Abstract
We use linear time temporal logic formulas to model strategic and extensive form games. This allows us to use temporal tableau to reason about the game structure. We order the nodes of the tableau according to the players’ preferences. Using this, we can derive a decision procedure for reasoning about the equilibria of these games. The main result developed in this paper is that every finite game can be converted into an equivalent bargaining game on temporal tableau, where the players negotiate the equilbrium outcome. The decision method proposed in this paper has a number of merits compared to others that can be found in the growing literature connecting games to logic – it captures a wide variety of game forms, it is easy to understand and implement, and it can be enhanced to take into account bounded rationality assumptions.
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References
Asheim, G.B., Dufwenberg, M.: Deductive Reasoning in Extensive Games. The Economic Journal 113, 305–325 (2003)
Bonanno, G.: Branching time logic, perfect information games and backward induction. In: 3rd Conference on Logic and Foundations of Game and Decision Theory, Torino, Italy (December 1998); International Centre for Economic Research (ICER)
Harrenstein, P.: A Game-Theoretical Notion of Consequence. In: 5th Conference on Logic and Foundations of Game and Decision Theory, Torino, Italy (June 2002); International Centre for Economic Research (ICER)
Harrenstein, P., van der Hoek, W., Meyer, J.-J., Witteven, C.: A Modal Characterization of Nash Equilibrium. Fundamenta Informaticae 57, 281–321 (2003)
Janssen, G.L.J.M.: Hardware verification using Temporal Logic: A Practical View. In: Claesen, L.J.M. (ed), IFIP 1990, pp. 159–168 (1990), Available at the TLA home page, http://research.microsoft.com/users/lamport/tla/logic-calculators.html
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.: Dynamically ordered probabilistic choice logic programming. In: Kapoor, S., Prasad, S. (eds.) FST TCS 2000. LNCS, vol. 1974, p. 227. Springer, Heidelberg (2000)
Osborne, M.J., Rubinstein, A.: A Course in Game Theory, 3rd edn. MIT Press, Cambridge (1996)
Stalnaker, R.: Extensive and strategic forms: Games and models for games. In: Research in Economics, vol. 53, pp. 293–319. Academic Press, London (1999)
van Benthem: Logic and Games. Lecture notes. ILLC Amsterdam & Stanford University (1999)
van Otterloo, S., van der Hoek, W., Woolridge, M.: Preferences in Game Logics. In: AAMAS 2004, New York (2004), http://www.aamas2004.org/proceedings/021_otterloos_preferences.pdf
Venkatesh, G.: A decision method for temporal logic based on resolution. In: Maheshwari, S.N. (ed.) FSTTCS 1985. LNCS, vol. 206, pp. 272–289. Springer, Heidelberg (1985)
Wolper, P.: The tableau method for temporal logic - an overview. Logique et Analyse 28, 119–152 (1985)
Woolridge, M., Dixon, C., Fisher, M.: A tableau based proof procedure for temporal logics of knowledge and belief. Journal of Applied Non-Classical Logics 8(3), 225–258 (1998)
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Venkatesh, G. (2004). Reasoning About Game Equilibria Using Temporal Logic. In: Lodaya, K., Mahajan, M. (eds) FSTTCS 2004: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2004. Lecture Notes in Computer Science, vol 3328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30538-5_42
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DOI: https://doi.org/10.1007/978-3-540-30538-5_42
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