Working Papers

Sender–receiver models in the style of Lewis (1969), Hurford (1989), or Nowak and Krakauer (1999) can be used to explain meaning of signals in situations of cooperative interaction. This paper provides a complete characterization of neutrally stable strategies of this game purely in terms of properties of the lexical matrices that agents use for sending and receiving messages. It is show that in a neutrally stable strategy there can be instances of both homonymy and synonymy as long as the degree of ambiguity is not too high. There be two (or more) events that are linked to the same signal or two (or more) signals that are linked to the same event, but there cannot be two (or more) signals that are linked to two (or more) events in parallel, and there cannot be no signal that remains idle in the presence of an event that is never possibly inferred. This has considerable consequences for the regularity patterns of the signaling system that can be explained to arise from a replicator dynamics in a population of individual agents. Building on a result by Bomze (2002) it can be shown that such an evolutionary dynamics does not necessarily lead to an optimal signaling system, but that it can be trapped in suboptimal situations, where due to ambiguous event–signal relations some of the potential of communication is left unexploited.