Large random graphs in pseudo-metric spaces

Abstract

This paper is motivated by a small economic literature modelling random trading groups or communication structures as random graphs. It relates this literature to recent work by the author which describes trade infra-structures by means of a ‘contacting cost-topology’. Conditions are found under which a given - finite or infinite - countable subset of a pseudo-metric space is almost certainly contained in a connected component of a random graph. In general, the same conditions neither imply nor exclude that the entire pseudo-metric space is almost certainly a connected component of a random graph. Based on these results, the likelihood of core equivalence properties for continuum economies with random communication structures is discussed.