Showing papers by "Alejandro Jofré published in 2006"
TL;DR: The class of better reply secure games was introduced by Reny as discussed by the authors, who showed the existence of a pure strategy Nash equilibrium for games in this class and provided two conditions that, when combined, become suf- ficient for a game to be betterreply secure.
Abstract: A convex, compact, and possibly discontinuous better reply secure game has a Nash equilibrium. We introduce a very weak notion of continuity that can be used to establish that a game is better reply secure and we show that this notion of continuity is satisfied by a large class of games. THE CLASS OF BETTER REPLY SECURE GAMES was introduced by Reny (1999) who showed the existence of a pure Nash equilibrium for games in this class. Furthermore, Reny provided two conditions that, when combined, become suf- ficient for a game to be better reply secure. The first condition is payoff secu- rity, which means that given a joint strategy x, every player can find a strategy that yields almost the same payoff at x, even when the other players slightly deviate from x. The second condition is reciprocal upper semicontinuity (rusc). This condition, roughly speaking, requires the payoff of one of the players to jump up whenever the payoff of another player jumps down. We introduce the notion of weak reciprocal upper semicontinuity (wrusc), a strict weakening of rusc, and prove that a game that is wrusc and payoff secure is better reply secure, and therefore has a pure strategy Nash equilibrium.
65 citations
TL;DR: A nonconvex separation property for general sets is proved which coincides with the Hahn-Banach separation theorem when sets are convexes and properties derived are used to compute the subgradient set to the distance function in special cases.
Abstract: In this paper we proved a nonconvex separation property for general sets which coincides with the Hahn-Banach separation theorem when sets are convexes. Properties derived from the main result are used to compute the subgradient set to the distance function in special cases and they are also applied to extending the Second Welfare Theorem in economics and proving the existence of singular multipliers in Optimization.
28 citations
TL;DR: In this paper, a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when preference correspondences are not convex-valued and/or when the total production set is non-convex.
Abstract: In this paper, we prove a new version of the Second Welfare Theorem for economies with a finite number of agents and an infinite number of commodities, when the preference correspondences are not convex-valued and/or when the total production set is not convex. For this kind of nonconvex economies, a recent result, obtained by one of the authors, introduces conditions which, when applied to the convex case, give for Banach commodity spaces the well-known result of decentralization by continuous prices of Pareto-optimal allocations under an interiority condition. In this paper, in order to prove a different version of the Second Welfare Theorem, we reinforce the conditions on the commodity space, assumed here to be a Banach lattice, and introduce a nonconvex version of the properness assumptions on preferences and the total production set. Applied to the convex case, our result becomes the usual Second Welfare Theorem when properness assumptions replace the interiority condition. The proof uses a Hahn-Banach Theorem generalization by Borwein and Jofre (in Joper Res Appl Math 48:169–180, 1997) which allows to separate nonconvex sets in general Banach spaces
16 citations
01 Jan 2006
TL;DR: In this paper, the authors model and analyze a market equilibrium structure working on a network, motivated by competition in electricity power generation markets, where consumers and producers are located in different nodes connected by power transmission lines.
Abstract: In this paper we model and analyze a market equilibrium structure working on a network. The model is motivated by competition in electricity power generation markets, where consumers and producers are located in different nodes connected by power transmission lines. We analyze two different equilibrium concepts, namely, the Walrasian and the noncooperative Nash outcomes. By using concepts coming from Variational Analysis and Game Theory, we prove that both equilibria exist. Our existence proofs rely on fixed point theorems and epiconvergence stable approximations.
9 citations
TL;DR: In this paper, a geometric characterization of both the free disposal hypothesis for production sets and the strict monotonicity condition for preference relations even for nonconvex economies is provided. But the analysis is restricted to the case of non-smooth sets.
2 citations