Dynamical Systems with a Continuum of Randomly Matched Agents
Many models postulate a continuum of agents of finitely many different types who are repeatedly randomly matched in pairs to perform certain activities (e.g. play a game) which may in turn make their types change. The random matching process is usually left unspecified, and some Law of Large Numbers is informally invoked to justify a deterministic approximation of the resulting stochastic system. Nevertheless, it is well-know that such laws of large numbers may not hold in this framework. This work shows that there exist random matching processes over a continuum of agents satisfying properties which are sufficient to simplify the analysis of the stochastic system. Moreover, the evolution of the population frequencies of types induced by this system can be described (almost surely) through a set of deterministic equations.
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