We define a non-tâtonnement dynamics in continuous-time for pure-exchange economies with outside and inside fiat money. Traders are myopic, face a cash-in-advance constraint and play dominant strategies in a short-run monetary strategic market game involving the limit-price mechanism. The profits of the Bank are redistributed to its private shareholders, but they can use them to pay their own debts only in the next period. Provided there is enough inside money, monetary trade curves converge ...