A zero-sum game is a situation in which one player can only be made better off by making another player worse off: the gains and losses of all players add up to zero. The idea comes from mathematical game theory, where John von Neumann proved his minimax theorem for two-player zero-sum games in 1928 and, with Oskar Morgenstern, built a full theory of games in 1944. Most business and economic exchanges are not zero-sum, because trade and investment can make both sides better off.
Add up what every player wins and loses and the total is zero (or another constant). Chess, Go and a two-player poker pot work this way.
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Interests are directly opposed
Because one side's gain is the other side's loss, there is nothing to gain from cooperating. Each player plays to protect against the worst case.
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Minimax gives a stable answer
Von Neumann showed that in two-player zero-sum games each side has a strategy that secures a guaranteed value, so the best defensive play and the best attacking play meet at the same point.
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Most real deals are not like this
When an exchange creates value, as most trade does, the game is positive-sum. Treating it as zero-sum is a common error known as zero-sum thinking.
Where you see it today
AI learned to win zero-sum games by playing itself
DeepMind’s AlphaZero taught itself chess, shogi and Go through self-play and beat the strongest specialised programs (Silver et al., 2018). In poker, Libratus beat four leading professionals at two-player no-limit Texas hold’em (Brown and Sandholm, 2018). These clean win-lose games were the first proving ground for game-playing AI.
A zero-sum game inside generative AI
Generative adversarial networks train two models against each other: a generator that makes fake samples and a discriminator that tries to spot them. The authors describe the set-up as a minimax two-player game (Goodfellow et al., 2014).
Zero-sum thinking in politics
A survey of 20,400 U.S. residents found that people with a more zero-sum mindset were more likely to support redistribution and more restrictive immigration policies (Chinoy et al., 2023, NBER). Earlier work found that both liberals and conservatives view life as zero-sum when it suits their beliefs (Davidai and Ongis, 2019).
The AI jobs debate
Arguments about AI and work often assume a fixed amount of work to share between people and machines. That is zero-sum framing. Whether AI shrinks or grows the pie of tasks is the real, open question, and it differs by occupation.
Zero-sum game and related ideas
Zero-sum game
What it meansOne side's gain is exactly the other side's loss
ExampleChess, a single pot of poker
Constant-sum game
What it meansPayoffs always add to the same total, not necessarily zero
ExampleSplitting a fixed prize between two teams
Positive-sum game
What it meansTotal payoff can grow, so both sides can gain
ExampleVoluntary trade, a joint venture
Negative-sum game
What it meansTotal payoff shrinks, so the players lose in aggregate
ExampleA price war that destroys margins for all
Zero-sum thinking
What it meansThe belief that gains for one tend to come at others' expense
Example"Their raise means a smaller one for me"
How to use it
Before a negotiation, ask whether the value on the table is fixed or can grow; most deals have more than one issue to trade.
If the contest really is zero-sum, such as a single contract with one winner, plan for the worst case and protect your downside.
Look for ways to turn a fixed-pie fight into a bigger pie: bundle issues, change timing, or add a partner.
Watch for zero-sum thinking in your team, for example treating another department's budget as your loss.
When you hear that AI will take a fixed number of jobs, ask which tasks it removes and which new ones it creates.
The Business Engineer lens
Most of the AI economy is positive-sum at the level of the market but zero-sum at specific chokepoints, such as scarce chips, power and top researchers. The Business Engineer separates the two: compete hard where the pie is fixed, and build where it can grow.
It is a situation in which the gains and losses of all players add up to zero, so one player can only gain if another loses.
Who came up with the idea?
It is rooted in game theory: John von Neumann proved the minimax theorem for two-player zero-sum games in 1928, and von Neumann and Morgenstern developed the wider theory in 1944.
Is the economy a zero-sum game?
Generally no. Voluntary trade and investment can make both sides better off, which makes them positive-sum.
How does AI relate to zero-sum games?
Game-playing AI such as AlphaZero and Libratus was built and tested on zero-sum games, and generative adversarial networks train two models against each other in a minimax game.
The complete explainer, cleaned up and reformatted for mobile.
Zero-Sum Game involves balanced participant gains and losses. Benefits include strategic thinking, while challenges relate to limited cooperation and misconceptions. Chess and poker are examples. Applicable in economics and international relations, it applies to business competition and negotiations, revealing dynamics of shared gains and losses.
Zero-Sum Game: A zero-sum game is a situation in game theory and economics where one participant’s gain or loss is exactly balanced by the losses or gains of other participants. In other words, the total amount of wealth, utility, or resources remains constant; any gain by one participant is matched by an equal loss by another.
Zero-sum games are often used to analyze competitive situations where the interests of participants are directly opposed to each other.
Key Concepts and Components
Fixed Total Resources: In a zero-sum game, the total amount of resources, wealth, or utility remains constant throughout the game. This fixed-sum constraint distinguishes zero-sum games from non-zero-sum games.
Win-Lose Dynamics: Participants in a zero-sum game compete for a finite pool of resources, and any gain made by one player is at the direct expense of the other player(s). As one participant wins, the others lose proportionally.
