On Stable Equilibria in Discrete-Space Social Interaction Models

Takashi Akamatsu, Shota Fujishima and Yuki Takayama ()

MPRA Paper from University Library of Munich, Germany

Abstract: We investigate the differences and connections between discrete-space and continuous-space social interaction models. Although our class of continuous-space model has a unique equilibrium, we find that discretized models can have multiple equilibria for any degree of discretization, which necessitates a stability analysis of equilibria. We present a general framework for characterizations of equilibria and their stability under a broad class of evolutionary dynamics by using the properties of a potential game. Although the equilibrium population distribution in the continuous space is uniquely given by a symmetric unimodal distribution, we find that such a distribution is not always stable in a discrete space. On the other hand, we also show that any sequence of a discrete-space model's equilibria converges with the continuous-space model's unique equilibrium as the discretization is refined.

Keywords: Social interaction; Agglomeration; Discrete space; Potential game; Stability; Evolutionary game theory (search for similar items in EconPapers)
JEL-codes: C62 C72 C73 D62 R12 (search for similar items in EconPapers)
Date: 2014-05-08
New Economics Papers: this item is included in nep-evo, nep-geo, nep-gth, nep-mic and nep-ure
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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https://mpra.ub.uni-muenchen.de/61184/8/MPRA_paper_61184.pdf revised version (application/pdf)
https://mpra.ub.uni-muenchen.de/65225/16/MPRA_paper_65225.pdf revised version (application/pdf)

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