An Ordinal Minimax Theorem

In the early 1950s Lloyd Shapley proposed an ordinal and set-valued solution concept for zero-sum games called weak saddle. We show that all weak saddles of a given zero-sum game are interchangeable and equivalent. As a consequence, every such game possesses a unique set-based value.

[1]  Bhaskar Dutta.  Covering sets and a new condorcet choice correspondence , 1988 .

[2]  Peter C. Fishburn,et al.  Non-cooperative stochastic dominance games , 1978 .

[3]  S. Vajda,et al.  GAMES AND DECISIONS; INTRODUCTION AND CRITICAL SURVEY. , 1958 .

[4]  S. Vajda.  Some topics in two-person games , 1971 .

[5]  Larry Samuelson,et al.  Dominated strategies and common knowledge , 1992 .

[6]  John Duggan,et al.  Dominance-based Solutions for Strategic Form Games , 1998 .

[7]  Yoav Shoham,et al.  Essentials of Game Theory: A Concise Multidisciplinary Introduction , 2008, Essentials of Game Theory: A Concise Multidisciplinary Introduction.

[8]  John Duggan,et al.  Mixed refinements of Shapley's saddles and weak tournaments , 2001, Soc. Choice Welf..

[9]  Felix A. Fischer,et al.  The Computational Complexity of Weak Saddles , 2009, SAGT.

[10]  David Gale,et al.  Review: R. Duncan Luce and Howard Raiffa, Games and decisions: Introduction and critical survey , 1958 .

[11]  Peter C. Ordeshook,et al.  Symmetric Spatial Games Without Majority Rule Equilibria , 1976, American Political Science Review.

[12]  Felix A. Fischer,et al.  Computational aspects of Shapley's saddles , 2009, AAMAS.

[13]  Felix A. Fischer,et al.  The Computational Complexity of Weak Saddles , 2009, Theory of Computing Systems.

[14]  Felix Brandt,et al.  Computing Dominance-Based Solution Concepts , 2012, EC '12.

[15]  John Duggan,et al.  Dutta's Minimal Covering Set and Shapley's Saddles , 1996 .

[16]  L. Shapley.  SOME TOPICS IN TWO-PERSON GAMES , 1963 .

[17]  Michel Le Breton,et al.  On the Uniqueness of Equilibrium in Symmetric Two-Player Zero-Sum Games with Integer Payoffs , 2007 .

[18]  E. Rowland.  Theory of Games and Economic Behavior , 1946, Nature.

[19]  J. Neumann.  Zur Theorie der Gesellschaftsspiele , 1928 .