The graph of Lindahl correspondence as the unique von Neumann-Morgenstern abstract stable set

Abstract

In this paper, we consider a continuum economy ℰ with a finite number of types of agent, and several private and public goods. The main result of the paper is that the graph of the equal-treatment Lindahl equilibria mapping is the unique abstract stable set with respect to the dominance relation in economies with crowding effects introduced by Vasil'ev et al. in 1995. The external stability of this mapping implies that, for any equal-treatment allocation x in ℰ, that is not a Lindahl equilibrium, there exists a subeconomy ℰ of ℰ such that one of its equal-treatment Lindahl allocations blocks x. This result is a counterpart of the theorem of Mas-Colell for Aumann's atomless market with private goods.