Reasoning About Game Equilibria Using Temporal Logic
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.
KeywordsNash Equilibrium Temporal Logic Strategic Game Chain Store Strongly Connect Component
Unable to display preview. Download preview PDF.
- 2.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)Google Scholar
- 3.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)Google Scholar
- 5.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
- 8.Osborne, M.J., Rubinstein, A.: A Course in Game Theory, 3rd edn. MIT Press, Cambridge (1996)Google Scholar
- 9.Stalnaker, R.: Extensive and strategic forms: Games and models for games. In: Research in Economics, vol. 53, pp. 293–319. Academic Press, London (1999)Google Scholar
- 10.van Benthem: Logic and Games. Lecture notes. ILLC Amsterdam & Stanford University (1999)Google Scholar
- 11.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
- 12.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)Google Scholar