Abstract
We analyse the notion of iterated admissibility, i.e., avoidance of weakly dominated strategies, as a solution concept for extensive games of infinite horizon. This concept is known to provide a valuable criterion for selecting among multiple equilibria and to yield sharp predictions in finite games. However, generalisations to the infinite are inherently problematic, due to unbounded dominance chains and the requirement of transfinite induction.
In a multi-player non-zero-sum setting, we show that for infinite extensive games of perfect information with only two possible payoffs (win or lose), the concept of iterated admissibility is sound and robust: all iteration stages are dominated by admissible strategies, the iteration is non-stagnating, and, under regular winning conditions, strategies that survive iterated elimination of dominated strategies form a regular set.
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References
Apt, K.R.: Order independence and rationalizability. In: TARK ’05: Proc. Theoretical aspects of rationality and knowledge, pp. 22–38 (2005)
Arnold, A., Vincent, A., Walukiewicz, I.: Games for synthesis of controllers with partial observation. Theoretical Comp. Science 303(1), 7–34 (2003), http://www.labri.fr/publications/l3a/2003/AVW03
Brandenburger, A., Friedenberg, A., Keisler, H.J.: Admissibility in games. To appear
Chatterjee, K.: Two-player nonzero-sum omega-regular games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 413–427. Springer, Heidelberg (2005)
Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Games with secure equilibria. In: Proc. LICS 2004, Logic in Computer Science, pp. 160–169 (2004)
Chatterjee, K., Majumdar, R., Jurdzinski, M.: On Nash equilibria in stochastic games. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 26–40. Springer, Heidelberg (2004)
Gale, D.: A theory of n-person games with perfect information. Proceedings of the National Academy of Sciences 39, 495–501 (1953)
Gimbert, H.: Jeux Positionels. PhD thesis, Université Paris 7 (2006)
Gretlein, R.J.: Dominance elimination procedures on finite alternative games. International Journal of Game Theory 12, 107–113 (1983)
Gurevich, Y., Harrington, L.: Trees, automata and games. In: Proc. of the 14th Annual ACM Symposium on Theory of Computing, STOC ’82, pp. 60–65. ACM Press, New York (1982)
Henzinger, T.A.: Games in system design and verification. In: Proc. Theoretical Aspects of Rationality and Knowledge (TARK-2005) (2005)
Hillas, J., Kohlberg, E.: Foundations of strategic equilibrium. In: Aumann, R.J., Hart, S. (eds.) Handbook of Game Theory with Economic Applications, vol. 3, pp. 1597–1663. Elsevier, Amsterdam (2002)
Kohlberg, E., Mertens, J.-F.: On the strategic stability of equilibria. Econometrica 54(5), 1003–1037 (1986)
Luce, D.R., Raiffa, H.: Games and Decisions. Wiley, Chichester (1957)
Mailath, G.J.: Do people play Nash equilibrium? Lessons from evolutionary game theory. Journal of Economic Literature 36(3), 1347–1374 (1998)
Marx, L.M., Swinkels, J.M.: Order independence for iterated weak dominance. Games and Economic Behavior 31(2), 324–329 (2000)
Mohalik, S., Walukiewicz, I.: Distributed games. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 338–351. Springer, Heidelberg (2003)
Østerdal, L.P.: Iterated weak dominance and subgame dominance. Journal of Mathematical Economics 41, 637–645 (2005)
Papadimitriou, C.: Algorithms, games, and the internet. In: STOC ’01: Proc. ACM symposium on Theory of computing, pp. 749–753. ACM Press, New York (2001)
Thomas, W.: Infinite games and verification. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 58–64. Springer, Heidelberg (2002)
Ummels, M.: Rational behaviour and strategy construction in infinite multiplayer games. Master’s thesis, RWTH Aachen University (2005)
Walukiewicz, I.: A landscape with games in the background. In: Proc. Logic in Computer Science (LICS 2004), pp. 356–366 (2004)
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Berwanger, D. (2007). Admissibility in Infinite Games. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_17
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DOI: https://doi.org/10.1007/978-3-540-70918-3_17
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