Examples of Zero-Sum Games
Two-Player Games:
Many classic board games, such as chess and tic-tac-toe, are zero-sum games. In these games, one player’s victory directly corresponds to the other player’s defeat.
Economics and Trade:
Zero-sum thinking is sometimes applied to economic situations, particularly in trade disputes. However, in real-world economics, trade can create value, leading to mutually beneficial outcomes, making it a non-zero-sum scenario.
Sports Competitions:
Sports matches are often viewed as zero-sum games because one team’s victory comes at the expense of the opposing team’s loss. However, sports also involve skill improvement and personal development, making them more complex than strict zero-sum situations.
Strategies in Zero-Sum Games
Maximin Strategy:
In a zero-sum game, players may adopt a “maximin” strategy, where they aim to maximize their minimum possible gain. This strategy focuses on minimizing potential losses rather than maximizing gains.
Nash Equilibrium:
A Nash equilibrium in a zero-sum game is reached when neither player can improve their position by unilaterally changing their strategy. In such a situation, both players adopt strategies that maximize their expected returns given the other player’s strategy.
Zero-Sum Game vs. Non-Zero-Sum Game
Non-Zero-Sum Games:
In contrast to zero-sum games, non-zero-sum games allow for scenarios where all participants can benefit without a corresponding loss for others. Cooperation and collaboration can lead to win-win outcomes in non-zero-sum games.
Cooperative Games:
Cooperative games involve players working together to achieve common goals. These games are characterized by the potential for all participants to benefit collectively.
Real-World Applications and Implications
International Relations:
Diplomatic negotiations and conflicts between nations are often seen through the lens of zero-sum thinking. However, diplomacy can also lead to win-win outcomes, such as trade agreements.
Economic Fallacy:
Zero-sum thinking can lead to economic fallacies, where individuals or groups mistakenly believe that gains by one party necessarily result in losses for others. In reality, economic growth can benefit all participants in an economy.
Challenges and Criticisms
Simplified Models: Critics argue that zero-sum game models oversimplify complex real-world interactions by focusing solely on competitive dynamics.
Cooperative Potential: Critics also highlight that many situations initially viewed as zero-sum can transform into cooperative, non-zero-sum scenarios through negotiation and collaboration.
Key highlights of “Zero-Sum Game”
Balanced Outcomes: In a Zero-Sum Game, one participant’s gain is offset by another participant’s loss, resulting in a balanced outcome.
Constant Total Payoff: The sum of gains and losses among participants remains constant throughout the game.
Strategic Thinking: Zero-Sum Games encourage strategic decision-making and competitive strategies to gain an advantage.
Resource Allocation: Insights into effective resource allocation within competitive environments can be derived from zero-sum dynamics.
Limited Cooperation: Due to competing interests, participants often engage in limited cooperation, prioritizing individual gains.
Zero-Sum Fallacy: A challenge is avoiding the misconception that any gain necessarily results in another’s loss.
Examples: Classic examples like chess and poker exemplify zero-sum scenarios in which one’s victory is at the expense of others.
Applications: The concept finds applications in competitive economics, international relations, and negotiations.
Use Cases: Businesses competing for market share and international negotiations often involve zero-sum dynamics.
In other words, the total amount of wealth, utility, or resources remains constant; any gain by one participant is matched by an equal loss by another.
Win-Lose Dynamics: Participants in a zero-sum game compete for a finite pool of resources, and any gain made by one player is at the direct expense of the other player(s).
Balanced Outcomes: In a Zero-Sum Game, one participant's gain is offset by another participant's loss, resulting in a balanced outcome.
Limited Cooperation: Due to competing interests, participants often engage in limited cooperation, prioritizing individual gains.
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Why it mattersFrom the article
Zero-sum games are often used to analyze competitive situations where the interests of participants are directly opposed to each other.
Strategic Thinking: Zero-Sum Games encourage strategic decision-making and competitive strategies to gain an advantage.
Cooperative Potential: Critics also highlight that many situations initially viewed as zero-sum can transform into cooperative, non-zero-sum scenarios through negotiation and collaboration.
The circle of competence describes a person’s natural competence in an area that matches their skills and abilities. Beyond this imaginary circle are skills and abilities that a person is naturally less competent at. The concept was popularised by Warren Buffett, who argued that investors should only invest in companies they know and understand. However, the circle of competence applies to any topic and indeed any individual.Drawing by The Business Engineer.
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Gennaro Cuofano is a CRO and tech executive who has worked in AI since late 2015, starting with bringing NLP, natural-language generation, voice and chatbot products to the marketing industry. His background is in law and finance: he holds a Master's degree in Law and an International MBA with an emphasis on corporate finance (LUISS Business School and the University of San Diego, 2012), and worked as a financial analyst at a real-estate investment firm in San Diego and as an assistant controller. His work focuses on business model strategy, business engineering and, more broadly, structural analysis: how companies make money, read from their own filings. He created FourWeekMBA and leads research there and at The Business Engineer, his newsletter on AI and business strategy, with over 95,000 subscribers and more than 1,000 published analyses. His writing has also appeared on Entrepreneur (for example, How to Digitize a Family Business in Europe) and HackerNoon. Find him on LinkedIn and Substack. See how we source.
