Noisy Convention Selection with Local Interaction

Stochastic evolutionary processes can be used to determine which equilibrium a society selects, but expected waiting times for the transition to such an equilibrium can be fantastically large. Waiting times are reduced if interaction is predominantly local or if the selection process is very noisy. This article uses simulation to study waiting times when interaction is local and selection is noisy simultaneously. Waiting times fall significantly, and increases in population size do not necessarily lead to increased waiting times. The form of local interaction is shown to be important to the effect on waiting times. The key to the speed of overall convergence is the speed of convergence of the first subgroup. Applications to the problem of convention selection rely on more frequent mistakes in learning, which weakens the selection result. The selection result is also weakened by local interaction.