games.

The Value Net. A key tool is the "Value Net," which visually maps these relationships. A firm is a "competitor" if customers value your product less when they have theirs, and a "complementor" if customers value your product more when they have theirs. This framework encourages businesses to look beyond traditional rivals and identify opportunities for complementary relationships, even with competitors (e.g., early automakers cooperating to build highways).

Leveraging added value. Understanding "added value" is crucial for negotiation. By strategically limiting the added value of suppliers or complementors (as Nintendo did with its security chip and game limits), a company can increase its own share of the pie. Conversely, a company can be "paid to play" by creating competition that benefits other players, even if it doesn't directly win the business (e.g., Holland Sweetener's competition with NutraSweet saved Coke and Pepsi millions). Ultimately, successful strategic thinking in business requires an "allocentric" perspective—seeing the world from other players' viewpoints and understanding their motivations.

Last updated: January 6, 2026