Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/275664 
Year of Publication: 
2023
Series/Report no.: 
Working Paper No. 417
Version Description: 
Revised version, August 2023
Publisher: 
University of Zurich, Department of Economics, Zurich
Abstract: 
As pointed out by Sion and Wolfe (1957), a non-cooperative game on the unit square need not admit a Nash equilibrium, neither in pure nor in randomized strategies. In this paper, we consider finite approximations of the Sion-Wolfe game. For all parameter constellations relevant for the limit consideration, we characterize the set of Nash equilibria in iteratively undominated strategies. Values of finite approximations of the Sion-Wolfe game are shown to accumulate around three values that do not correspond in a simple way to the majorant and minorant values of the continuous game. To understand why this is happening, we apply the iterated elimination of weakly dominated strategies to the continuous game as well. The existence of ε-equilibrium, however, does not seem to be related to the properties of finite approximations.
Subjects: 
Two-person zero-sum games
Sion-Wolfe game
existence of Nash equilibrium
finite approximations
iterated elimination of dominated strategies
ε-equilibrium
Colonel Blotto games
JEL: 
C62
C72
D72
Persistent Identifier of the first edition: 
Document Type: 
Working Paper

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