Local Independence, Monotonicity and Axiomatic Characterization of Price-Money Message Mechanism

To characterize money in a static economic model, it is known to be important to consider the agent- commodity double-in nity settings, i.e., the overlapping-generations framework. There does not seem to exist any papers, however, treating the axiomatic characterization problems for such monetary Walras allocations under the social choice and/or mechanism design settings. We show that the monetary Walras allocation for the economy with double in nities is characterized by weak Pareto- optimality, individual rationality, local independence or the monotonicity conditions of social choice correspondence among the allocation mechanisms with messages under the category theoretic approach in Sonnenschein (1974). We utilize Sonnenschein's market extension axiom for swamped economies that is closely related to the replica stability axiom of Thomson (1988). We can see how these conditions characterize the price-money message mechanism universally among a wide class of mechanisms, and efficiently in the sense that it has the minimal message spaces (price-money dictionary theorems). Moreover, by using the category theoretic framework, we can obtain the up-to-isomorphism uniqueness for such a dictionary object (isomorphism theorems).