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Epistemic Reasoning About Rationality and Bids in Auctions

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Part of the Lecture Notes in Computer Science book series (LNAI,volume 12678)

Abstract

In this paper, we investigate strategic reasoning in the context of auctions. More precisely, we establish an explicit link between bidding actions and bounded rationality. To do so, we extend the Auction Description Language with an epistemic operator and an action choice operator and use it to represent a classical auction where agents have imperfect information about other agents’ valuations. We formalize bounded rationality concepts in iterative protocols and show how to use them to reason about the players’ actions. Finally, we provide a model checking algorithm.

Keywords

  • Logics for multi-agent systems
  • Game description language
  • Bounded rationality
  • Auction-based markets

This research is supported by the ANR project AGAPE ANR-18-CE23-0013 and by the EU project TAILOR (EU Horizon 2020 program, GA No 952215).

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References

  1. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. ACM (JACM) 49(5), 672–713 (2002)

    MathSciNet  CrossRef  Google Scholar 

  2. Aumann, R.: Backward induction and common knowledge of rationality. Games Econ. Behav. 8, 6–19 (1995)

    MathSciNet  CrossRef  Google Scholar 

  3. Bonanno, G.: Epistemic foundations of game theory. In: van Ditmarsch, H., Halpern, J.Y., van der Hoek, W., Kooi, B. (eds.) Handbook of Logics for Knowledge and Belief, chap. 9, pp. 411–450. College Publications (2015)

    Google Scholar 

  4. Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Inf. Comput. 208(6), 677–693 (2010)

    MathSciNet  CrossRef  Google Scholar 

  5. Chen, J., Micali, S.: Leveraging possibilistic beliefs in unrestricted combinatorial auctions. Games 7(32), 83–101 (2016)

    Google Scholar 

  6. Chen, J., Micali, S., Pass, R.: Tight revenue bounds with possibilistic beliefs and level-k rationality. Econometrica 83(4), 1619–1639 (2015)

    MathSciNet  CrossRef  Google Scholar 

  7. Fagin, R., Moses, Y., Halpern, J.Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  8. Feige, U., Feldman, M., Immorlica, N., Izsak, R., Lucier, B., Syrgkanis, V.: A unifying hierarchy of valuations with complements and substitutes. In: Proceedings of AAAI 2015, pp. 872–878. AAAI Press (2015)

    Google Scholar 

  9. Genesereth, M., Thielscher, M.: General Game Playing. Synthesis Lectures on Artificial Intelligence and Machine Learning. Morgan & Claypool Publishers, San Rafael (2014)

    CrossRef  Google Scholar 

  10. Jamroga, W., van der Hoek, W.: Agents that know how to play. Fundamenta Informaticae 63(2–3), 185–219 (2004)

    MathSciNet  MATH  Google Scholar 

  11. Jiang, G., Perrussel, L., Zhang, D.: On axiomatization of epistemic GDL. In: Baltag, A., Seligman, J., Yamada, T. (eds.) LORI 2017. LNCS, vol. 10455, pp. 598–613. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-55665-8_41

    CrossRef  Google Scholar 

  12. Jiang, G., Zhang, D., Perrussel, L., Zhang, H.: Epistemic GDL: a logic for representing and reasoning about imperfect information games. In: Procedings of IJCAI-2016 (2016)

    Google Scholar 

  13. Krishna, V.: Auction Theory. Academic Press, San Diego (2009)

    Google Scholar 

  14. Lorini, E.: A minimal logic for interactive epistemology. Synthese 193(3), 725–755 (2015). https://doi.org/10.1007/s11229-015-0960-5

    MathSciNet  CrossRef  MATH  Google Scholar 

  15. Mittelmann, M., Perrussel, L.: Auction description language (ADL): a general framework for representing auction-based markets. In: ECAI 2020. IOS Press, Santiago de Compostela (2020)

    Google Scholar 

  16. Parkes, D.C.: Iterative Combinatorial Auctions. Combinatorial Auctions. MIT Press, Cambridge (2006). https://doi.org/10.7551/mitpress/9780262033428.003.0003

  17. Ramanujam, R., Simon, S.: Dynamic logic on games with structured strategies. In: Proceedings of KR-2008, pp. 49–58. AAAI Press (2008)

    Google Scholar 

  18. Thielscher, M.: A general game description language for incomplete information games. In: Proceedings of AAAI 2010, pp. 994–999 (2010)

    Google Scholar 

  19. Thielscher, M.: GDL-III: a description language for epistemic general game playing. In: Proceedings of IJCAI-2017, pp. 1276–1282 (2017)

    Google Scholar 

  20. Van Benthem, J.: Games in dynamic-epistemic logic. Bull. Econ. Res. 53(4), 219–248 (2001). https://doi.org/10.1111/1467-8586.00133

    MathSciNet  CrossRef  MATH  Google Scholar 

  21. Zhang, D., Thielscher, M.: A logic for reasoning about game strategies. In: Proceedings of AAAI 2015, pp. 1671–1677. AAAI Press (2015)

    Google Scholar 

  22. Zhang, D., Thielscher, M.: Representing and reasoning about game strategies. J. Philos. Logic 44(2), 203–236 (2014). https://doi.org/10.1007/s10992-014-9334-6

    MathSciNet  CrossRef  MATH  Google Scholar 

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Correspondence to Munyque Mittelmann .

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Mittelmann, M., Herzig, A., Perrussel, L. (2021). Epistemic Reasoning About Rationality and Bids in Auctions. In: Faber, W., Friedrich, G., Gebser, M., Morak, M. (eds) Logics in Artificial Intelligence. JELIA 2021. Lecture Notes in Computer Science(), vol 12678. Springer, Cham. https://doi.org/10.1007/978-3-030-75775-5_9

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  • DOI: https://doi.org/10.1007/978-3-030-75775-5_9

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