www.vanderbilt.edu/econ Existence of equilibrium with unbounded short sales: A new approach ∗

We introduce a new approach to showing existence of equilibrium in models of economies with unbounded short sales. Inspired by the pioneering works of Hart (1974) on asset market models, Grandmont (1977) on temporary economic equilibrium, and of Werner (1987) on general equilibrium exchange economies, all papers known to us stating conditions for existence of equilibrium with unbounded short sales place conditions on recession cones of agents ’ preferred sets or, more recently, require compactness of the utility possibilities set.. In contrast, in this paper, we place conditions on the preferred sets themselves. Roughly, our condition is that the sum of the weakly preferred sets is a closed set. We demonstrate that our condition implies existence of equilibrium. In addition to our main theorem, we present two theoremsshowingcasestowhichour main theorem can we applied. We also relate our condition to the classic condition of Hart (1974). ∗We are pleased to dedicate this paper to Cuong Le Van, a great economist and a wonderful friend. Without the hospitality of the Centre for Economics of the Sorbonne, whose first Director was Professor Le Van, and the hospitality of CERMSEM and Paris 1 the idea of this paper would probably not have happened. It was sitting outside a cafe across the street from the Maison des Sciences Economiques that one the authors of this paper raised the question of "why not assumptions simply on preferred sets " and another author took up the idea. We are honored to have benefitted from Cuong Le Van’s intellectual generosity and to advance a line of research to which he has been one of the main contributors. We would also like to thank Nizar Allouch for comments and the participants at the Paris conference in honor of Cuong Le Van, December 2011. 1

Condorcet domains of tiling type

A Condorcet domain (CD) is a collection of linear orders on a set of candidates satisfying the following property: for any choice of preferences of voters from this collection, a simple majority rule does not yield cycles. We propose a method of constructing "large" CDs by use of rhombus tiling diagrams and explain that this method unifies several constructions of CDs known earlier. Finally, we show that three conjectures on the maximal sizes of those CDs are, in fact, equivalent and provide a counterexample to them.Comment: 16 pages. To appear in Discrete Applied Mathematic