Abstract: This paper develops a new existence result for pure-strategy Nash equilibrium. In succinct form, for a two-player game with scalar action sets, existence entails that one reaction curve be increasing and continuous and the other quasi-increasing (i.e, not have any downward jumps). The latter property amounts to strategic quasi-complementarities. We also prove some extensions to n-player games, at the cost of some further plausible assumptions. Along the way, the paper provides a number of ancillary results of independent interest, including sufficient conditions for a quasi-increasing argmax, comparative statics of equilibria, and new sufficient conditions for uniqueness of fixed points. For maximal accessibility of the results, in addition to a general lattice-theoretic treatment, the main results are presented in a Euclidean setting. We argue that all these results have broad and elementary applicability by providing simple illustrations with four commonly used models from applied microeconomic fields.

报告人简介: Prof Amir is currently the J. Edward Lundy Professor of Economics, and the director of PhD Program in Economics, of University of Iowa. His main research interests are game theory and industrial economics. He has published dozens of influential papers in many first-class economic journals, including Review of Economic Studies, Journal of Economic Theory, Games and Economic Behavior et al. Prof. Amir serves as an associate editor for 10 important journals, including Games and Economic Behavior, International Journal of Industrial Organization, Economic Theory. Prof Amir is a fellow of Society for the Advancement of Economic Theory (SAET) since 2013, and a council member of Game Theory Society since 2015.