Abstract
Game theory based semantics has provided good insights into the decidability and completeness of several modal logics [24]. On the other hand, we can formalise the language and reasoning used in game theory using appropriate types of modal logic [1, 3, 12–15, 23, 25]. This paper is concerned with the latter issue. The starting point in games is a set of players (agents) having certain strategies (decisions) and preferences on the game’s outcomes. Hence we have to represent both the game structure and the agents’ preference relations. When reasoning about the games, we wish to determine the properties that hold in the equilibrium to which the game naturally evolves.
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References
Asheim G. B., and Dufwenberg M. Deductive reasoning in extensive games, Econ. J., 113: 305–325, April 2003. Blackwell Publishing.
Bacchus F., and Grove A. Graphical models for preference and utility. In Proceedings of the 11th Conference on Uncertainty and AI (UAI ’95). pages 3–10, 1995.
Bonanno G. Branching time logic, perfect information games and backward induction. In 3rd Conference on Logic and Foundations of Game and Decision Theory, International Centre for Economic Research (ICER), Torino, Italy, Dec 1998.
Boutilier C. Toward a logic for qualitative decision theory. In Proceedings of the KR94, pages 75–86, 1994.
Boutilier C. Conditional logics of normality: A modal approach, Artif. Intell., 68: 87–154, 1994.
Boutilier C. A POMDP formulation of preference elicitation problems. In Proceedings of AAAI-02, AAAI Press, 2002.
Boutilier C., Brafman R. I., Domshlak C., Hoos H. H., and Poole D. Preference based constrained optimisation based on CP-Nets. Comput. Intell., 202: 137–157, 2004.
Conlisk J. Why bounded rationality? J. Econ. Lit., XXXIV: 669–700, June 1996.
Coste-Marquis S., Lang J., Liberatore P., and Marquis P. Expressivity and succinctness of preference representation languages. In Proceedings of the 9th International Conference on Knowledge Representation and Reasoning (KR-2004), AAAI Press, pages 203–212, 2004.
Dastani M., and van der Torre L. Decisions and games for BD agents. In Proceedings of AAAI-02, AAAI Press, 2002.
Gonzales C., and Perny P. Graphical models for utility elicitation. In Proceedings of 9th Knowledge Representation and Reasoning Conference (KR-2004), AAAI Press, pages 224–233, 2004.
Harrenstein P. A game-theoretical notion of consequence. In 5th Conference on Logic and Foundations of Game and Decision Theory, International Centre for Economic Research (ICER), Torino, June 2002.
Harrenstein P., van der Hoek W., Meyer J.-J., and Witteven C. A modal characterization of nash equilibrium, Fundam. Informaticae, 57: 281–321, 2003.
De Vos M., and Vermeir D. Choice logic programs and Nash equilibria in strategic games. In J. Flum and M. Rodriguez-Artalejo, editors, Computer Science Logic (CSL ’99), LNCS-1683, pages 266–276. Springer, 1999.
De Vos M., and Vermeir D. Dynamically Ordered Probabilistic Choice Logic Programming. (FST & TCS -20, LNCS-1974), Springer, 2000.
La Mura P., and Shoham Y. Expected utility networks. In Proceedings of UAI ’99. pages 366–373, 1999.
Lang J. Logical preference representation and combinatorial vote. Ann. Math. ArtifI. Intell., 421–3: 37–71, 2004.
Lang J. Conditional desires and utilities – An alternative approach to qualitative decision theory. In Proceedings of the European Conference on Artificial Intelligence (ECAI96), pages 318–322, 1996.
Makinson D. General theory of cumulative inference, In M. Reinfrank et al., editors, Non-monotonic Reasoning. Springer, Berlin, 1989.
Osborne M. J., and Rubinstein A. A Course in Game Theory, (3rd edition). The MIT Press, Cambridge, MA; London, , 1996.
Shoham Y. Reasoning About Change: Time and Causation from the Standpoint of Artificial Intelligence. MIT Press, Cambridge, 1988.
Simon, H A. A behavioral model of rational choice, Q. J. Econ., 69(1): 99–118, Feb. 1955.
Stalnaker R. Extensive and strategic forms: Games and models for games, Res. Econ., 53: 293–319, 1999. Academic Press.
van Benthem J. Logic and Games. Lecture Notes. ILLC Amsterdam & Stanford University, 1999.
van Otterloo S., van der Hoek W., and Woolridge M. preferences in game logics. In AAMAS 2004. New York, NY, http://www.aamas2004.org/proceedings/021_ otterloos_ preferences.pdf
Venkatesh G. Reasoning about game equilibria using temporal logic. In Proceedings of the FST & TCS Conference 2004. LNCS-3328, pages 503–514, Springer, 2004.
Wilson N. Extending CP-nets with stronger conditional preference statements. In Proceedings of AAAI-04. 2004.
Wolper P. The tableau method for temporal logic – An overview. Logique Anal., 28: 119–152, 1985.
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Venkatesh, G. (2011). Temporal Logic with Preferences and Reasoning About Games. In: van Benthem, J., Gupta, A., Parikh, R. (eds) Proof, Computation and Agency. Synthese Library, vol 352. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0080-2_14
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