Proper equilibrium

Proper equilibrium
A solution concept in game theory
Relationship
Subset of	Trembling hand perfect equilibrium
Significance
Proposed by	Roger B. Myerson

Proper equilibrium is a refinement of Nash Equilibrium due to Roger B. Myerson. Proper equilibrium further refines Reinhard Selten's notion of a trembling hand perfect equilibrium by assuming that more costly trembles are made with significantly smaller probability than less costly ones.

Given a normal form game and a parameter ${\displaystyle \epsilon >0}$, a totally mixed strategy profile ${\displaystyle \sigma }$ is defined to be ${\displaystyle \epsilon }$-proper if, whenever a player has two pure strategies s and s' such that the expected payoff of playing s is smaller than the expected payoff of playing s' (that is ${\displaystyle u(s,\sigma _{-i})<u(s',\sigma _{-i})}$), then the probability assigned to s is at most ${\displaystyle \epsilon }$ times the probability assigned to s'.

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