Evolution of Conventions in Uncertain Environments

We study the role of uncertainty in the evolution of conventions in coordination games when agents are myopic best responders. We introduce uncertainty of the choice environment by means of an ergodic Markov process ruling the switching across a collection of 2-player symmetric coordination games with the same strategy sets but different payoffs, referred to as scenarios. We apply stochastic stability analysis to study long run equilibria when there are multiple scenarios. We show that the stochastically stable states may be entirely determined by scenarios that are played rarely, so changing dramatically predictions based exclusively on the most likely scenarios. Moreover, we show that the error model determines which scenarios play such crucial role, indicating that any abstraction from low probability scenarios should be evaluated in the light of the considered error model. Finally, we show how to compute radii and coradii of a convention in this setup