Mean-Field Approximation of Forward-Looking Population Dynamics

 We consider equilibrium dynamics under  large finite population games and examine how they can be approximated by a continuum-population model.  New agents stochastically  arrive and make irreversible action choices for stochastic length of durations. The key assumption is they only observe imperfect signals about the action distribution in the population.  We first show that the process of action distribution can be approximated by its mean-field  dynamics, uniformly across all
equilibrium strategies. Based on this, we establish continuity properties of equilibria as the population size goes to infinity. In particular, this implies that each agent almost ignores the effect of her action when the population size is large, as in the continuum-population model. Finally, focusing on  binary-action supermodular games, we show that there is a unique equilibrium when the observational noise is small and agents are patient.

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