Refinements and Selection

Original article (link) posted: 25/07/2005

Myerson (1991) mentions the distinction between equilibrium refinements and criteria for selection among the set of equilibria.

A refinement of Nash equilibria is a solution concept that is intended to offer a more accurate characterization of rational intelligent behavior in games. However, the ultimate refinement that exactly characterizes rational behavior can still include multiple equilibria for many games. (e.g., the Battle of the Sexes)
A selection criterion is then any objective standard, defined in terms of the given structure of the mathematical game, that can be used to determine the focal equilibrium that everyone expects. Equity and efficiency criteria of cooperative game theory can be understood as such selection criteria.

(p. 241)

According to him, the concept of "cheap-talk" should be considered as an equilibrium selection criterion (NOT as a refinement), because it is based on the assumption that players share a rich natural language for communication, and hence rational and intelligent players may not reach that equilibrium without some cultural environment.

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