Skip to main content

Computation of Stackelberg Equilibria of Finite Sequential Games

  • Conference paper
  • First Online:
  • 1134 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9470))

Abstract

The Stackelberg equilibrium is a solution concept that describes optimal strategies to commit to: Player 1 (the leader) first commits to a strategy that is publicly announced, then Player 2 (the follower) plays a best response to the leader’s choice. We study Stackelberg equilibria in finite sequential (i.e., extensive-form) games and provide new exact algorithms, approximate algorithms, and hardness results for finding equilibria for several classes of such two-player games.

This is a preview of subscription content, log in via an institution.

Notes

  1. 1.

    To be precise they assumed that the correlated strategies can use a finite history.

References

  1. Bosansky, B., Cermak, J.: Sequence-form algorithm for computing stackelberg equilibria in extensive-form games. In: Proceedings of AAAI (2015)

    Google Scholar 

  2. Conitzer, V., Korzhyk, D.: Commitment to correlated strategies. In: Proceedings of AAAI, pp. 632–637 (2011)

    Google Scholar 

  3. Conitzer, V., Sandholm, T.: Computing the optimal strategy to commit to. In: Proceedings of ACM-EC, pp. 82–90 (2006)

    Google Scholar 

  4. De Berg, M., Van Kreveld, M., Overmars, M., Schwarzkopf, O.C.: Computational Geometry, 2nd edn. Springer, Heidelberg (2000)

    Book  Google Scholar 

  5. Gritzmann, P., Sturmfels, B.: Minkowski addition of polytopes: computational complexity and applications to Gröbner bases. SIAM J. Discrete Math. 6(2), 246–269 (1993)

    Article  MathSciNet  Google Scholar 

  6. Letchford, J.: Computational aspects of Stackelberg games. Ph.D. thesis, Duke University (2013)

    Google Scholar 

  7. Letchford, J., Conitzer, V.: Computing optimal strategies to commit to in extensive-form games. In: Proceedings of ACM-EC, pp. 83–92. ACM (2010)

    Google Scholar 

  8. Letchford, J., MacDermed, L., Conitzer, V., Parr, R., Isbell, C.L.: Computing optimal strategies to commit to in stochastic games. In: Proceedings of AAAI, pp. 1380–1386 (2012)

    Google Scholar 

  9. Paruchuri, P., Pearce, J., Marecki, J., Tambe, M., Ordonez, F., Kraus, S.: Playing games for security: an efficient exact algorithm for solving bayesian stackelberg games. In: Proceedings of AAMAS, pp. 895–902 (2008)

    Google Scholar 

  10. von Stackelberg, H.: Marktform und gleichgewicht. Springer-Verlag (1934)

    Google Scholar 

  11. von Stengel, B., Forges, F.: Extensive-form correlated equilibrium: definition and computational complexity. Math. Oper. Res. 33(4), 1002–1022 (2008)

    Article  MathSciNet  Google Scholar 

  12. Tambe, M.: Security and Game Theory: Algorithms, Deployed Systems, Lessons Learned. Cambridge University Press, Cambridge (2011)

    Book  Google Scholar 

  13. Xu, H., Rabinovich, Z., Dughmi, S., Tambe, M.: Exploring information asymmetry in two-stage security games. In: Proceedings of AAAI (2015)

    Google Scholar 

Download references

Acknowledgements

We would like to thank the reviewers for useful feedback. This work was supported by the Danish National Research Foundation and The National Science Foundation of China (under the grant 61361136003) for the Sino-Danish Center for the Theory of Interactive Computation, by the Center for Research in Foundations of Electronic Markets (CFEM) supported by the Danish Strategic Research Council, and by the Czech Science Foundation (grant no. 15-23235S).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Branislav Bošanský .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bošanský, B., Brânzei, S., Hansen, K.A., Miltersen, P.B., Sørensen, T.B. (2015). Computation of Stackelberg Equilibria of Finite Sequential Games. In: Markakis, E., Schäfer, G. (eds) Web and Internet Economics. WINE 2015. Lecture Notes in Computer Science(), vol 9470. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48995-6_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-48995-6_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-48994-9

  • Online ISBN: 978-3-662-48995-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics