 Finite approximations of the Sion-Wolfe gameLeopold Aspect and Christian Ewerhart No 417, ECON - Working Papers from Department of Economics - University of 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. Keywords: Two-person zero-sum games; Sion-Wolfe game; existence of Nash equilibrium; finite approximations; iterated elimination of dominated strategies; ε-equilibrium; Colonel Blotto games (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:zur:econwp:417 Access Statistics for this paper More papers in ECON - Working Papers from Department of Economics - University of Zurich Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.