Titlebook: Equilibrium Theory in Infinite Dimensional Spaces; M. Ali Khan,Nicholas C. Yannelis Book 1991 Springer-Verlag Berlin Heidelberg 1991 Gleic

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Set-Valued Functions of Two Variables in Economic TheorySeveral properties of set-valued functions of two variables are studied. Specifically, we study the existence of (i) Carathéodory-type selections, (ii) random fixed points and (iii) random maximal elements. An application to the problem of the existence of a random price equilibrium is also given.

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An Equivalence Theorem for the Core of an Economy with Commodity Space L, — , (L, ,L,)The equivalence of the core and the set of competitive equilibrium is proved, for an economy with an atomless measure space of agents and with a commodity space which is .. endowed with the Mackey-topology . (L. ,L.).

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The Principle of EquivalenceA general principle of obtaining equivalence of core and quasiWalrasian allocations in nonatomic markets with an infinite number of commodities is formulated through four ingredients: the set of arbitrage, the coalitional representation, the space of allocations and the (weak) Lyapunov Convexity Theorem.

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A Very Weak Theorem on the Existence of Equilibria in Atomless Economies with Infinitely Many CommodThe equilibrium existence theorem we obtain resembles Robert Aumann’s (1966) Auxiliary Theorem, in which he assumes that preferences are commodity-wise saturated. Our result may therefore be looked upon as a first step towards a satisfactory existence theorem for .. (if such a theorem exists).

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1431-8849 r on many counts. Some were written in the early seventies while others are reports of ongoing research done especially with this volume in mind. Some are surveys of material that can, at least at this point in time, be deemed to have attained a satisfactory solution of the problem, while oth­ ers r

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Hmed Ben-Nasr,Mongi Saoudi,Riadh Badraouiandard fixed point theorem arguments. The difficulty arises because the key steps in the argument deal with subsets of the commodity space and its dual. But when the commodity space becomes infinite dimensional, these subsets lose many of the nice properties they have when they lie in ℝ..