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Pretty Good Strategies and Where to Find Them

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Multi-Agent Systems (EUMAS 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14282))

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Abstract

Synthesis of bulletproof strategies in imperfect information scenarios is a notoriously hard problem. In this paper, we suggest that it is sometimes a viable alternative to aim at “reasonably good” strategies instead. This makes sense not only when an ideal strategy cannot be found due to the complexity of the problem, but also when no winning strategy exists at all. We propose an algorithm for synthesis of such “pretty good” strategies. The idea is to first generate a surely winning strategy with perfect information, and then iteratively improve it with respect to two criteria of dominance: one based on the amount of conflicting decisions in the strategy, and the other related to the tightness of its outcome set. We focus on reachability goals and evaluate the algorithm experimentally with very promising results.

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Notes

  1. 1.

    i.e., initial states of the strategy.

  2. 2.

    Preliminary experiments for coalitions of drones are presented in Sect. 6.

References

  1. Alur, R., et al.: MOCHA: modularity in model checking. Technical report, University of Berkeley (2000)

    Google Scholar 

  2. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. In: Proceedings of the 38th Annual Symposium on Foundations of Computer Science (FOCS), pp. 100–109. IEEE Computer Society Press (1997)

    Google Scholar 

  3. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM 49, 672–713 (2002). https://doi.org/10.1145/585265.585270

    Article  MathSciNet  MATH  Google Scholar 

  4. Aminof, B., Malvone, V., Murano, A., Rubin, S.: Graded modalities in strategy logic. Inf. Comput. 261, 634–649 (2018). https://doi.org/10.1016/j.ic.2018.02.022

    Article  MathSciNet  MATH  Google Scholar 

  5. Belardinelli, F., Condurache, R., Dima, C., Jamroga, W., Jones, A.: Bisimulations for verification of strategic abilities with application to ThreeBallot voting protocol. In: Proceedings of the 16th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 1286–1295. IFAAMAS (2017)

    Google Scholar 

  6. Belardinelli, F., Lomuscio, A.: Agent-based abstractions for verifying alternating-time temporal logic with imperfect information. In: Proceedings of AAMAS, pp. 1259–1267. ACM (2017)

    Google Scholar 

  7. Berthon, R., Maubert, B., Murano, A., Rubin, S., Vardi, M.Y.: Strategy logic with imperfect information. In: Proceedings of LICS, pp. 1–12 (2017). https://doi.org/10.1109/LICS.2017.8005136

  8. Berthon, R., Maubert, B., Murano, A., Rubin, S., Vardi, M.Y.: Strategy logic with imperfect information. ACM Trans. Comput. Log. 22(1), 5:1–5:51 (2021). https://doi.org/10.1145/3427955

  9. Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35(8), 677–691 (1986)

    Article  MATH  Google Scholar 

  10. Bulling, N., Dix, J., Jamroga, W.: Model checking logics of strategic ability: complexity. In: Dastani, M., Hindriks, K., Meyer, J.J. (eds.) Specification and Verification of Multi-agent Systems, pp. 125–159. Springer, Boston (2010). https://doi.org/10.1007/978-1-4419-6984-2_5

    Chapter  MATH  Google Scholar 

  11. Bulling, N., Jamroga, W.: What agents can probably enforce. Fund. Inform. 93(1–3), 81–96 (2009)

    MathSciNet  MATH  Google Scholar 

  12. Bulling, N., Jamroga, W.: Alternating epistemic mu-calculus. In: Proceedings of IJCAI-11, pp. 109–114 (2011)

    Google Scholar 

  13. Burch, J.R., Clarke, E.M., McMillan, K.L., Dill, D.L., Hwang, L.J.: Symbolic model checking: 10-20 states and beyond. In: Proceedings of 4th Annual IEEE Symposium on Logic in Computer Science (LICS), pp. 428–439. IEEE Computer Society (1990)

    Google Scholar 

  14. Busard, S.: Symbolic model checking of multi-modal logics: uniform strategies and rich explanations. Ph.D. thesis, Universite Catholique de Louvain (2017)

    Google Scholar 

  15. Busard, S., Pecheur, C., Qu, H., Raimondi, F.: Improving the model checking of strategies under partial observability and fairness constraints. In: Merz, S., Pang, J. (eds.) ICFEM 2014. LNCS, vol. 8829, pp. 27–42. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11737-9_3

