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.
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Vives, X. (2018). Supermodularity and Supermodular Games. In: The New Palgrave Dictionary of Economics. Palgrave Macmillan, London. https://doi.org/10.1057/978-1-349-95189-5_2443
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DOI: https://doi.org/10.1057/978-1-349-95189-5_2443
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