Non-emptiness of the alpha-core

We prove non-emptiness of the alpha-core for balanced games with non-ordered preferences, extending and generalizing in several aspects the results of Scarf (1971), Border (1984), Florenzano (1989), Yannelis (1991) and Kajii (1992). In particular we answer an open question in Kajii (1992) regarding the applicability of the non-emptiness results to models with infinite dimensional strategy spaces. We provide two models with Knightian and voting preferences for which the results of Scarf (1971) and Kajii (1992) cannot be applied while our non-emptiness result applies.

Laws of large numbers for non-additive probabilities

We apply the concept of exchangeable random variables to the case of non-additive robability distributions exhibiting ncertainty aversion, and in the lass generated bya convex core convex non-additive probabilities, ith a convex core). We are able to rove two versions of the law of arge numbers (de Finetti's heorems). By making use of two efinitions. of independence we rove two versions of the strong law f large numbers. It turns out that e cannot assure the convergence of he sample averages to a constant. e then modal the case there is a true" probability distribution ehind the successive realizations of the uncertain random variable. In this case convergence occurs. This result is important because it renders true the intuition that it is possible "to learn" the "true" additive distribution behind an uncertain event if one repeatedly observes it (a sufficiently large number of times). We also provide a conjecture regarding the "Iearning" (or updating) process above, and prove a partia I result for the case of Dempster-Shafer updating rule and binomial trials.

Market clearing sealed-bid auctions for non-identical objects with single-unit demands

We consider a version of the cooperative buyer-seller market game of Shapley and Shubik (1972). For this market we propose a c1ass of sealed- bid auctions where objects are sold simultaneously at a market c1earing price rule. We ana1yze the strategic games induced by these mechanisms under the complete information approach. We show that these noncooperative games can be regarded as a competitive process for achieving a cooperative outcome: every Nash equilibrium payoff is a core outcome of the cooperative market game. Precise answers can be given to the strategic questions raised.