An individual with known preferences over lotteries can be led to accept random wealth distributions different from his initial endowment by a sequential process in which some uncertainty is resolved and he is offered a new lottery in place of the remaining uncertainty. This paper examines the restrictions that can be placed on an individual's preferences by axioms that stipulate that such a process not be able to generate a new wealth distribution that is prima facie inferior to the original. The relationship of these axioms to the independence axiom of von Neumann and Morgenstern and to the quasi convexity of preferences in the wealth distribution are explored.

When a decision rule is implemented using a Bayesian incentive compatible mechanism in which the messages are publically obser vable, the players' information is augmented by their observation of each others' strategies. In this paper the authors study the set of Bayesian implementable decision rules which have the further property that the information c onveyed in the process of thier implementation does not invalidate the optimality of the players' strategies. Such rules are called posterior implementable. The authors concentrate on a two-person problem with two possible decisions and, for this problem, they obtain a complete characterization of the set of posterior implementable decision rules.