On Stable Equilibria in Discrete-Space Social Interaction Models

Akamatsu, Takashi and Fujishima, Shota and Takayama, Yuki (2014): On Stable Equilibria in Discrete-Space Social Interaction Models.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Social interaction; Agglomeration; Discrete space; Potential game; Stability; Evolutionary game theory
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games; D - Microeconomics > D6 - Welfare Economics > D62 - Externalities; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R1 - General Regional Economics > R12 - Size and Spatial Distributions of Regional Economic Activity

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