Discrete-Space Social Interaction Models: Stability and Continuous Limit

Akamatsu, Takashi and Fujishima, Shota and Takayama, Yuki (2015): Discrete-Space Social Interaction Models: Stability and Continuous Limit.

Abstract

We study the equilibrium properties, including stability, of discrete-space social interaction models with a single type of agents, and their continuous limit. We show that, even though the equilibrium in discrete space can be non-unique for all finite degree of discretization, any sequence of discrete-space models' equilibria converges to the continuous-space model's unique equilibrium as the discretization of space is refined. Showing the existence of multiple equilibria resorts to the stability analysis of equilibria. A general framework for studying equilibria and their stability is presented by characterizing the discrete-space social interaction model as a potential game.

• 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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