Gale-Nikaido-Debreu and Milgrom-Shannon: Market Interactions with Endogenous Community Structures

Alexey Savvateev (), Shlomo Weber and Daniil Musatov

No 10641, CEPR Discussion Papers from C.E.P.R. Discussion Papers

Abstract: This paper examines a model of market interactions with a continuum of agents whose characteristics are distributed over the unidimensional interval. The society is endogenously partitioned into several communities, whose members are engaged in costly market interactions. The interaction or communication costs between every pair of agents depend on their identity and the size and composition of community to which they belong. By using the celebrated Gale-Nikaido-Debreu Lemma and invoking the Kantorovich continuity over agents' distributions, we prove that there exists a partition of the society into a given number of connected intervals which satisfies the Border Indifference Property (BIP). Namely, individuals on the border of each community are indifferent between joining either of the adjacent communities. We demonstrate that while BIP does not, in general, yield Nash equilibria, the equilibrium existence is erescued under the Milgrom-Shannon (1994) monotone comparative statics conditions.

Keywords: Nash stability; Continuity; Increasing differences; Monotonicity; Group formation; Market interactions (search for similar items in EconPapers)
JEL-codes: D70 H20 H73 (search for similar items in EconPapers)
Date: 2015-05
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