    Chapter  Google Scholar 

  16. Busard, S., Pecheur, C., Qu, H., Raimondi, F.: Reasoning about memoryless strategies under partial observability and unconditional fairness constraints. Inf. Comput. 242, 128–156 (2015). https://doi.org/10.1016/j.ic.2015.03.014

    Article  MathSciNet  MATH  Google Scholar 

  17. Calta, J., Shkatov, D., Schlingloff, H.: Finding uniform strategies for multi-agent systems. In: Dix, J., Leite, J., Governatori, G., Jamroga, W. (eds.) CLIMA 2010. LNCS (LNAI), vol. 6245, pp. 135–152. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14977-1_12

    Chapter  MATH  Google Scholar 

  18. Čermák, P., Lomuscio, A., Mogavero, F., Murano, A.: MCMAS-SLK: a model checker for the verification of strategy logic specifications. In: Biere, A., Bloem, R. (eds.) CAV 2014. LNCS, vol. 8559, pp. 525–532. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-08867-9_34

    Chapter  Google Scholar 

  19. Cermák, P., Lomuscio, A., Murano, A.: Verifying and synthesising multi-agent systems against one-goal strategy logic specifications. In: Proceedings of AAAI, pp. 2038–2044 (2015)

    Google Scholar 

  20. Chatterjee, K., Doyen, L., Henzinger, T., Raskin, J.F.: Algorithms for omega-regular games of incomplete information. Log. Methods Comput. Sci. 3(3), 4 (2007)

    MATH  Google Scholar 

  21. Clarke, E., Emerson, E.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. Lecture Notes in Computer Science, vol. 131, pp. 52–71. Springer, Cham (1981). https://doi.org/10.1007/bfb0025774

    Chapter  Google Scholar 

  22. Dembiński, P., et al.: \(\surd \)erics: a tool for verifying timed automata and estelle specifications. In: Garavel, H., Hatcliff, J. (eds.) TACAS 2003. LNCS, vol. 2619, pp. 278–283. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36577-X_20

    Chapter  Google Scholar 

  23. Dima, C., Maubert, B., Pinchinat, S.: The expressive power of epistemic \(\mu \)-calculus. CoRR abs/1407.5166 (2014)

    Google Scholar 

  24. Dima, C., Maubert, B., Pinchinat, S.: Relating paths in transition systems: the fall of the modal mu-calculus. In: Italiano, G.F., Pighizzini, G., Sannella, D.T. (eds.) MFCS 2015. LNCS, vol. 9234, pp. 179–191. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48057-1_14

    Chapter  MATH  Google Scholar 

  25. Dima, C., Tiplea, F.: Model-checking ATL under imperfect information and perfect recall semantics is undecidable. CoRR abs/1102.4225 (2011)

    Google Scholar 

  26. Doyen, L., Raskin, J.F.: Games with imperfect information: theory and algorithms. In: Lecture Notes in Game Theory for Computer Scientists, pp. 185–212. Cambridge University Press (2011)

    Google Scholar 

  27. Gammie, P., van der Meyden, R.: MCK: model checking the logic of knowledge. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 479–483. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-27813-9_41

    Chapter  Google Scholar 

  28. Huang, X., van der Meyden, R.: Symbolic model checking epistemic strategy logic. In: Proceedings of AAAI Conference on Artificial Intelligence, pp. 1426–1432 (2014)

    Google Scholar 

  29. Jamroga, W.: Logical Methods for Specification and Verification of Multi-agent Systems. ICS PAS Publishing House (2015)

    Google Scholar 

  30. Jamroga, W., Dix, J.: Model checking ATL\(_{ir}\) is indeed \(\Delta _2^P\)-complete. In: Proceedings of EUMAS. CEUR Workshop Proceedings, vol. 223 (2006)

    Google Scholar 

  31. Jamroga, W., Penczek, W., Dembiński, P., Mazurkiewicz, A.: Towards partial order reductions for strategic ability. In: Proceedings of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 156–165. IFAAMAS (2018)

    Google Scholar 

  32. Jamroga, W., Knapik, M.: Some things are easier for the dumb and the bright ones (beware the average!). In: Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence IJCAI, pp. 1734–1740 (2019). https://doi.org/10.24963/ijcai.2019/240

  33. Jamroga, W., Knapik, M., Kurpiewski, D., Mikulski, Ł.: Approximate verification of strategic abilities under imperfect information. Artif. Intell. 277 (2019). https://doi.org/10.1016/j.artint.2019.103172

