INSTITUTE OF MATHEMATICAL ECONOMICS

Axel Ostmann Martha Saboyá

Working-Paper No. 314

Nov. 1999

Abstract

Modelling social interdependence has to deal with the fact, that interaction, communication, and competition is mainly limited to other people located in a neighbourhood. The concept of social space uses geometric structure for describing neighbourhoods. The evolution of social processes like segregation or the decay and rise of conventions then can be described by corresponding cellular automata. Studies in local interaction by psychologist, sociologists, philosophers and economists (cp. Lewenstein/Novak/Latané 1992, Hegselmann 1992, Kandori/Mailath/Rob 1993, Ellison 1993, Berninghaus/Schwalbe 1993) focus on only two special cases of finite homogeneous spaces: the circle and the torus endowed with the `natural' metric. The study is motivated by the discovery of some counterexamples showing other kinds of attractors in the evolution of coordination problem as derived in Ellison 1993 and Kandori/Mailath/Rob 1993. In order to identify the causes of such strange behaviour we redefine the concept of local interaction by help of geometrical axioms. We classify all possible symmetric homogeneous local interaction structures for small numbers and develop some tools that can be used for describing the dynamics of evolutionary processes in such spaces.