Forward-neologism-proof equilibrium and better response dynamics

We study pure perfect Bayesian equilibria in sender-receiver games with finitely many types for the sender. Such equilibria are characterized by incentive compatible (IC) partitions of the sender's types. In the case of ordered types, real-valued decisions and well-behaved utility functions (namely, strictly concave, single-peaked, single-crossing and with an upward bias for the sender), we propose a family of iterative optimization processes that all converge to a unique IC partition Π*. We show that Π* is undefeated in the sense of Mailath et al. (1993). Equivalently, Π* is forward-neologism-proof, a variant of Farrell's (1993) neologism-proof concept that we introduce. While the latter refinement (as many other ones) starts from a putative equilibrium and identifies types that would deviate if they were properly identified by the receiver, our iterative optimization processes take the opposite direction. Starting typically from a completely revealing strategy of the sender, types are gradually pooled as long as some of them envy decisions associated with other types. The process can be interpreted as a better response dynamics.