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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.

A first version of this paper has been presented at the 11th Conference on Real Analysis and Measure Theory in Ischia (Italy, 2004). This version was presented at the Debreu Memorial Conference in Berkeley (USA, 2005); International audience; This paper studies production economies in a commodity space that is an ordered locally convex space. We establish a general theorem on the existence of equilibrium without requiring that the commodity space or its dual be a vector lattice. Such commodity spaces arise in models of portfolio trading where the absence of some option usually means the absence of a vector lattice structure. The conditions on preferences and production sets are at least as general as those imposed in the literature dealing with vector lattice commodity spaces. The main assumption on the order structure is that the Riesz-Kantorovich functionals satisfy a uniform properness condition that can be formulated in terms of a duality property that is readily checked. This condition is satisfied in a vector lattice commodity space but there are many examples of other commodity spaces that satisfy the condition, which are not vector lattices, have no order unit, and do not have either the decomposition property or its approximate versions.

International audience; An F-cone is a pointed and generating convex cone of a real vector space that is the union of a countable family of finite dimensional polyedral convex cones such that each of which is an extremel subset of the subsequent one. In this paper, we study securities markets with countably many securities and arbitrary finite portfolio holdings. Moreover, we assume that each investor is constrained to have a non-negative end-of-period wealth. If, under the portfolio dominance order, the positive cone of the portfolio space is an F-cone, then Edgeworth allocations and non-trivial quasi-equilibria exist. This result extend the case where, as in Aliprantis et al.[JME 30 (1998a) 347-366], the positive cone is a Yudin cone.

The second welfare theorem and the core-equivalence theorem have been proved to be fundamental tools for obtaining equilibrium existence theorems, especially in an infinite dimensional setting. For well-behaved exchange economies that we call proper economies, this paper gives (minimal) conditions for supporting with prices Pareto optimal allocations and decentralizing Edgeworth equilibrium allocations as non-trivial equilibria. As we assume neither transitivity nor monotonicity on the preferences of consumers, most of the existing equilibrium existence results are a consequence of our results. A natural application is in Finance, where our conditions lead to new equilibrium existence results, and also explain why some financial economies fail to have equilibrium., Résumé. Le second théorème de l'économie du bien-être et le théorème d'équivalence coeur-équilibre sont des outils fondamentaux pour obtenir des théorèmes d'existence de l'équilibre, spécialement quand l'espace des biens n'est pas de dimension finie. Pour des économies d'échange que nous appelons propres, cet articles donne des conditions (minimales) de décentralisation par des prix des allocations Pareto-optimales et des équilibres d'Edgeworth. Comme nous ne supposons ni transitivité, ni monotonicité des préférences des consommateurs, la plupart des théorèmes existants d'existance de l'équilibre sont une conséquence de nos résultats. Une appication naturelle de ces résultats est en Finance où nos conditions conduisent à des résultats nouveaux, en même temps qu'elles expliquent pourquoi certains modèles financiers n'ont pas d'équilibre.

It is difficult to argue that coalition formation is costless and freely. Thus, in this paper, only a subset of the set of all possible coalitions in an economy or a game, is considered to be really formed. The consequences that such restriction has on the veto mechanism are analyzed. The restricted veto mechanism is extended to the pondered veto mechanism with rates of participations of the agents or the players. It is shown that it is enough to consider the veto power of a subset S of coalitions, which differs from the set of all coalitions, in order to obtain the Walrasian allocations or, alternatively, the Edgeworth equilibria. In particular, it is shown that the pondered veto power, with strictly positive rates of participation, of only one coalition, namely, the coalition of all agents, blocks any non Walrasian allocation. N/A