Many standard solution concepts rule out those Nash equilibria that are susceptible to deviations. We propose a framework for considering not only which equilibria are not susceptible to deviations, but also which equilibria are likely to persist in the long run because they are repeatedly deviated to. We call such equilibria recurrent. We explore which equilibria are recurrent based on the deviations underlying each of several prominent signaling refinements. We show that the set of recurrent equilibria based on Cho and Krep's (1987) intuitive criterion and Kohlberg and Mertens's (1986) NWBR criterion are precisely what those papers already predict. In contrast, we show that applying our framework to cheap-talk refinements proposed by Farrell (1993) and Matthews, Okuno-Fujiwara, and Postlewaite (1991) can 1) make those solution concepts more realistic, 2) guarantee existence, and 3) guarantee meaningful communication in at least one class of games where it is not guaranteed by either Farrell or MOP.
