Abstract
This paper studies the notion of qualitative game theory in the context of multi-agent decision making. We use logic programs with ordered disjunction (LPODs), invented by Brewka, as representation and reasoning language for strategic form of games. Structure and rules of a game are represented as a LPODin which preferences of players are encoded as ordered disjunctive rules. Solution of a game is defined in terms of equilibria such that preferred answer sets of a LPOD representing a game correspond exactly to respective types of equilibria of the game. We also discuss games in which rules have been changed or players are wrong informed about the rules of a game.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benferhat, S., et al.: Towards a possibilistic logic handling of preferences. Applied Intelligence 14, 303–317 (2001)
Brewka, G.: Logic Programs with Ordered Disjunction. In: Proc. AAAI, Canada, pp. 100–105 (2002)
Brewka, G.: Implementing Ordered Disjunction Using Answer Set Solvers for Normal Programs. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 444–455. Springer, Heidelberg (2002)
Doyle, J., Thomason, R.: Background to qualitative decision theory. AI. Mag. 20, 55–68 (1997)
Dastani, M., Van der Torre, L.: What is a joint goal? Games with beliefs and defeasible desires. In: NMR 2002, France, pp. 33–40 (2002)
De Vos, M., Vermeir, D.: Choice Logic Programs and Nash Equilibria in Strategic Games. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 266–276. Springer, Heidelberg (1999)
De Vos, M., Vermeir, D.: Logic Programming Agents and Game Theory. In: Proc. AAAI Spring Symposium on Answer Set Programming, USA, pp. 27–33 (2001)
De Vos, M., Vermeir, D.: Dynamic Decision Making in Logic Programming and Game Theory. In: AI 2002, Australia, pp. 36–57 (2002)
Grabos, R.: Qualitative Model of Decision Making. In: Bussler, C.J., Fensel, D. (eds.) AIMSA 2004. LNCS (LNAI), vol. 3192, pp. 480–489. Springer, Heidelberg (2004)
Lifschitz, V.: Answer set programming and plan generation. AI 138, 39–54 (2002)
Niemelä, I., Simons, P.: Smodels-an implementation of the stable model and well-founded semantics for normal logic programs. In: Fuhrbach, U., Dix, J., Nerode, A. (eds.) LPNMR 1997. LNCS, vol. 1265, pp. 420–429. Springer, Heidelberg (1997)
Tennenholtz, M.: On Stable Social Laws and Qualitative Equilibria. AI 102, 1–20 (1998)
Osorio, M. et.al.: Generalized Ordered Disjunction and its Applications (not published)
Tan, S.W., Pearl, J.: Qualitative Decision Theory. In: Proc. AAAI 1994, USA, pp. 70–75 (1994)
Von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior, 2nd edn. Princeton University Press, Princeton (1944)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Graboś, R. (2005). Qualitative Model of Game Theory. In: Torra, V., Narukawa, Y., Miyamoto, S. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2005. Lecture Notes in Computer Science(), vol 3558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526018_6
Download citation
DOI: https://doi.org/10.1007/11526018_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27871-9
Online ISBN: 978-3-540-31883-5
eBook Packages: Computer ScienceComputer Science (R0)