Strategic stability of equilibria in multi-sender signaling games

Competition in Signaling

“…Bagwell and Ramey (1991) introduce the concept of "unprejudiced beliefs," which formalize the idea that the decision maker should rule out the possibility that multiple senders are deviating at the same time whenever it is possible that only a single sender is deviating. Vida and Honryo (2019) show that, in generic multi-sender signaling games, strategic stability (Kohlberg & Mertens, 1986) implies unprejudiced beliefs. Apart from their association with the notion of strategic stability, unprejudiced beliefs are intuitive, easily applicable, and consistent with the notion of Nash equilibrium and, as such, constitute a sensible way to refine equilibria in multi-sender signaling games when other criteria fail to do so.…”

“…The following definition formalizes unprejudiced beliefs. 20 Definition 2 (Vida & Honryo, 2019). Given senders' strategies ρ j , the decision maker's posterior beliefs p are unprejudiced if, for every pair of reports (r 1 , r 2 ) such that ρ j (θ ) = r j for some θ ∈ Θ and j ∈ {1, 2}, we have that p(θ |r 1 , r 2 ) > 0 only if there is a sender…”

The Insurance Is the Lemon: Failing to Index Contracts

“…This kind of multiplicity is common in multi-sender signaling games (in our context, each lender is sending a signal about the common type). For this reason, we employ two refinements, unprejudiced beliefs and D1, in the spirit of common practice in the literature on multi-sender signaling games (Vida and Honryo (2019)). 17…”

“…In our setting, the intuitive criterion has no bite, but D1, which is a similar but stronger refinement, does. As noted byVida and Honryo (2019), unprejudiced beliefs, the intuitive criterion, and D1 are all related to strategic stability(Kohlberg and Mertens (1986)); however, we are not aware of any other papers that have applied unprejudiced beliefs and D1 simultaneously.…”

“…As discussed byVida and Honryo (2019), it is common in multi-sender signaling games to require that equilibria satisfy both unprejudiced beliefs and the intuitive criterion ofCho and Kreps (1987). Unprejudiced beliefs allows the receiver to identify the deviating sender, and the intuitive criterion, usually applied in single-sender games, is applied to this deviating sender.…”