An act maps states of nature to outcomes: deterministic outcomes, as well as random outcomes, are included. Two acts f and g are comonotonic, by definition, if it never happens that f(s) > f(t) and g(t) > g(s) for some states of nature s and t. An axiom of comonotonic independence is introduced here. It weakens the von Neumann-Morgenstern axiom of independence as follows: If f > g and if f, g and h are comonotonic then $f + (1 - $)h > $g + (1 - $)h. If a nondegenerate, continuous, and monotonic (state independent) weak order over acts satisfies comonotonic independence, then it induces a unique non-(necessarily-) additive probability and a von Neumann-Morgenstern utility. Furthermore, one can compute the expected utility of an act with respect to the nonadditive probability, using the Choquet integral. This extension of the expected utility theory covers situations, such as the Ellsberg paradox, which are inconsistent with additive expected utility. The concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included. Copyright 1989 by The Econometric Society.(This abstract was borrowed from another version of this item.)

[This note provides a rigorous description of a game in a strategic form whose Nash equilibria are all strong equilibriaccoinciding with the Walras equilibria of the underlying Arrow-Breau pure exchange economy.]

In an atomless economy any allocation that is not blocked by coalitions is in the core. Hence, in such an economy, a competitive equilibrium is characterized by the blocking power of part of the coalitions which excludes all big coalitions. THE CORE of an economy consists of all the allocations that are not blocked by any coalition. In this note we prove that for any positive number 8, the core of an atomless economy coincides with the set of allocations that are not blocked by any coalition of measure less than s. This result implies that even if the large coalitions cannot be formed, any unblocked allocation is still in equilibrium with respect to some price system. In particular, the formation of the coalition of all traders or any large coalition is not needed to insure the Pareto-optimality of final allocation. We prove here directly that the core is equal to the set of allocations that are not blocked by small coalitions. The same result can also be obtained by proving that Aumann's [1], Vind's [5], or Hildenbrand's [2] equivalence theorems hold with the additional restriction on the measure of the blocking coalitions. In any case the proof is a simple application of Liapunov's convexity theorem [3 and 4] (for the statement of the theorem see also [2, Appendix, p. 451]).

It is shown that a market with a continuum of traders possesses a competitive equilibrium even when the preferences are not complete. This generalizes further a result of Aumann, ('Econometrica'; 32: 39-50 (1964); 34: 1-17(1966)) who showed that the convexity assumption may be dispensed within the presence of a continuum of traders. The proof is inspired by the Arrow-Debreu ('Econometrica; 22: 265-290(1954)) proof for the finite case. (Author)

Recent formulations of social decisions problems focus on rules by which a group of individuals (the society) arrives at a choice among available alternatives. Such a rule, which we shall call the outcome function (Gibbard's "game form, " see [ 3 J), specifies the

Elisha A. Pazner, David Schmeidler; A Difficulty in the Concept of Fairness12, The Review of Economic Studies, Volume 41, Issue 3, 1 July 1974, Pages 441–443, h