How much ambiguity can persist? A complete characterization of neutrally stable states for an evolutionary proto-language game

In an evolutionary sender–receiver game that describes how signals become associated with objects (Hurford, 1989; Nowak and Krakauer, 1999), the set of evolutionarily stable states coincides with the set of strict Nash strategies—and a language is a strict Nash strategy if and only if it links each possible referent exclusively to 1 signal and vice versa (Trapa and Nowak, 2000). As a consequence, a language that displays homonymy (or synonymy)—the property that one signal is linked to more than one referent (or one referent to more than one signal)—cannot be an evolutionarily stable state. This seems to conflict with the results of the computer simulation reported in Nowak and Krakauer (1999) that lend support to the conjecture that a language in which the same signal is used for more than one object can be evolutionarily stable. This paper provides necessary and suffcient conditions for a neutrally stable state of this game—and, importantly, these conditions directly characterize a single strategy—showing that a language displaying homonymy or synonymy, even though it fails to be evolutionarily stable (in the strict sense), may still satisfy neutral stability, explaining why an evolutionary process does not necessarily lead away from it.