Abstract
A two person zero sum game is regarded as Silverman-like if the strategy sets are sets of real numbers bounded below, the payoff function is bounded, the maximum payoff is achieved whenever the second player's numbery exceeds the first player's numberx by “too much”, and the minimum is achieved wheneverx exceedsy by “too much”. Explicit upper bounds are obtained for pure strategies to be included in an optimal mixed strategy in such games. In particular, if the strategy sets are discrete, the games may be reduced to games on specified finite sets.
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References
Evans RJ (1977) Silverman's game on discrete sets. Preprint, Univ. Cal. San Diego, USA
Evans RJ (1979) Silverman's game on intervals. Amer Math Monthly 86:277–281
Heuer GA (1982) Odds versus evens in Silverman-type games. Internat J Game Theory 11:183–194
Heuer GA (1984) A family of games on [1, ∞)2 with payoff a function ofy/x. Naval Research Logistics Quarterly31:229–249
Heuer GA (1988) Extension of Evan's work on symmetric discrete Silverman games to smaller values ofv. Preprint, Graz University, Austria
Heuer GA, Rieder WD (1988) Silverman games on disjoint discrete sets. SIAM J on Discrete Mathematics (Nov. 1988)
Mendelsohn NS (1946) A psychological game. Amer Math Monthly 53:86–88
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This work was done while the author was Gastprofessor, Institut für Statistik, Ökonometrie und Operations Research, Universität Graz, Herdergasse 9-11, A-8010 Graz, Austria. The support and hospitality of the Institut are gratefully acknowledged.
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Heuer, G.A. Reduction of Silverman-like games to games on bounded sets. Int J Game Theory 18, 31–36 (1989). https://doi.org/10.1007/BF01248493
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DOI: https://doi.org/10.1007/BF01248493