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THE LOGIC OF JOINT ABILITY IN TWO-PLAYER TACIT GAMES

Published online by Cambridge University Press:  27 March 2017

PETER HAWKE
PETER HAWKE*
Affiliation:
Stanford University, Department of Philosophy
*
*DEPARTMENT OF PHILOSOPHY STANFORD UNIVERSITY 450 SERRA MALL STANFORD, CA 94305, USA E-mail: phawke@stanford.edu
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Abstract

Logics of joint strategic ability have recently received attention, with arguably the most influential being those in a family that includes Coalition Logic (CL) and Alternating-time Temporal Logic (ATL). Notably, both CL and ATL bypass the epistemic issues that underpin Schelling-type coordination problems, by apparently relying on the meta-level assumption of (perfectly reliable) communication between cooperating rational agents. Yet such epistemic issues arise naturally in settings relevant to ATL and CL: these logics are standardly interpreted on structures where agents move simultaneously, opening the possibility that an agent cannot foresee the concurrent choices of other agents. In this paper we introduce a variant of CL we call Two-Player Strategic Coordination Logic (SCL2). The key novelty of this framework is an operator for capturing coalitional ability when the cooperating agents cannot share strategic information. We identify significant differences in the expressive power and validities of SCL2 and CL2, and present a sound and complete axiomatization for SCL2. We briefly address conceptual challenges when shifting attention to games with more than two players and stronger notions of rationality.

Keywords

03: Mathematical logic and foundations 91: Game theoryeconomicssocial and behavioral scienceslogics of abilitystrategic coordination logicalternating-time temporal logiccoalition logiccoordinationjoint abilityimperfect informationtacit game
Type
Research Article
Information
The Review of Symbolic Logic , Volume 10 , Issue 3 , September 2017 , pp. 481 - 508
Copyright
Copyright © Association for Symbolic Logic 2017 

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References

BIBLIOGRAPHY

Ågotnes, T., Goranko, V., & Jamroga, W. (2007). Alternating-time temporal logics with irrevocable strategies. In Samet, D., editor. Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XI). New York, NY, USA: Presses Universitaires de Louvain, pp. 15–24.Google Scholar
Alur, R., Henzinger, T. A., & Kupferman, O. (2002). Alternating-time temporal logic. Journal of the ACM, 49, 672–713.Google Scholar
Bacharach, M. (2006). Beyond Individual Choice. Princeton, NJ, USA: Princeton University Press.Google Scholar
Broersen, J., Herzig, A., & Troquard, N. (2006). Embedding alternating-time temporal logic in strategic stit logic of agency. Journal of Logic and Computation, 16(5), 559–578.CrossRefGoogle Scholar
Chopra, S., Pacuit, E., & Parikh, R. (2004). Knowledge-theoretic properties of strategic voting. In Alferes, J. and Leite, J., editors. Proceedings of Logics in Artificial Intelligence: 9th European Conference (JELIA), LNCS, Vol. 3229. Berlin, Heidelberg: Springer, pp. 18–30.Google Scholar
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about Knowledge. Massachusetts, USA: MIT Press.Google Scholar
Ghaderi, H., Lesperance, Y., & Levesque, H. (2007). A logicial theory of coordination and joint ability. In Huhns, M. and Shehory, O., editors. Proceedings of Twenty-Second Conference on Artifical Intelligence (AAAI07). Vancouver, BC: ACM, pp. 421–426.Google Scholar
Goranko, V. & Hawke, P. (2010). On the dynamics of information and abilities of players in multi-player games. In Proceedings of LOFT 10. Paper presented at the 9th Conference on Logic and the Foundations of Game and Decision Theory (LOFT 9), University of Toulouse, France, July 2010.Google Scholar
Goranko, V. & Jamroga, W. (2004). Comparing semantics for logics of multi-agent systems. Synthese, 139(2), 241–280.Google Scholar
Goranko, V., Jamroga, W., & Turrini, P. (2013). Strategic games and truly playable effectivity functions. Autonomous Agents and Multi-Agent Systems, 26, 288–314.CrossRefGoogle Scholar
Harsanyi, J. (1977). Rational Behavior and Bargaining Equilibrium in Games and Social Situations. New York, NY, USA: Cambridge University Press.Google Scholar
Horty, J. & Belnap, N. (1995). A study of action, omission, ability and obligation. Journal of Philosophical Logic, 24, 583–644.CrossRefGoogle Scholar
Horty, J. F. (2001). Agency and Deontic Logic. New York, NY, USA: Oxford University Press.Google Scholar
Leyton-Brown, K. & Shoham, Y. (2008). Essentials of Game Theory: A Concise, Multidisciplinary Introduction. Synthesis Lectures on Artificial Intelligence and Machine Learning. San Rafael, CA: Morgan and Claypool Publishers.Google Scholar
Mele, A. R. (2003). Agent’s abilities. Nous, 37(3), 447–470.Google Scholar
Pacuit, E. & Roy, O. (2016). Epistemic foundations of game theory. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy. CA, USA: Metaphysics Research Lab, Stanford University. Available at: https://plato.stanford.edu/archives/win2016/entries/epistemic-game/.Google Scholar
Pacuit, E. & Simon, S. (2011). Reasoning with protocols under imperfect information. The Review of Symbolic Logic, 4(3), 412–444.CrossRefGoogle Scholar
Pauly, M. (2001). Logic for Social Software. Ph.D. Thesis, University of Amsterdam.Google Scholar
Schelling, T. (1960). The Strategy of Conflict. Massachusetts, USA: Harvard University Press.Google Scholar
van Benthem, J. (2007). Rational dynamics and epistemic logic in games. International Game Theory Review, 9(1), 13–45.Google Scholar
van Benthem, J. (2014). Logic in Games. Massachusetts, USA: MIT Press.CrossRefGoogle Scholar
van der Hoek, W. & Jamroga, W. (2004). Agents who know how to play. Fundamenta Informaticae, 62, 1–35.Google Scholar
van der Hoek, W. & Pauly, M. (2007). Modal logic for games and information. In Blackburn, P., van Benthem, J., and Wolter, F., editors. Handbook of Modal Logic. Amsterdam, Netherlands: Elsevier, pp. 1077–1148.Google Scholar
van der Hoek, W., & Wooldridge, M. (2003). Cooperation, knowledge and time: Alternating-time temporal epistemic logic and its applications. Studia Logica, 75, 125–127.Google Scholar
van Ditmarsch, H., Lang, J., & Saffidine, A. (2012). Strategic voting and the logic of knowledge. In Proceedings of 14th TARK. Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 3, International Foundation for Autonomous Agents and Multi-agent Systems, Richland, SC, USA, pp. 1247–1248.Google Scholar
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2008). Dynamic Epistemic Logic. Dordrecht, The Netherlands: Springer.Google Scholar
van Drimmelen, G. & Goranko, V. (2006). Complete axiomatization and decidability of alternating-time temporal logic. Theoretical Computer Science, 353, 93–117.Google Scholar