journal of economic theory 73, 183198 (1997) Comparative Statics of Fixed Points* J. Miguel Villas-Boas Haas School of Business, University of California at Berkeley, Berkeley, California 94720-1900 Received March 17, 1993; revised March 28, 1996 Comparing fixed points of different mappings is often required when doing economic analysis. I present here some results on the comparison of fixed points of different mappings that generalize and have as a particular case the super- modularity results on the same topic. The main result is that if we take a certain order  for which the mappings are increasing and ordered, then the fixed points of the different mappings are also ordered in that same order: every fixed point of a lower (higher) mapping has at least one higher (lower) fixed point in a higher (lower) mapping. These results allow us, for example, to make comparisons among equilibria of Cournot games with any number of firms, which were not possible under the supermodularity results. Journal of Economic Literature Classification Numbers: C62, C70, L13.  1997 Academic Press 1. INTRODUCTION Comparing equilibria of different games is essential in many areas of economic analysis. It is often crucial to know how the outcome of a model changes when some of its parameters are altered. These comparative statics can sometimes be implemented by direct computation, but, in many cases, a more general and powerful tool can prove very useful. Several authors have recently presented techniques for comparing equi- libria of supermodular games (for example, [3, 5, 7, 9, 10, 12]). In this paper, I present a generalization of the supermodularity results to other types of games where supermodularity is no longer an essential component of the analysis. The supermodularity results can only be stated in terms of the componentwise order, while here I present results for any order. I also present an application of the results to an example for which the supermodularity results do not apply. The example is given by Cournot competition with any number of firms. In this example, the super- modularity results only apply for the particular case in which there are two article no. ET962224 183 0022-053197 25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved. * I am grateful to Drew Fudenberg, Ben Hermalin, Andreu Mas-Colell, Jorge-Nuno Silva, Birger Wernerfelt, and Jeff Zwiebel for helpful comments on an earlier version of this paper. All remaining errors are my responsibility alone.