Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/322280 
Year of Publication: 
2025
Series/Report no.: 
Working Paper No. 417
Version Description: 
Revised version, May 2025
Publisher: 
University of Zurich, Department of Economics, Zurich
Abstract: 
Sion and Wolfe (1957) presented a two-person zero-sum game on the unit square without a value. In the present paper, we analyze finite-grid approximations of the Sion-Wolfe game. We find that, as the number of grid points tends to infinity and the payoff function approaches that of the infinite game, the limiting value of finite approximations may lie within, on the boundary of, or even outside the interval defined by the lower and upper values of the infinite game. Although these observations can be attributed to offsetting effects, our findings underscore the need for great care, even in the case of two-person zero-sum games, when using finite approximations for the analysis of infinite games.
Subjects: 
Two-person zero-sum games
Minimax theorem
Finite approximations
JEL: 
C62
C72
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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