Abstract
An unrealistic assumption in classical extensive game theory is that the complete game tree is fully perceivable by all players. To weaken this assumption, a class of games (called games with short sight) was proposed in literature, modelling the game scenarios where players have only limited foresight of the game tree due to bounded resources and limited computational ability. As a consequence, the notions of equilibria in classical game theory were refined to fit games with short sight. A crucial issue that thus arises is to determine whether a strategy profile is a solution for a game. To study this issue and address the underlying idea and theory on players’ decisions in such games, we adopt a logical way. Specifically, we develop a logic through which features of these games are demonstrated. More importantly, it enables us to characterize the solutions of these games via formulas of this logic. This work not only provides an insight into a more realistic model in game theory, but also enriches the possible applications of logic.
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References
van Benthem, J.: Modal Logic for Open Minds. Center for the Study of Language and Information Lecture Notes. Stanford University (2010)
van Benthem, J., Pacuit, E., Roy, O.: Toward a theory of play: A logical perspective on games and interaction. Games 2(1), 52–86 (2011)
Blackburn, P., de Rijke, M., Venema, Y.: Modal logic. Cambridge University Press (2001)
Bonanno, G., Magill, M., Van Gaasback, K.: Branching time logic, perfect information games and backward induction. Working Papers 9813, University of California, Davis, Department of Economics (2003)
Cui, J., Luo, X., Sim, K.M.: A new epistemic logic model of regret games. In: Wang, M. (ed.) KSEM 2013. LNCS, vol. 8041, pp. 372–386. Springer, Heidelberg (2013)
Fischer, M.J., Ladner, R.E.: Propositional dynamic logic of regular programs. J. Comput. Syst. Sci. 18(2), 194–211 (1979)
Grossi, D., Turrini, P.: Short sight in extensive games. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012), pp. 805–812 (2012)
Halpern, J.Y., Pucella, R.: A logic for reasoning about evidence. Journal of Artificial Intelligence Research 26, 1–34 (2006)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic logic. In: Handbook of Philosophical Logic, pp. 497–604. MIT Press (1984)
Harrenstein, P., van der Hoek, W., Meyer, J.J.C., Witteveen, C.: A modal characterization of Nash equilibrium. Fundamenta Informaticae 57(2–4), 281–321 (2003)
Liu, C., Liu, F., Su, K.: A logic for extensive games with short sight. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 332–336. Springer, Heidelberg (2013)
Lorini, E., Moisan, F.: An epistemic logic of extensive games. Electronic Notes in Theoretical Computer Science 278, 245–260 (2011)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory. MIT Press (1994)
Ramanujam, R., Simon, S.E.: Dynamic logic on games with structured strategies. In: Principles of Knowledge Representation and Reasoning: Proceedings of the Eleventh International Conference, KR 2008, Sydney, Australia, September 16–19, pp. 49–58. AAAI Press (2008)
Shoham, Y., Leyton-Brown, K.: Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. Cambridge University Press, New York (2008)
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Liu, C., Liu, F., Su, K. (2015). A Dynamic-Logical Characterization of Solutions in Sight-Limited Extensive Games. In: Chen, Q., Torroni, P., Villata, S., Hsu, J., Omicini, A. (eds) PRIMA 2015: Principles and Practice of Multi-Agent Systems. PRIMA 2015. Lecture Notes in Computer Science(), vol 9387. Springer, Cham. https://doi.org/10.1007/978-3-319-25524-8_29
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DOI: https://doi.org/10.1007/978-3-319-25524-8_29
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