journal of economic theory 73, 453459 (1997) Nonemptiness of the Largest Consistent Set* Licun Xue Department of Economics, McGill University, 855 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2T7 Received February 5, 1996; revised June 4, 1996 This article extends Chwe's ( J. Econ. Theory 63 (1994), 299325) nonemptiness result (Proposition 2) of the largest consistent set by relaxing both conditions of his proposition, including the countability of the set of alternatives. Such an extension enables the largest consistent set to be applied to models (e.g., the Cournot oligopoly model) with continuum of alternatives. Journal of Economic Literature Classification Numbers: C70, C71, C72.  1997 Academic Press 1. INTRODUCTION Chwe [1] defined the largest consistent set, a solution concept for social environments where coalitions can freely form without binding agreements, act publicly, and are farsighted. Chwe [1] showed that the largest consistent set is nonempty for a wide range of social environments. This article extends Chwe's nonemptiness result [1, Proposition 2] of the largest consistent set by relaxing both conditions of his proposition, including the countability of the set of alternatives, thereby considerably enlarging the domain where the largest consistent set can be applied. 2. THE LARGEST CONSISTENT SET Consider a social environment with a set of individuals, N, who face a set of alternatives Z. Each individual i # N has a strict preference relation article no. ET962242 453 0022-053197 25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved. * This article is based on an appendix to Chapter 2 of my Ph.D. thesis at McGill University. I thank Professors Joseph Greenberg (my thesis supervisor), Benyamin Shitovitz, and Dov Monderer for guidance and suggestions, and an anonymous referee for valuable comments. Financial support from Social Sciences and Humanities Research Council of Canada through a doctoral fellowship is gratefully acknowledged.