Comparative statics in a simple class of strategic market games

This paper investigates the e¤ects of entry in two-sided markets where buyers and sellers act strategically. Applying new tools from supermodular optimization/games, su¢ cient conditions for di¤erent comparative statics results are obtained. While normality of one good is su¢ cient for the equilibrium price to be increasing in the number of buyers, normality of both goods is required for equilibrium bids and sellers’equilibrium utilities to be increasing in the number of buyers. When the economy is replicated, normality of both goods and gross substitutes guarantee that the equilibrium of the strategic market game converges monotonically (in quantities) to the competitive equilibrium. Simple counter-examples are provided to settle other potential conjectures of interest. jel: D43, D51, L13 keywords: Strategic market games, two-sided markets, bilateral oligopoly, supermodularity and comparative statics, market entry. We are grateful to an anonymous referee of this Journal, Stefano Demichelis, Jean-Francois Mertens and Ben Zissimos for helpful suggestions and/or feedback. Thanks also go to participants of the workshop in honor of Jean Gabszewicz (CORE, Louvain-la-Neuve, 2002) and of the VIth SAET Meeting (Rhodos, 2003) for their comments. yDepartment of Economics, University of Arizona, Tucson, AZ 85721 (E-mail: [email protected]) zGREQAM, Aix-Marseille Universités. (E-mail:[email protected]) Francis Bloch is also a¢ liated with the University of Warwick.