Supermodularity and Complementarity in Economics: An Elementary Survey

Abstract

The literature on supermodular optimization and games is surveyed from the per- spective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analy- sis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of one- dimensional parameter and actions sets, with the emphasis being on wide accessibil- ity. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R§D, search and matching. Wherever appropriate, useful tricks for applications and comparative com- ments are inserted.