Walrasian non-tâtonnement with incomplete and imperfect markets

Static competitive equilibria in economies with incomplete markets are generically constrained suboptimal. Allocations induced by strategic equilibria of imperfectly competitive markets are also generically inefficient. In both cases, there is scope for Pareto-improving amendments. Considering an extension of the limit-price process introduced in Giraud (2004) to the setting of incomplete markets (with infinitely many uncertain states) populated by finitely many players, we show that these two celebrated inefficiency problems can be overcomed when rephrased in a non-tâtonnement process lasting sufficiently long. In our model, traders are myopic and trade financial securities in continuous time, by sending limit-orders in order to select a portfolio that maximizes the (linear) first-order approximation of the conditional expectation of their indirect utility (for assets). We show that financial trade curves converge (in probability) to some interim second-best efficient rest-point unless some miscoordination stops the dynamics at some inefficient, but locally unstable point