Reflective Reason and Equilibrium Refinements
If we allow that human life can be governed by reason, the possibil-
ity of life is annihilated.
If one weight is twice another, it will take half as long to fall over a
Aristotle, On the Heavens
In previous chapters, we have stressed the need for a social epistemology to account for the behavior of rational agents in complex social interactions. However, there are many relatively simple interactions in which we can use some form of reflective reason to infer how individuals will play. Since reflective reason is open to the players as well as to us, in such cases we expect Nash equilibria to result from play. However, in many cases there are a plethora of Nash equilibria, only some of which will be played by reasonable agents.
A Nash equilibrium refinement of an extensive form game is a criterion that applies to all Nash equilibria that are deemed reasonable but fails to apply to other Nash equilibria that are deemed unreasonable, based on our informal understanding of how rational individuals might play the game. A voluminous literature has developed in search of an adequate equilibrium refinement criterion. A number of criteria have been proposed, including subgame perfect, perfect, perfect Bayesian, sequential, and proper equilibrium (Harsanyi 1967; Myerson 1978; Selten 1980; Kreps and Wilson 1982; Kohlberg and Mertens 1986), which introduce player error, model beliefs off the path of play, and investigate the limiting behavior of perturbed systems as deviations from equilibrium play go to zero.1
I present a new refinement criterion that better captures our intuitions and elucidates the criteria we use implicitly to judge a Nash equilibrium as reasonable or unreasonable. The criterion does not depend on counterfactual
1 Distinct categories of equilibrium refinement for normal-form games, not addressed
in this chapter, are focal point (Schelling 1960; Binmore and Samuelson 2006), and risk
dominance (Harsanyi and Selten 1988) criteria. The perfection and sequential criteria are
virtually coextensive (Blume and Zame 1994) and extend the subgame perfection criterion.