Zero-sum game

A zero-sum game is one in which a win for one player entails a loss for another. The concept marks a crucial contrast in the book’s account of cooperation: not every apparent contest requires one side to be defeated, and changes in circumstances or rules can turn rivalry into a situation in which both sides gain. The distinction depends not only on what players want, but on how a game distributes outcomes and what its participants know about one another and the future.

Definition and Strategic Contrast

In chess, the book’s clear example of a zero-sum game, one player’s aim to win necessarily means making the other lose. Prisoner’s Dilemma works differently. A banker pays out money, so the players need not take their winnings from one another: they may cooperate and both earn more. The game is therefore nonzero-sum, even though its players can still choose actions that undermine each other. The contrast separates a true conflict of outcomes from a conflict that is intensified by how players interpret their relationship.

The distinction also clarifies why a strategy that appears to concede victory can be successful. Tit for Tat is described as nice because it never defects first, forgiving because it has a short memory for past misdeeds, and not envious because it does not seek to earn more than its partner. It cannot outscore an opponent in an individual game; at most it draws. Yet it can achieve those draws with a high shared score. In such an interaction, treating the other player as an opponent may obscure the common opportunity: both can do better by cooperating against the banker than by trying to do one another down.

Rules That Shape Conflict

The book applies the distinction to divorce. A marriage is treated as a nonzero-sum relationship based on mutual cooperation, and the ending of a marriage does not eliminate every reason for the former partners to cooperate. Child welfare is one reason; avoiding the expense of two lawyers is another. Yet in England and, until recently, all fifty states of the United States, professional rules prevented one lawyer from representing both members of a couple. The lawyer had to accept one as a client and turn the other away, who then had to proceed without legal advice or find another lawyer.

The arrangement can recast a dispute as an adversarial contest even when the couple themselves do not feel adversarial and have agreed to be amicable. The case may be listed as “Smith versus Smith,” while the lawyers speak in terms of “us” and “them”: not one spouse and the other, but each lawyer and client against the opposing pair. In this structure, the clients may lose money through a zero-sum contest while the lawyers benefit from the fees it generates. The book stresses that the lawyers need not consciously organize this result; professional rules can make the adversarial pattern work on their own. It also notes that some lawyers do the opposite, persuading clients eager for a fight to reach a mutually beneficial settlement out of court.

The proposed remedy is institutional rather than violent: changing the law is cleaner than Shakespeare’s joke about killing lawyers. But reform faces a political obstacle, since many parliamentarians come from the legal profession and the British House of Commons is presented as an especially adversarial setting. Teaching legislators and lawyers game theory is offered as a possibility, while the book leaves broader questions open: whether wage bargaining and pay differentials encourage envy or cooperation, and whether people mistake nonzero-sum situations for zero-sum ones. It does not claim to settle those questions; it uses them to show that perceived conflict and actual conflict need not coincide.

The Football Match That Changed Character

The 1977 English Football League match between Bristol and Coventry demonstrates a zero-sum contest changing in the middle of play. At the end of the season, the bottom three clubs in the First Division faced relegation. Two places had already been decided; the third remained between Sunderland, Bristol, and Coventry. Bristol and Coventry were playing each other, while Sunderland played a separate opponent. If Sunderland lost, Bristol and Coventry would both stay up by drawing. If Sunderland won, one of the two would be relegated, depending on their result.

The matches were supposed to be simultaneous, but the Bristol–Coventry game was running five minutes late. For most of it, the teams played hard; by the eightieth minute the score was 2–2. Two minutes from the end, news arrived that Sunderland had lost. Coventry’s manager had the result displayed on the ground’s electronic message board. Once the players knew that a draw would keep both clubs in the First Division, scoring became the wrong objective: sending players forward could weaken a defence and risk the very defeat that would cause relegation.

The players consequently turned from attacking one another to preserving the draw. Supporters who had been fierce rivals joined in celebration, while the referee watched the players move the ball around with little challenge to the player in possession. A piece of outside information had changed the incentives without changing the basic contest or its participants. What had been zero-sum became nonzero-sum: an external “banker,” in the book’s analogy, had made the same outcome advantageous to both teams. The match is a concrete demonstration that a contest’s strategic character can depend on circumstances that emerge while it is underway.

Repetition and the Possibility of Cooperation

The football episode leads to a broader claim about life beyond sport. Spectator games are generally organized as zero-sum contests because audiences find determined opposition more exciting than amicable collusion. Human life, and the lives of plants and animals, are not arranged for spectators. In many real situations, Nature can play the role of banker: individuals may benefit from one another’s success rather than needing to defeat rivals. Cooperation and mutual assistance can therefore arise in a world still governed by the book’s selfish-gene perspective.

But mutual advantage is not enough by itself. The game must be iterated, and players must know—or behave as if they know—that the present encounter will not be their last. The book calls this continuing prospect the “shadow of the future.” If two players know in advance that a game will end after exactly 100 rounds, the last round becomes a one-off Prisoner’s Dilemma, in which each has reason to defect. Once both anticipate defection on round 100, the same reasoning applies to round 99, then round 98, and successively backward through the game. If both are strictly rational and know the fixed endpoint, the reasoning leaves them defecting throughout.

For this reason, the theoretical Repeated Prisoner’s Dilemma assumes that the ending is unpredictable or known only to the banker. Real players may still estimate how near the end is: noticing the banker fidget and look at a watch could make a player suspect that the game is about to stop and feel tempted to defect first. The possibility that the other player has made the same inference adds another layer of strategic uncertainty. Thus, a zero-sum outcome is not simply a property of rivalry; expectations about the endpoint can erode cooperation, while an uncertain future can give reciprocal restraint room to work.