Core Equivalences for Equilibria Supported by Non-linear Prices

The goal of this paper is to provide some new cooperative characterizations and optimality properties of competitive equilibria supported by non-linear prices. The general framework is that of economies whose commodity space is an ordered topological vector space which need not be a vector lattice. The central notion of equilibrium is the one of personalized equilibrium introduced by Aliprantis et al. (J Econ Theory 100:22–72, 2001). Following Herves-Beloso and Moreno-Garcia (J Math Econ 44:697–706, 2008), the veto power of the grand coalition is exploited in the original economy and in a suitable family of economies associated to the original one. The use of Aubin coalitions allows us to connect results with the arbitrage free condition due to non-linear supporting prices. The use of rational allocations allows us to dispense with Lyapunov convexity theorem. Applications are provided in connection with strategic market games and economies with asymmetric information.