Levin, V. L. Exchange models with indivisible commodities, and implementation of competitive equilibria in games of auction type. (English. Russian original) Zbl 0832.90024 Russ. Acad. Sci., Dokl., Math. 49, No. 1, 15-19 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 1, 16-19 (1994). Summary: Exchange models with indivisible commodities have been studied in mathematical economics from the beginning of the 1970’s. Competitive equilibria occupy an important place in these investigations. It is usually assumed that each participant of an exchange can own at most one indivisible commodity, along with an amount of money (exchange of homes). Exchange models without money were also studied.We consider models of both types in the absence of constraints on the number of commodities that can be owned and exchanged by participants. We shall be interested in what can be called a realization (or implementation) of specified allocations of commodities by means of Nash equilibria in a certain game of auction type. This is connected with the study of equilibrium and quasi-equilibrium properties of realizable allocations. MSC: 91B26 Auctions, bargaining, bidding and selling, and other market models 91A12 Cooperative games 91A40 Other game-theoretic models 91B52 Special types of economic equilibria 91B54 Special types of economic markets (including Cournot, Bertrand) Keywords:exchange models with indivisible commodities; Nash equilibria; game of auction type PDFBibTeX XMLCite \textit{V. L. Levin}, Russ. Acad. Sci., Dokl., Math. 49, No. 1, 15--19 (1994; Zbl 0832.90024); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 334, No. 1, 16--19 (1994)