A basic problem in the theory of noncooperative games is the following: which Nash equilibria are strategically stable, i.e. self-enforcing, and does every game have a strategically stable equilibrium?We list three conditions which seem necessary for strategic stabilitybackwards induction, iterated dominance, and invariance-and define a set-valued equilibrium concept that satisfies all three of them.We prove that every game has at least one such equilibrium set.Also, we show that the departure from the usual notion of single-valued equilibrium is relatively minor, because the sets reduce to points in all generic games.

[This paper is a natural outgrowth of recent studies in markets with a "continuum" of traders. An equivalence theorem for the core of such economies was obtained, under the assumption that the measure space of economic agents is atomless. We introduce a sufficient condition under which the preceding result can be extended to economies containing "atomic" traders. The condition bears on the measure of the atoms.]

‘If empirically meaningful interpersonal comparisons have to be based on indifference maps, as we have argued, then the Independence of Irrelevant Alternatives must be violated. The information which enables us to assert that individual A prefers x to y more strongly than B prefers y to x must be based on comparisons by A and B of x and y not only to each other but also to other alternatives. Kenneth J. Arrow, ‘Social Choice and Individual Values, p. 112. In a framework of preferences over lotteries, we show that an axiom system consisting of weakened versions of Arrow's axioms has a unique solution. ‘Relative Utilitarianism’ consists of first normalizing individual von Neumann-Morgenstern utilities between 0 and 1 and then summing them.

In a differential information economy with quasi–linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints: the associated ex ante core is generically nonempty. However, we exhibit a well–behaved exchange economy in which this core is empty, even if goods are allocated through random mechanisms.