Equilibrium Points in N-Person Games.

Nash, J. F. (1950). Equilibrium Points in N-Person Games. Proceedings of the National Academy of Sciences, 36(1), 48-49.

Type

Journal article

Intellectual base

Primary research

Year

1950

DOI

10.1073/pnas.36.1.48

Link

https://doi.org/10.1073/pnas.36.1.48

Cited from

biology_ecology, economics_finance, information_theory, mathematics, physics

Cited by

7 citations across 7 artifacts.

Each citation links to the sentence it supports in the citing article.

Primes

• Competition
  • Treating every interaction as zero-sum competition is a common misreading — the prime identifies where negative coupling exists, not that it exists everywhere.

    This sourceFirst appearance of the existence theorem for the Nash equilibrium: every finite n-person game — including non-cooperative, non-zero-sum games — has an equilibrium in mixed strategies, establishing that strategic structure (not just zero-sum rivalry) determines stable outcomes and that non-zero-sum settings form a well-defined family.

• Equilibrium
  • Not stasis. Dynamic equilibrium (a chemical reaction, a steady-state ecosystem, a market at price-clearing) involves vigorous activity; only the net on the balanced dimension is zero. Not optimality. An equilibrium is a balance point, not necessarily a good one. Nash equilibria in non-cooperative games

    This sourceThe originating existence theorem — every finite game has an equilibrium in mixed strategies — for the Nash equilibrium, a profile in which no player gains by a unilateral deviation.

• Fixed Point
  • Take a Cournot duopoly: the state space is the pair of output quantities (q1, q2); the self-map sends each firm's quantity to its profit- maximizing best response given the other's current quantity; a fixed state is a pair where neither firm wants to change — a Nash equilibrium, self-consistency under the best-response update.

    This sourceProves existence of Nash equilibrium as a fixed point of the best-response correspondence, via a fixed-point theorem.

• Game-Theoretic Strategy
  • … the strategy type: pure (one action per information set), mixed (a probability distribution over pure strategies), behavioural (independent randomisation at each information set), or correlated (joint randomisation through a public signal); (3) the solution concept that justifies the strategy — Nash equilibrium

    This sourceThe single most-cited solution concept in game theory and the foundation for nearly all subsequent equilibrium analysis.)

• Nash Equilibrium
  • The deep structural fact is that interdependent rational choice under common knowledge has fixed-point solutions — guaranteed to exist in any finite game once mixed strategies are admitted, by a fixed-point argument.

    This sourceProves that every finite game has at least one equilibrium point in mixed strategies via a fixed-point argument — the existence theorem.

• Social Dilemma
  • It separates two outcomes (mutual cooperation and mutual defection), specifies that the worse one is the only one self-interested play can reach, and names the wedge between private optimization and joint welfare that makes the failure structural rather than accidental.

    This sourceThe single most-cited solution concept in game theory and the foundation for nearly all subsequent equilibrium analysis.)

Domain-specific

• Nash equilibrium computation
  • Nash-equilibrium computation turns the equilibrium existence concept into a search problem with representation- and approximation-sensitive complexity.

Verification

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