Abstract
We propose a general approach for encoding epistemic strategies for playing incomplete information games. A game strategy involves selecting actions in order to maximise an outcome (e.g., winning the game). In an epistemic strategy the selection of actions is based on reasoning about the knowledge of other players. We show how epistemic strategies can be encoded by supplementing a GDL-II game description with a set of epistemic rules to produce a GDL-III game that an appropriate reasoner can use to play the original GDL-II game. We prove the formal correctness of this approach and provide a practical evaluation to show its efficacy for playing the co-operative multi-player game of Hanabi. It was found that the encoded epistemic rules were able to provide players with a strategy that allowed them to play Hanabi near optimally.
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Notes
- 1.
- 2.
For the full Hanabi GDL-II encoding see: https://git.io/fhbVz.
- 3.
For the complete GDL-III information strategy encoding see: https://git.io/fhbVo.
- 4.
For the complete GDL-III implicit strategy encoding see: https://git.io/fhbVK.
References
Ågotnes, T., Harrenstein, P., van der Hoek, W., Wooldridge, M.: Boolean games with epistemic goals. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 1–14. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40948-6_1
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49(5), 672–713 (2002)
Apt, K.R., Blair, H.A., Walker, A.: Towards a theory of declarative knowledge. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 89–148. Morgan Kaufmann Publishers Inc., San Francisco (1987)
Baffier, J., et al.: Hanabi is NP-complete, even for cheaters who look at their cards. In: FUN. LIPIcs, Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, vol. 49, pp. 4:1–4:17 (2016)
Bard, N., et al.: The Hanabi challenge: a new frontier for AI research. CoRR abs/1902.00506 (2019). http://arxiv.org/abs/1902.00506
van Benthem, J.: In praise of strategies. In: Eijck, J.V., Verbrugge, R. (eds.) Games, Actions, and Social Software. ILLC Scientific Publications, Institute for Logic, Language and Computation (ILLC), University of Amsterdam (2008)
Bouzy, B.: Playing Hanabi near-optimally. In: Winands, M.H.M., van den Herik, H.J., Kosters, W.A. (eds.) ACG 2017. LNCS, vol. 10664, pp. 51–62. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-71649-7_5
Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Inf. Comput. 208(6), 677–693 (2010)
Cox, C., De Silva, J., Deorsey, P., Kenter, F.H., Retter, T., Tobin, J.: How to make the perfect fireworks display: two strategies for Hanabi. Math. Mag. 88(5), 323–336 (2015)
Eger, M., Martens, C., Córdoba, M.A.: An intentional AI for Hanabi. In: IEEE Conference on Computational Intelligence and Games (CIG), pp. 68–75. IEEE (2017)
Genesereth, M., Love, N., Pell, B.: General game playing: overview of the AAAI competition. AI Mag. 26(2), 62 (2005)
Genesereth, M., Thielscher, M.: General game playing. Synth. Lect. Artif. Intell. Mach. Learn. 8(2), 20, 172–178 (2014)
Genesereth, M.R., Björnsson, Y.: The international general game playing competition. AI Mag. 34(2), 107–111 (2013)
van der Hoek, W., Jamroga, W., Wooldridge, M.: A logic for strategic reasoning. In: Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multi Agent Systems (AAMAS 2005), pp. 157–164. ACM (2005)
Lloyd, J., Topor, R.: A basis for deductive database systems II. J. Logic Program. 3(1), 55–67 (1986)
Love, N., Henrichs, T., Haley, D., Schkufza, E., Genesereth, M.: General game playing: game description language specification. Technical report, Stanford Logic Group Computer Science Department Stanford University (2006)
Osawa, H.: Solving Hanabi: estimating hands by opponent’s actions in cooperative game with incomplete information. In: AAAI Workshop: Computer Poker and Imperfect Information, pp. 37–43 (2015)
Schiffel, S., Thielscher, M.: Reasoning about general games described in GDL-II. In: AAAI, vol. 11, pp. 846–851 (2011)
Schiffel, S., Thielscher, M.: Representing and reasoning about the rules of general games with imperfect information. JAIR 49, 171–206 (2014)
van den Bergh, M.J.H., Hommelberg, A., Kosters, W.A., Spieksma, F.M.: Aspects of the cooperative card game Hanabi. In: Bosse, T., Bredeweg, B. (eds.) BNAIC 2016. CCIS, vol. 765, pp. 93–105. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67468-1_7
Thielscher, M.: A formal description language for epistemic games. Technical report, UNSW-CSE-TR-201708, The University of New South Wales (2017)
Thielscher, M.: GDL-III: a description language for epistemic general game playing. In: Sierra, C. (ed.) IJCAI, pp. 1276–1282. AAAI Press, Melbourne, August 2017
Walther, D., van der Hoek, W., Wooldridge, M.: Alternating-time temporal logic with explicit strategies. In: Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 269–278. ACM (2007)
Walton-Rivers, J., Williams, P.R., Bartle, R., Perez-Liebana, D., Lucas, S.M.: Evaluating and modelling Hanabi-playing agents. In: 2017 IEEE Congress on Evolutionary Computation (CEC), pp. 1382–1389. IEEE (2017)
Zhang, D., Thielscher, M.: A logic for reasoning about game strategies. In: AAAI, vol. 15, pp. 1671–1677 (2015)
Acknowledgements
This research was supported under the Australian Research Council’s (ARC) Linkage Projects funding scheme (project number LP 180100080).
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Manuel, S., Rajaratnam, D., Thielscher, M. (2019). Encoding Epistemic Strategies for General Game Playing. In: Nayak, A., Sharma, A. (eds) PRICAI 2019: Trends in Artificial Intelligence. PRICAI 2019. Lecture Notes in Computer Science(), vol 11670. Springer, Cham. https://doi.org/10.1007/978-3-030-29908-8_44
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