Infinite Coordination Games

We investigate the prescriptive power of sequential iterated admissibility in coordination games of the Gale-Stewart style, i.e., perfect-information games of infinite duration with only two payoffs. We show that, on this kind of games, the procedure of eliminating weakly dominated strategies is independent of the elimination order and that, under maximal simultaneous elimination, the procedure converges after at most ω many stages.

[1]  Krzysztof R. Apt,et al.  Uniform Proofs of Order Independence for Various Strategy Elimination Procedures , 2004, ArXiv.

[2]  Jaikumar Radhakrishnan,et al.  FST TCS 2003: Foundations of Software Technology and Theoretical Computer Science , 2004, Lecture Notes in Computer Science.

[3]  Eitan Zemel,et al.  On the order of eliminating dominated strategies , 1990 .

[4]  Dietmar Berwanger,et al.  Admissibility in Infinite Games , 2007, STACS.

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

[6]  Pierpaolo Battigalli,et al.  On Rationalizability in Extensive Games , 1997 .

[7]  R. J. Gretlein,et al.  Dominance elimination procedures on finite alternative games , 1983 .

[8]  Thomas A. Henzinger,et al.  Games in system design and verification , 2005, TARK.

[9]  Moshe Tennenholtz,et al.  Distributed Games , 1998, TARK.

[10]  David Gale,et al.  13. Infinite Games with Perfect Information , 1953 .

[11]  Thomas A. Henzinger,et al.  Alternating-time temporal logic , 1999 .

[12]  Robert Wilson,et al.  On Forward Induction , 2007 .

[13]  Michael Ummels,et al.  Solution Concepts and Algorithms for Infinite Multiplayer Games , 2008 .

[14]  Leslie M. Marx,et al.  Adaptive Learning and Iterated Weak Dominance , 1999 .

[15]  Igor Walukiewicz,et al.  Distributed Games , 2003, FSTTCS.

[16]  George J. Mailath,et al.  Extensive form reasoning in normal form games , 1993 .

[17]  H. Moulin.  Dominance solvability and cournot stability , 1984 .

[18]  Krzysztof R. Apt,et al.  New Perspectives on Games and Interaction , 2008 .

[19]  Thomas Wilke,et al.  Automata logics, and infinite games: a guide to current research , 2002 .

[20]  Thomas Wilke,et al.  Automata Logics, and Infinite Games , 2002, Lecture Notes in Computer Science.

[21]  Oliver Schulte,et al.  Common reasoning about admissibility , 1996, Erkenntnis.

[22]  Jeroen M. Swinkels,et al.  Order Independence for Iterated Weak Dominance , 1997, Games Econ. Behav..