On the observational equivalence of random matching

Random matching is often used in economic models as a means of introducing uncertainty in sequential decision problems. We show that random matching processes that satisfy standard proportionality laws are not unique. We give conditions on the payoffs and transition functions of sequential decision models that insure that economic models are robust to the nonuniqueness of the matching process. Under these conditions, the information contained in the proportionality laws is all that is needed to know about the matching process to formulate the model.