Abstract
Arrow and Debreu (1) were the first to consider N-person games with constraints and showed the existence of equilibrium points in some special cases. Furtermore, using game-theoretic methods, they proved the existence of an equilibrium for a competitive economy. Makarov and Rubinov (7) developed a game-theoretic Arrow-Debreu model (see chapters 5 and 6). But their proof of the existence of an equilibrium in such a model contains a few errors. Namely, the constraints for players are not well-defined (see 7 p. 284).
In our paper we generalize their model. We define a non-cooperative game with constraints and prove the existence of an equilibrium for it. We extend the Arrow-Debreu model to countably many agents. Under some assumptions we prove the existence of an equilibrium in such a generalized Arrow-Debreu model.
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References
Arrow, K.J. and G. Debreu, 1954, Existence of an equilibrium for a competitive economy, Econometrica 22, 265–290.
Berge, C.,1963, Topological spaces (Oliver and Boyd Ltd, Edinburg-London).
Debreu, G.,1952, A social equilibrium existence theorem, Proc. Nat. Acad. Sci. USA 38, 886–893.
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Kuratowski, K.,1966, Topology, Vol.1 (Academic Press, N.Y.-London).
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Makarov, V.L. and A.M. Rubinov, l973, Mathematical theory of economic dynamics and equilibrium (in Bussian) (Nauka, Moskva).
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© 1983 ACADEMIA, Publishing House of the Czechoslovak Academy of Sciences, Prague
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Idzik, A., Simonsen, P.B. (1983). A Game-Theoretic Arroi-Debreu Model. In: Transactions of the Ninth Prague Conference. Czechoslovak Academy of Sciences, vol 9A. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7013-7_37
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DOI: https://doi.org/10.1007/978-94-009-7013-7_37
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-009-7015-1
Online ISBN: 978-94-009-7013-7
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