Nash equilibrium
Let an agent explain Nash equilibrium, relay definitions, existence, refinements and applications from game theory and economics sources, describe the named concepts, and distinguish Nash equilibrium from Pareto optimality, dominant strategy equilibrium, minimax solutions and social optimum.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain Nash equilibrium, relay definitions, existence, refinements and applications from game theory and economics sources, describe the named concepts, and distinguish Nash equilibrium from Pareto optimality, dominant strategy equilibrium, minimax solutions and social optimum.
A solution concept in game theory, introduced by John Nash in 1950 and 1951, in which no player can improve their payoff by unilaterally changing strategy given the other players strategies, existing in mixed strategies for every finite game, with refinements and related concepts the registry aliases name such as pure strategy Nash equilibria, subgame perfect equilibrium introduced by Reinhard Selten, evolutionarily stable strategies from John Maynard Smith and George Price, and zero-sum and strictly determined games, where von Neumann s minimax theorem applies; Nash, Selten and Harsanyi shared the 1994 Nobel memorial prize in economics.
What it is for: Predicting stable outcomes in strategic interactions.
It can be explain the concept; relay existence and refinements; describe named concepts; distinguish related solution concepts.
Distinguishing features
No unilateral gain
Mixed strategy existence
May be inefficient
Many refinements
What it looks like
Not a visible object; shown as highlighted cells in payoff matrices.
Physical character
Nash s thesis: 1950 year
von Neumann minimax theorem: 1928 year
Nobel memorial prize: 1994 year - Nash, Harsanyi, Selten
How it is recognised
Strategy profile with no profitable unilateral deviation
Zero-sum game, finite two-player zero-sum game, strictly determined game, evolutionarily stable strategy, pure strategy Nash equilibrium, subgame perfect equilibrium
Pareto optimality maximises joint welfare; dominant strategies are best regardless; minimax applies to zero-sum; social optimum may differ
Related models
is a kind of - in registry terms
was introduced by -
includes - as a refinement
is contrasted with -
In practice
Families and kinds
pure and mixed strategy equilibria
subgame perfect equilibria
Bayesian Nash equilibria
evolutionarily stable strategies
minimax solutions of zero-sum games
Standards and regulation
No regulation; used in competition and auction policy analysis
Failure modes and hazards
Assuming equilibria are socially optimal
Ignoring multiple equilibria
Overapplying rationality assumptions
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Understand What a Nash equilibrium is.
Science.
Definition
Definition.
Definition
Definition.
- What is a Nash equilibrium, and how does it differ from Pareto optimality, dominant strategies, minimax and social optimum? definition
- Is the question about maths, economics, biology or a specific game? boundary
Named
Named concepts.
Named
Named.
- What are zero-sum and strictly determined games, ESS, pure strategy and subgame perfect equilibria? definition
- Which entry fits the specific concept? action
Theory Theory.
Science.
Existence
Existence.
Existence
Existence.
- Why does every finite game have a mixed strategy equilibrium? provenance
- Which references are standard? provenance
Refinements
Refinements.
Refinements
Refinements.
- Why were refinements such as subgame perfection introduced? provenance
- Which sources are cited? provenance
Applications Applications.
Attribution.
Economics
Economics.
Economics
Economics.
- How is Nash equilibrium used in oligopoly, auctions and bargaining? provenance
- Which entry fits Cournot competition? action
Biology
Evolutionary game theory.
Biology
Biology.
- How do evolutionarily stable strategies apply to animal behaviour? provenance
- Which entry fits evolutionary game theory? action
Context Examples and critiques.
Context.
Dilemma
Prisoner s dilemma.
Dilemma
Dilemma.
- Why is mutual defection a Nash equilibrium in the prisoner s dilemma? provenance
- Which entry fits prisoner s dilemma? action
Behaviour
Behavioural critiques.
Behaviour
Behaviour.
- What do experiments show about when people play Nash equilibria, with findings attributed? provenance
- Which entry fits behavioral game theory? action
What the second pass must settle
- Should the named refinements be separate entries?
- How should game theory sources be linked?
- How should behavioural critiques be presented?