  34. Kurpiewski, D., Jamroga, W., Knapik, M.: STV: Model checking for strategies under imperfect information. In: Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems AAMAS 2019, pp. 2372–2374. IFAAMAS (2019)

    Google Scholar 

  35. Kurpiewski, D., Knapik, M., Jamroga, W.: On domination and control in strategic ability. In: Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems AAMAS 2019, pp. 197–205. IFAAMAS (2019)

    Google Scholar 

  36. Kurpiewski, D., Pazderski, W., Jamroga, W., Kim, Y.: STV+reductions: towards practical verification of strategic ability using model reductions. In: Proceedings of AAMAS, pp. 1770–1772. ACM (2021)

    Google Scholar 

  37. Lomuscio, A., Qu, H., Raimondi, F.: MCMAS: an open-source model checker for the verification of multi-agent systems. Int. J. Softw. Tools Technol. Transf. 19(1), 9–30 (2017). https://doi.org/10.1007/s10009-015-0378-x

    Article  Google Scholar 

  38. Lomuscio, A., Raimondi, F.: Model checking knowledge, strategies, and games in multi-agent systems. In: Proceedings of International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS), pp. 161–168 (2006). https://doi.org/10.1145/1160633.1160660

  39. Mogavero, F., Murano, A., Perelli, G., Vardi, M.: Reasoning about strategies: on the model-checking problem. ACM Trans. Comput. Log. 15(4), 1–42 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  40. Mogavero, F., Murano, A., Vardi, M.: Reasoning about strategies. In: Proceedings of FSTTCS, pp. 133–144 (2010)

    Google Scholar 

  41. Peterson, G., Reif, J.: Multiple-person alternation. In: Proceedings of the 20th Annual Symposium on Foundations of Computer Science (FOCS), pp. 348–363. IEEE Computer Society Press (1979)

    Google Scholar 

  42. Pilecki, J., Bednarczyk, M.A., Jamroga, W.: Synthesis and verification of uniform strategies for multi-agent systems. In: Bulling, N., van der Torre, L., Villata, S., Jamroga, W., Vasconcelos, W. (eds.) CLIMA 2014. LNCS (LNAI), vol. 8624, pp. 166–182. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-09764-0_11

    Chapter  MATH  Google Scholar 

  43. Pilecki, J., Bednarczyk, M., Jamroga, W.: SMC: synthesis of uniform strategies and verification of strategic ability for multi-agent systems. J. Log. Comput. 27(7), 1871–1895 (2017). https://doi.org/10.1093/logcom/exw032

    Article  MathSciNet  MATH  Google Scholar 

  44. Raimondi, F., Lomuscio, A.: Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams. J. Appl. Log. 5(2), 235–251 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. Schobbens, P.Y.: Alternating-time logic with imperfect recall. Electron. Notes Theor. Comput. Sci. 85(2), 82–93 (2004)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The work was supported by NCBR Poland and FNR Luxembourg under the PolLux/FNR-CORE projects STV (POLLUX-VII/1/2019 and C18/IS/12685695/IS/STV/Ryan), SpaceVote (POLLUX-XI/14/SpaceVote/2023 and C22/IS/17232062/SpaceVote) and PABLO (C21/IS/16326754/PABLO). The work of Damian Kurpiewski was also supported by the CNRS IEA project MoSART.

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Authors and Affiliations

  1. Interdisciplinary Centre for Security, Reliability and Trust, SnT, University of Luxembourg, Esch-sur-Alzette, Luxembourg

    Wojciech Jamroga

  2. Institute of Computer Science, Polish Academy of Sciences, Warsaw, Poland

    Wojciech Jamroga & Damian Kurpiewski

  3. Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, Toruń, Poland

    Damian Kurpiewski

Authors
  1. Wojciech Jamroga
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  2. Damian Kurpiewski
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Correspondence to Damian Kurpiewski .

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Editors and Affiliations

  1. Télécom Paris, Paris, France

    Vadim Malvone

  2. Universitá degli Studi di Napoli Federico II, Naples, Italy

    Aniello Murano

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Jamroga, W., Kurpiewski, D. (2023). Pretty Good Strategies and Where to Find Them. In: Malvone, V., Murano, A. (eds) Multi-Agent Systems. EUMAS 2023. Lecture Notes in Computer Science(), vol 14282. Springer, Cham. https://doi.org/10.1007/978-3-031-43264-4_23

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  • DOI: https://doi.org/10.1007/978-3-031-43264-4_23

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