Exploring the importance of stochasticity to Hybrid Equilibria in a Discrete Signaling Game.

Communication via evolved signals is ubiquitous (both within and between species) in the natural world. However, how honest we should expect signals to be remains an open question. Hybrid equilibria are a form of equilibria predicted by discrete signaling games in which signalers are sometimes dishonest and signals do not completely reliably convey information on signaler quality. While these equilibria have been theoretically demonstrated in several signaling games, their dynamics in a stochastic simulation of evolutionary trajectories (that include representation of the inherent noise expected in evolution in the natural world) have not previously been studied. In this paper, we present an agent-based simulation of a discrete signaling game which exhibits hybrid equilibria. We find that while hybrid equilibria are evolutionarily attractive where they exist, populations exhibit variable and often drastic oscillating behavior around the predicted equilibrium values. We discuss how these dynamics might offer valuable opportunity for detecting hybrid equilibria in natural populations.