The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Supermodularity and Supermodular Games

  • Xavier Vives
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_2443

Abstract

The mathematical concept of supermodularity formalizes the idea of complementarity and opens the way for a rigorous treatment of monotone comparative statics and games with strategic complementarities. The approach is based on lattice methods and provides conditions under which optimal solutions to optimization problems change in a monotone way with a parameter. The theory of supermodular games exploits order properties to ensure that the best response of a player to the actions of rivals is increasing in their level. It yields strong results that apply to a wide range of games including dynamic games and games of incomplete information.

Keywords

Assortative matching Bertrand oligopoly Comparative statics Complementarity Correspondence principle Cournot competition Existence of equilibrium Global games Incomplete information games Indivisibilities Kakutani’s fixed point th Leontieff utility function Mixed strategy outcomes Monotone comparative statics Multiple equilibria Patent races Stochastic dominance Strategic complementarities Strategic substitutability Supermodular games Supermodularity Tarski’s fixed point th 
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© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Xavier Vives
    • 1
  1. 1.