title: Dynamics in atomic signaling games.
abstract: We study an atomic signaling game under stochastic evolutionary dynamics. There are a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss.
authors: School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
authors: Michael J
authors: MJ
authors: Fox
authors: School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
authors: Behrouz
authors: B
authors: Touri
authors: School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA; CEMSE Division, King Abdullah University of Science and Technology, Thuwal, Kingdom of Saudi Arabia. Electronic address: shamma@gatech.edu.
authors: Jeff S
authors: JS
authors: Shamma
mesh_terms: D005716:Game Theory; D008954:Models, Biological; D015398:Signal Transduction
keywords: Game theory; Language evolution; Signaling; Stochastic stability