Abstract
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.
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References
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time Temporal Logic. J. ACM 49, 672–713 (2002)
Apt, K.R.: Uniform Proofs of Order Independence for Various Strategy Elimination Procedures Contrib. Theoret. Econ. 4(1), article 5 (2004)
Battigalli, P.: On Rationalizability in Extensive Games. J. Econ. Theory 74, 40–61 (1997)
Berwanger, D.: Admissibility in infinite games. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 188–199. Springer, Heidelberg (2007)
Bicchieri, C., Schulte, O.: Common Reasoning About Admissibility. Erkenntnis 45, 299–325 (1997)
Gale, D., Stewart, F.M.: Infinite Games with Perfect Information Kuhn. In: Kuhn, H.W., Tucker, A.W. (eds.) Contributions to the Theory of Games II, Princeton. Annals of Mathematics Studies, vol. 28, pp. 245–266 (1953)
Gilboa, I., Kalai, E., Zemel, E.: On the Order of Eliminating Dominated Strategies. Oper. Res. Letters 9, 85–89 (1988)
Govindan, S., Wilson, P.: On Forward Induction. Econometrica 77, 1–28 (2009)
Grädel, E., Thomas, W., Wilke, T. (eds.): Automata, Logics, and Infinite Games. LNCS, vol. 2500. Springer, Heidelberg (2002)
Grädel, E., Ummels, M.: Solution Concepts and Algorithms for Infinite Multiplayer Games. In: Apt, K., van Rooij, R. (eds.) New Perspectives on Games and Interaction. Texts in Logic and Games, vol. 4, pp. 151–178. Amsterdam University Press, Amsterdam (2008)
Gretlein, R.J.: Dominance Elimination Procedures on Finite Alternative Games. Int. J. Game Theory 12, 107–113 (1983)
Henzinger, T.A.: Games in System Design and Verification. In: van der Meijden, R. (ed.) TARK 2005, pp. 1–4. National University of Singapore (2005)
Mailath, G.J., Samuelson, L., Swinkels, J.M.: Extensive Form Reasoning in Normal Form Games. Econometrica 61, 273–302 (1993)
Marx, L.: Adaptive Learning and Iterated Weak Dominance. Games Econ. Behav. 26, 254–278 (1999)
Marx, L.M., Swinkels, J.M.: Order Ondependence for Iterated Weak Dominance. Games Econ. Behav. 18, 219–245 (1997)
Mohalik, S., Walukiewicz, I.: Distributed games. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 338–351. Springer, Heidelberg (2003)
Moulin, H.: Dominance Solvability and Cournot Stability. Math. Soc. Sci. 7, 83–102 (1984)
Samuelson, L.: Dominated Strategies and Common Knowledge. Games Econ. Behav. 4, 284–313 (1992)
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Berwanger, D. (2010). Infinite Coordination Games. In: Bonanno, G., Löwe, B., van der Hoek, W. (eds) Logic and the Foundations of Game and Decision Theory – LOFT 8. LOFT 2008. Lecture Notes in Computer Science(), vol 6006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15164-4_1
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DOI: https://doi.org/10.1007/978-3-642-15164-4_1
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