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

23 Pages Posted: 1 Jun 2015

See all articles by Daniil Musatov

Daniil Musatov

Moscow Institute of Physics and Technology; New Economic School (NES)

Alexei V. Savvateev

New Economic School (NES); New Economic School, Moscow; Moscow Institute of Physics and Technology

Shlomo Weber

Southern Methodist University (SMU) - Department of Economics; New Economic School

Date Written: May 2015

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: continuity, group formation, increasing differences, market interactions, monotonicity, Nash stability

JEL Classification: D70, H20, H73

Suggested Citation

Musatov, Daniil and Savvateev, Alexei Vladimirovich and Savvateev, Alexei Vladimirovich and Weber, Shlomo, Gale-Nikaido-Debreu and Milgrom-Shannon: Market Interactions with Endogenous Community Structures (May 2015). CEPR Discussion Paper No. DP10641, Available at SSRN: https://ssrn.com/abstract=2613038

Daniil Musatov (Contact Author)

Moscow Institute of Physics and Technology ( email )

Institusky lane, 9
Dolgoprudny, Moskovskaya oblast
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New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026
Russia

Alexei Vladimirovich Savvateev

New Economic School (NES) ( email )

100A Novaya Street
Moscow, Skolkovo 143026
Russia
+7 495 129 17 00, ext 136 (Phone)
+7 495 129 37 22 (Fax)

HOME PAGE: http://www.nes.ru/~savvateev

New Economic School, Moscow ( email )

100A Novaya Street
Moscow, Skolkovo 143026
Russia
+7 495 129 17 00, ext 136 (Phone)
+7 495 129 37 22 (Fax)

HOME PAGE: http://www.nes.ru/~savvateev

Moscow Institute of Physics and Technology ( email )

Institusky lane, 9
Dolgoprudny, Moskovskaya oblast
Russia

Shlomo Weber

Southern Methodist University (SMU) - Department of Economics ( email )

Dallas, TX 75275
United States
214-768-3577 (Phone)
214-768-1821 (Fax)

New Economic School ( email )

Moscow
Russia
+ 7-495-9569508 (Phone)

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