MathLiveNash equilibrium condition
A strategy profile is a Nash equilibrium when no player can increase their payoff by unilaterally changing their own strategy, given the others' equilibrium strategies. The inequality checks this for every player and every alternative strategy.
\forall i,\; x_i \in S_i:\; f_i(x^*_i, x^*_{-i}) \geq f_i(x_i, x^*_{-i})What the symbols mean
| index of a player | |
| an alternative strategy available to player i | |
| strategy set of player i | |
| equilibrium strategy of player i | |
| equilibrium strategies of all players other than i | |
| payoff function of player i |
About this formula
- FieldMathematics
- TopicGame theory
- LevelUniversity
- Also calledNash equilibrium, Nash solution, best response condition, non-cooperative game equilibrium, Nash equilibrium definition, no profitable unilateral deviation
- SourceWikidata Q23389
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