Dynamical Systems with a Continuum of Randomly Matched Agents

Many models postulate a continuum of agents of finitely many 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. If the random matching process is left unspecified, no "law of large numbers" holds in this framework, casting doubts on the deterministic approximations which are usually informally invoked. This work shows that there exist random matching processes for a continuum of agents satisfying properties which simplify the analysis of the stochastic system. In particular, the evolution of the population frequencies of types is (almost surely) deterministic. Journal of Economic Literature Classification Numbers: C73, C78, D83.