Noncooperative general exchange with a continuum of traders: Two models

Price formation and trade in a large exchange economy is modelled as a non-atomic strategic game in two contrasting forms. (1) The 'pay-later' form uses paper money or IOUs which the players must redeem at the final accounting or face overdraft penalties. (2) The 'cash-in-advance' form uses a valuable commodity as money with no need for a central clearing house. Several results connecting strategic equilibrium (Cournot-Nash) and competitive equilibrium (Walras) are obtained for (1) and (2). In the final section, a basic problem of measurability when strategies are selected independently by a continuum of agents is raised, and a way of resolving it is proposed.