nonzerosum

Nonzero-sum, or nonzero-sum game, is a concept in game theory describing strategic interactions among two or more players in which the sum of payoffs is not constant. In such games, a gain by one player does not necessarily imply an equivalent loss by another, and there can be mutually beneficial outcomes where cooperation leads to higher payoffs for all participants.

Formal representation of a nonzero-sum game uses the usual normal-form framework: a set of players, a set of possible actions for each player, and payoff functions for each player. The key distinction is that the total payoff across all players for a given outcome is not fixed, allowing combinations of outcomes where at least one player can improve without making others worse off, or where several players can jointly improve.

Examples often cited include the Prisoner's Dilemma, which illustrates how cooperation can yield higher collective payoffs even though defection may appear individually rational, as well as coordination games like Battle of the Sexes and various public goods games. These examples show how outcomes can be Pareto superior to others, meaning at least one player is better off without making anyone worse off.

Implications of nonzero-sum interactions include the possibility of cooperation, bargaining, and coalition formation, alongside incentives to defect or free-ride. Analyzing such games typically involves concepts like Nash equilibria, Pareto efficiency, and potential for mutual gains, as well as considerations from cooperative game theory in some contexts.

Applications span economics, political science, biology, and computer science, particularly in settings with multiple agents whose interests partially align or conflict.