Epsilon-equilibrium

Epsilon-equilibrium
A solution concept in game theory
Relationship
Superset of	Nash Equilibrium
Significance
Used for

In game theory, an epsilon-equilibrium, or near-Nash equilibrium, is a strategy profile that approximately satisfies the condition of Nash equilibrium. In a Nash equilibrium, no player has an incentive to change his behavior. In an approximate Nash equilibrium, this requirement is weakened to allow the possibility that a player may have a small incentive to do something different. This may still be considered an adequate solution concept, assuming for example status quo bias. This solution concept may be preferred to Nash equilibrium due to being easier to compute, or alternatively due to the possibility that in games of more than 2 players, the probabilities involved in an exact Nash equilibrium need not be rational numbers.

There is more than one alternative definition.

Given a game and a real non-negative parameter ${\displaystyle \varepsilon }$, a strategy profile is said to be an ${\displaystyle \varepsilon }$-equilibrium if it is not possible for any player to gain more than ${\displaystyle \varepsilon }$ in expected payoff by unilaterally deviating from his strategy. Every Nash Equilibrium is equivalent to an ${\displaystyle \varepsilon }$-equilibrium where ${\displaystyle \varepsilon =0}$.

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