IN THIS NOTE, we present a stochastic adjustment process which has nice optimality and (probablistic) dynamic stability properties for a large class of economic environments. In addition, the process relies on a strikingly simple information exchange procedure at each iteration. It can also be termed as strongly locally individually incentive compatible2 in that each consumer agent has no incentive to lie about his preferences provided he is concerned only with maximization of one-step expected utility gain at each iteration. The obvious source of inspiration for this process is the stochastic decentralized resource allocation mechanism (the B process) by Hurwicz, Radner, and Reiter [2]. Indeed, it should be regarded as the latter's informationally simplified descendent. For general background information on resource allocation mechanisms and motivations for designing such mechanisms, see Hurwicz, Radner, and Reiter [2] and Hahn [1]. In order to simplify the exposition, we present the process only for the case of pure exchange economies with possible consumption externalities. For more general cases, see Mitsui [4]. Mitsui [4] also constructs a core-convergent version of the process.