Working Paper: CEPR ID: DP10641
Authors: Daniil Musatov; Alexei Savvateev; Shlomo Weber
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 Codes: D70; H20; H73
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| border indifference property (BIP) (F55) | Nash stable partition (C72) |
| monotonic comparative statics conditions (D50) | Nash stable partition (C72) |
| border indifference property (BIP) (F55) | Nash stability (C62) |