Global uniqueness and money non-neutrality in a Walrasian dynamics without rational expectations

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 towards Pareto optimal allocations; money has a positive value along each trade curve, except on the optimal rest-point where it becomes a veil while trades vanish. Moreover, generically, given initial conditions, there is a piecewise globally unique trade-and-price curve not only in real, but also in nominal variables. Finally, money is locally neutral in the short-run and non-neutral in the long-run