Existence of equilibrium for Walrasian endowment games
Suppose that, in an exchange economy, the Walrasian prices and the corresponding equilibrium allocations are calculated with respect to the data declared by the traders. These data are: traders' initial endowments and their preferences. It is well known [\textit{L. Hurwicz}, Decision Organization, Vol. in Honor of Jacob Marschak, Studies Math. Managerial Economics 12, 297-236 (1972; Zbl 0254.90009) or \textit{A. Postlewaite}, Rev. Econ. Stud. 46, 255-262 (1979; Zbl 0409.90014)] that traders may gain by declaring the data different from the true ones. The reviewed paper studies the game with finitely many players in which players- traders' strategies are just declarations of their endowments, generally (though not necessarily) not exceeding the true endowments; special emphasis is given to the existence of Nash equilibria in such games. In particular, the author considers sequences of exchange economies \(E_ k\) with finitely many traders, tending to an exchange economy E with a continuum of traders and investigates the assumptions guaranteeing that a competitive equilibrium for E is a limit of a sequence of Nash equilibria for \(E_ k\), or vice versa.
scientific article; zbMATH DE number 3932728