A profile of strategies in a strategic game such that each player's strategy is a best response to the other players' strategies: no single player can increase their payoff by unilaterally changing their own strategy given the others' choices.

Principle

Stability by unilateral optimality: an outcome is an equilibrium if every player, holding others' strategies fixed, has no profitable unilateral deviation.

Demonstration

Illustrative scenario — Situation: Two firms choose Prices simultaneously. Recognition: Given Firm B's price, Firm A computes that any alternative price would lower its profit. Action: Both firms keep their chosen prices. Consequence: The resulting price pair is a Nash equilibrium because neither firm can improve profit by changing price alone.

Misapplication

Assuming a Nash equilibrium guarantees collective optimality or fairness; the error is to conflate non-deviation stability with efficiency—an equilibrium can be Pareto-dominated by another outcome.

Consequence

Provides a predictive and normative tool for noncooperative strategic interaction: equilibria identify strategy profiles that are self-enforcing absent external enforcement, but they do not by themselves resolve multiplicity, selection, or welfare questions.

Reversal

Equilibrium analysis changes when players can form binding agreements (cooperative games), when dynamics, learning, or repeated interaction alter incentives (leading to different equilibrium sets), or when mixed strategies are required because no pure‑strategy equilibrium exists.

Boundary

Applies to strategic-form games with defined players, strategy sets, and payoffs; excludes contexts where binding coalition formation, enforceable contracts, or external enforcement change the strategic structure, and does not by itself prescribe which equilibrium will arise when multiple exist.

Semantic Tension

Prediction ↔ Prescription: Nash equilibrium is a descriptive stability concept that may conflict with normative criteria (efficiency, fairness), creating tension between what self-interested agents will do and what a social planner might prefer.

Synthesis

Nash equilibrium captures non-deviation stability—the minimal requirement for self-enforcement—but interpreting it requires separate analysis of selection, dynamic plausibility, and normative desirability.