Finite Approximations of the Sion–Wolfe Game

References

• [1] Aspect L, Ewerhart C (2022) Colonel Blotto games with a head start. Preprint, submitted September 16, http://dx.doi.org/10.2139/ssrn.4204082.Google Scholar
• [2] Avis D, Rosenberg GD, Savani R, von Stengel B (2010) Enumeration of Nash equilibria for two-player games. Econom. Theory 42(1):9–37.Crossref, Google Scholar
• [3] Ben-El-Mechaiekh H, Dimand RW (2010) Von Neumann, Ville, and the minimax theorem. Internat. Game Theory Rev. 12(02):115–137.Crossref, Google Scholar
• [4] Bohnenblust HF, Girshick MA, Snow RN, Dresher M, Helmer-Hirschberg O, McKinsey JCC, Shapley LS, Harris TE (1948) Mathematical theory of zero-sum two-person games with a finite number or a continuum of strategies. Report, RAND Corporation, Santa Monica, CA.Google Scholar
• [5] Boudreau JW, Schwartz J (2019) A knife-point case for Sion and Wolfe’s game. Working paper, Bagwell Center for the Study of Markets and Economic Opportunity, Kennesaw State University, Kennesaw, GA.Google Scholar
• [6] Carmona G (2005) On the existence of equilibria in discontinuous games: Three counterexamples. Internat. J. Game Theory 33(2):181–187.Crossref, Google Scholar
• [7] Dasgupta P, Maskin E (1986) The existence of equilibrium in discontinuous economic games, I: Theory. Rev. Econom. Stud. 53(1):1–26.Crossref, Google Scholar
• [8] Duggan J (2007) Equilibrium existence for zero-sum games and spatial models of elections. Games Econom. Behav. 60(1):52–74.Crossref, Google Scholar
• [9] Evans RJ (1979) Silverman’s game on intervals. Amer. Math. Monthly 86(4):277–281.Crossref, Google Scholar
• [10] Evans RJ, Heuer GA (1992) Silverman’s game on discrete sets. Linear Algebra Appl. 166:217–235.Crossref, Google Scholar
• [11] Fan K (1952) Fixed-point and minimax theorems in locally convex topological linear spaces. Proc. Natl. Acad. Sci. USA 38(2):121–126.Crossref, Google Scholar
• [12] Glicksberg IL (1952) A further generalization of the Kakutani fixed point theorem, with application to Nash equilibrium points. Proc. Amer. Math. Soc. 3(1):170–174.Google Scholar
• [13] Hellwig M, Leininger W, Reny PJ, Robson AJ (1990) Subgame perfect equilibrium in continuous games of perfect information: An elementary approach to existence and approximation by discrete games. J. Econom. Theory 52(2):406–422.Crossref, Google Scholar
• [14] Heuer GA (2001) Three-part partition games on rectangles. Theoret. Comput. Sci. 259(1–2):639–661.Crossref, Google Scholar
• [15] Heuer GA, Leopold-Wildburger U (2012) Silverman’s Game: A Special Class of Two-Person Zero-Sum Games (Springer, Berlin).Google Scholar
• [16] Holzman R (2025) The minimax property in infinite two-person win-lose games. Math. Oper. Res. 50(3):2287–2300.Link, Google Scholar
• [17] Kindler J (1983) A general solution concept for two-person, zero-sum games. J. Optim. Theory Appl. 40(1):105–119.Crossref, Google Scholar
• [18] Liang D, Wang Y, Cao Z, Yang X (2023) Discrete Colonel Blotto games with two battlefields. Internat. J. Game Theory 52(4):1111–1151.Crossref, Google Scholar
• [19] Monteiro PK, Page FH Jr (2007) Uniform payoff security and Nash equilibrium in compact games. J. Econom. Theory 134(1):566–575.Crossref, Google Scholar
• [20] Nikaidô H (1954) On von Neumann’s minimax theorem. Pacific J. Math. 4(1):65–72.Crossref, Google Scholar
• [21] Parthasarathy T (1970) On games over the unit square. SIAM J. Appl. Math. 19(2):473–476.Crossref, Google Scholar
• [22] Peck JEL (1958) Yet another proof of the minimax theorem. Canadian Math. Bull. 1(2):97–100.Crossref, Google Scholar
• [23] Prokopovych P, Yannelis NC (2014) On the existence of mixed strategy Nash equilibria. J. Math. Econom. 52:87–97.Crossref, Google Scholar
• [24] Reny PJ (1999) On the existence of pure and mixed strategy Nash equilibria in discontinuous games. Econometrica 67(5):1029–1056.Crossref, Google Scholar
• [25] Simon LK (1987) Games with discontinuous payoffs. Rev. Econom. Stud. 54(4):569–597.Crossref, Google Scholar
• [26] Simon LK, Zame WR (1990) Discontinuous games and endogenous sharing rules. Econometrica 58(4):861–872.Crossref, Google Scholar
• [27] Sion M, Wolfe P (1957) On a game without a value. Contributions to the Theory of Games III, Annals of Mathematics Studies (Princeton University Press, Princeton, NJ), 299–306.Google Scholar
• [28] Tijs SH (1977) ε-equilibrium point theorems for two-person games. Methods Oper. Res. 26:755–766.Google Scholar
• [29] Ville J (1938) Applications aux Jeux de Hasard: Cours Professé a la Faculté des Sciences de Paris. Traité du Calcul des Probabilités et de ses Applications: Tome IV, Applications Diverses et Conclusion, Fascicule II (Gauthier-Villars, Paris).Google Scholar
• [30] von Neumann J (1928) Zur Theorie der Gesellschaftsspiele. Math. Ann. 100(1):295–320.Crossref, Google Scholar
• [31] Wald A (1945) Generalization of a theorem by v. Neumann concerning zero sum two person games. Ann. Math. 46(2):281–286.Crossref, Google Scholar
• [32] Yanovskaya EB (1970) The solution of infinite zero-sum two-person games with finitely additive strategies. Theory Probab. Its Appl. 15(1):153–158.Crossref, Google Scholar