A Strategic Market Game of a Finite Economy with a Mutual Bank

We introduce a strategic market game for an exchange economy not having enough commodity money. We show the existence of a non-cooperative equilibrium for any finite replication economy with a mutual bank, we then show that efficient trade can be achieved in the limiting economy by expanding the money supply through the use of fractional reserves, where the commodity money is demonetized and used for reserves. The means of exchange becomes bank credit backed in part, by “gold.” However, efficiency can not be achieved in general as a non-cooperative equilibrium of a finite player game or a finite exchange economy.