Modeling convention emergence by observation with memorization

Abstract

Convention emergence studies how global convention arises from local interactions among agents. Traditionally, the studies on convention emergence are conducted by means of agent-based simulations, whereas very few studies are based on model-based approaches. In this paper, we employ model-based approach to study the convention emergence by observation with memorization in a large population under social learning. In particular, we derive the recurrence equations of the population dynamic, which is the evolution of action distribution over time, under the external majority (EM) strategy. The recurrence equations precisely predict the behaviour of the multi-agent system at any time point, which is verified with the agent-based simulations. Based on the recurrence equations, We prove the converge behavior under various situations and work out the optimal memory length under different number of actions. Finally, we show that the EM strategy outperforms other popular strategies such as Q-learning and Highest Cumulative Reward (HCR) in convergence speed under social learning, even in very large convention space.