Browsing by Author "Yannelis, Nicholas C."
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Item Caratheodory-Type Selections and Random Fixed Point Theorems(Center for Economic Research, Department of Economics, University of Minnesota, 1985-06) Kim, Taesung; Prikry, Karel; Yannelis, Nicholas C.We provide some new Caratheodory-type selection theorems, i.e, selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael's [21] continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski [10]. Random fixed point theorems (which generalize ordinary fixed point theorems, e.g., Browder's [6]) follow as easy corollaries of our results.Item The Core of an Economy without Ordered Preferences(Center for Economic Research, Department of Economics, University of Minnesota, 1985-06) Yannelis, Nicholas C.Core existence results are proved for exchange economies with an infinite dimensional commodity space. In particular, the commodity space may be any ordered Hausdorff linear topological space, and agents' preferences need not be transitive, complete, monotone or convex; preferences may even be interdependent. Under these assumptions a quasi equilibrium may not exist.Item Core-Walras Equivalence in Economies with a Continuum of Agents and Commodities(Center for Economic Research, Department of Economics, University of Minnesota, 1987-04) Rustichini, Aldo; Yannelis, Nicholas C.This paper contains the following results for economies with infinite dimensional commodity spaces. (i) He establish a core-Walras equivalence theorem for economies with an atomless measure space of agents and with an ordered separable Banach commodity space whose positive cone has a non-empty norm interior. This result includes as a special case the Aumann (1964) and Hildenbrand (1974) finite dimensional theorems. (ii) We provide a counterexample which shows that the above result fails in ordered Banach spaces whose positive cone has an empty interior even if preferences are strictly convex, monotone and weak* continuous and initial endowments are strictly positive. (iii) After introducing a new assumption on preferences called "commodity pair desirability," (which is automatically satisfied whenever preferences are monotone and the positive cone of the commodity space has a non-empty interior), we establish core-Walras equivalence in any arbitrary separable Banach lattice whose positive cone may have an empty (norm) interior. (iv) We provide a proof that in some concrete spaces whose positive cone may have an empty interior, the assumption of an extremely desirable commodity or uniform properness suffices for core-Walras equivalence. Finally, (v) we indicate how our methods can be used to obtain core-Walras equivalence results for the space M(~) of measures on a compact metric space.Item An Elementary Proof of Fatou's Lemma in Finite Dimensional Spaces(Center for Economic Research, Department of Economics, University of Minnesota, 1986-11) Rustichini, Aldo; Yannelis, Nicholas C.We provide an elementary and very short proof of the Fatou Lemma in n-dimensions. In particular, we show that the latter result follows directly from Aumann's (1976) elementary proof of the fact that integration preserves upper-semicontinuity.Item Equilibria in Abstract Economies with a Measure Space of Agents and with an Infinite Dimensional Strategy Space(Center for Economic Research, Department of Economics, University of Minnesota, 1985-07) Kim, Taesung; Prikry, Karel; Yannelis, Nicholas C.The existence of an equilibrium for an abstract economy with a measure space of agents and with an infinite dimensional strategy space is proved. Agent's preferences need not be ordered, i.e., need not be transitive or complete, and therefore need not be representable by utility functions. The proof which follows closely the arguments in Yannelis-Prabhakar [26] is based on a Caratheodory-type selection theorem.Item Equilibria in Noncooperative Models of Competition(Center for Economic Research, Department of Economics, University of Minnesota, 1985-06) Yannelis, Nicholas C.Item Equilibrium Points of Non-Cooperative Random and Bayesian Games(Center for Economic Research, Department of Economics, University of Minnesota, 1987-08) Yannelis, Nicholas C.We provide random equilibrium existence theorems for noncooperative random games with a countable number of players. Our results give as corollaries generalized random versions of the ordinary equilibrium existence result of Nash [18]. Moreover, they can be used to obtain equilibrium existence results for games with incomplete information, and in particular Bayesian games. In view of recent work on applications of Bayesian games and Bayesian equilibria, the latter results seem to be quite useful since they delineate conditions under which such equilibria exist.Item Existence and Fairness of Value Allocation without Convex Preferences(Center for Economic Research, Department of Economics, University of Minnesota, 1983-08) Yannelis, Nicholas C.Shafer [8] proved that in a finite exchange economy value allocations exist, provided that each agent has convex, complete, transitive, compact and monotone preferences. However, if preferences are not convex, then value allocations may not exist. To remedy this difficulty we enlarge the set of value allocations introducing the concept of approximate value allocations, and show that in a finite exchange economy approximate value allocations exist, even if preferences are not convex, or compact, or monotone. This value existence result can be used to provide a very general value existence theorem for a sequence of finite economies. Further, we show that value allocations do discriminate in favor of or against any coalition of agents.Item Existence of Maximal Elements and Equilibria in Linear Topological Spaces(Center for Economic Research, Department of Economics, University of Minnesota, 1983-08) Yannelis, Nicholas C.; Prabhakar, N.D.We present some mathematical theorems which are used to generalize previous results on the existence of maximal elements and of equilibria. Our main theorem in this paper is a new existence proof of an equilibrium in an abstract economy, which is closely related to a previous result of Shafer-Sonnenschein and Borglin-Keiding, but allows for an infinite number of commodities and a countably infinite number of agents.Item Fatou's Lemma in Infinite Dimensional Spaces(Center for Economic Research, Department of Economics, University of Minnesota, 1986-07) Yannelis, Nicholas C.Item Non-Cooperative Random Games(Center for Economic Research, Department of Economics, University of Minnesota, 1986-07) Yannelis, Nicholas C.Item On a Caratheodory-Type Selection Theorem(Center for Economic Research, Department of Economics, University of Minnesota, 1985-07) Kim, Taesung; Prikry, Karel; Yannelis, Nicholas C.We offer a new Caratheodory-type selection theorems. This result arose naturally from the authors' [9] study of equilibria in abstract economies (generalized games) with a measure space of agents.Item On a Market Equilibrium Theorem with an Infinite Number of Commodities(Center for Economic Research, Department of Economics, University of Minnesota, 1984-01) Yannelis, Nicholas C.We give a direct proof of the market equilibrium theorem of Gale-Nikaido-Debreu for an infinite, dimensional commodity space. Our theorem is closely related to a recent result of Aliprantis-Browu, but allows for excess demand correspondences rather than excess demand functions.Item On Cores of Weakly Balanced Games Without Ordered Preferences(Center for Economic Research, Department of Economics, University of Minnesota, 1985-10) Yannelis, Nicholas C.A new concept of balancedness for games in normal form is introduced, called weak balanacedness. It is shown that the a-core of a weakly balanced game with an infinite dimensional strategy space and without ordered preferences is nonempty. Using this result we prove core existence theorems for economies (either exchange economies of coalitional production economies) with infinitely many commodities and without ordered preferences, by converting the economy to a game and showing that the derived game is weakly balanced. Surprisingly, no convexity assumption on preferences is needed to demonstrate that the game derived from the economy is weakly balanced.Item On the Lebesque-Aumann Dominated Convergence Theorem in Infinite Dimensional Spaces(Center for Economic Research, Department of Economics, University of Minnesota, 1987-08) Yannelis, Nicholas C.The Lebesgue-Aumann dominated convergence Theorem (see Aumann [1]) is generalized to correspondences taking values in a Banach space.