Skip to main content
SpringerLink
Log in

From Reachability to Temporal Specifications in Cost-Sharing Games

  • Conference paper
Book cover Automated Reasoning (IJCAR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8562))

Included in the following conference series:

  • 878 Accesses

Abstract

Multi-agents cost-sharing games are commonly used for modeling settings in which different entities share resources. For example, the setting in which entities need to route messages in a network is modeled by a network-formation game: the network is modeled by a graph, and each agent has to select a path satisfying his reachability objective. In practice, the objectives of the entities are often more involved than reachability. The need to specify and reason about rich specifications has been extensively studied in the context of verification and synthesis of reactive systems. This paper suggests and analyzes a generalization of cost-sharing games that captures such rich specifications. In particular, we study network-formation games with regular objectives. In these games, the edges of the graph are labeled by alphabet letters and the objective of each player is a regular language over the alphabet of labels. Thus, beyond reachability, a player may restrict attention to paths that satisfy certain properties, referring, for example, to the providers of the traversed edges, the actions associated with them, their quality of service, or security. Our results show that the transition to regular objectives makes the game considerably less stable.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albers, S., Elits, S., Even-Dar, E., Mansour, Y., Roditty, L.: On Nash Equilibria for a Network Creation Game. In: Proc. 17th SODA, pp. 89–98 (2006)

    Google Scholar 

  2. Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, É., Wexler, T., Roughgarden, T.: The Price of Stability for Network Design with Fair Cost Allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  3. Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)

    Article  MathSciNet  Google Scholar 

  4. Aminof, B., Kupferman, O., Lampert, R.: Reasoning about online algorithms with weighted automata. ACM Transactions on Algorithms 6(2) (2010)

    Google Scholar 

  5. Avni, G., Kupferman, O., Tamir, T.: Network-formation games with regular objectives. In: Muscholl, A. (ed.) FOSSACS 2014 (ETAPS). LNCS, vol. 8412, pp. 119–133. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  6. Alpern, B., Schneider, F.B.: Recognizing safety and liveness. Distributed Computing 2, 117–126 (1987)

    Article  MATH  Google Scholar 

  7. Brihaye, T., Bruyère, V., De Pril, J., Gimbert, H.: On subgame perfection in quantitative reachability games. Logical Methods in Computer Science 9(1) (2012)

    Google Scholar 

  8. Chatterjee, K.: Nash equilibrium for upward-closed objectives. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 271–286. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Chatterjee, K., Henzinger, T.A., Jurdzinski, M.: Games with secure equilibria. Theoretical Computer Science 365(1-2), 67–82 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  10. Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 59–73. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  11. Chatterjee, K., Majumdar, R., Jurdziński, M.: On Nash equilibria in stochastic games. In: Marcinkowski, J., Tarlecki, A. (eds.) CSL 2004. LNCS, vol. 3210, pp. 26–40. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Chen, H., Roughgarden, T.: Network Design with Weighted Players. Theory of Computing Systems 45(2), 302–324 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  13. Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: Selfish Routing in Capacitated Networks. Mathematics of Operations Research 29, 961–976 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  14. Daniele, M., Giunchiglia, F., Vardi, M.Y.: Improved automata generation for linear temporal logic. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 249–260. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. Springer (2009)

    Google Scholar 

  16. Dwork, C., Naor, M.: Pricing via Processing or Combatting Junk Mail. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 139–147. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  17. Fisman, D., Kupferman, O., Lustig, Y.: Rational synthesis. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 190–204. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  18. Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: Proc. 22nd PODC, pp. 347–351 (2003)

    Google Scholar 

  19. Feldman, M., Tamir, T.: Conflicting Congestion Effects in Resource Allocation Games. Journal of Operations Research 60(3), 529–540 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  20. von Falkenhausen, P., Harks, T.: Optimal Cost Sharing Protocols for Scheduling Games. In: Proc. 12th EC, pp. 285–294 (2011)

    Google Scholar 

  21. Fabrikant, A., Papadimitriou, C., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proc. 36th STOC, pp. 604–612 (2004)

    Google Scholar 

  22. de Giacomo, G., Vardi, M.Y.: Automata-Theoretic Approach to Planning for Temporally Extended Goals. In: Biundo, S., Fox, M. (eds.) ECP 1999. LNCS, vol. 1809, pp. 226–238. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  23. Harel, D., Pnueli, A.: On the development of reactive systems. In: LMCS. NATO Advanced Summer Institutes, vol. F-13, pp. 477–498. Springer (1985)

    Google Scholar 

  24. Herzog, S., Shenker, S., Estrin, D.: Sharing the “Cost” of Multicast Trees: An Axiomatic Analysis. IEEE/ACM Transactions on Networking (1997)

    Google Scholar 

  25. Koutsoupias, E., Papadimitriou, C.: Worst-case Equilibria. Computer Science Review 3(2), 65–69 (2009)

    Article  Google Scholar 

  26. Kupferman, O., Tamir, T.: Coping with selfish on-going behaviors. Information and Computation 210, 1–12 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  27. Mavronicolas, M., Milchtaich, I., Monien, B., Tiemann, K.: Congestion Games with Player-specific Constants. In: Kučera, L., Kučera, A. (eds.) MFCS 2007. LNCS, vol. 4708, pp. 633–644. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  28. Milchtaich, I.: Weighted Congestion Games With Separable Preferences. Games and Economic Behavior 67, 750–757 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  29. Mohri, M.: Finite-state transducers in language and speech processing. Computational Linguistics 23(2), 269–311 (1997)

    MathSciNet  Google Scholar 

  30. Monderer, D., Shapley, L.: Potential Games. Games and Economic Behavior 14, 124–143 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  31. Moulin, H., Shenker, S.: Strategyproof Sharing of Submodular Costs: Budget Balance Versus Efficiency. Journal of Economic Theory 18, 511–533 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  32. Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press (2007)

    Google Scholar 

  33. Nerode, A., Yakhnis, A., Yakhnis, V.: Concurrent programs as strategies in games. In: Proc. Logic from Computer Science, pp. 405–480 (1992)

    Google Scholar 

  34. Papadimitriou, C.: Algorithms, games, and the internet (Extended abstract). In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds.) ICALP 2001. LNCS, vol. 2076, pp. 1–3. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  35. Pnueli, A., Rosner, R.: On the synthesis of a reactive module. In: Automata, Languages and Programming, vol. 372, pp. 652–671. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  36. Paes Leme, R., Syrgkanis, V., Tardos, E.: The curse of simultaneity. In: Innovations in Theoretical Computer Science (ITCS), pp. 60–67 (2012)

    Google Scholar 

  37. Reed, M.G., Syverson, P.F., Goldschlag, D.M.: Anonymous Connections and Onion Routing. IEEE J. on SAC, Issue on Copyright and Privacy Protection (1998)

    Google Scholar 

  38. Reif, J.H.: The complexity of two-player games of incomplete information. Journal of Computer and Systems Science 29, 274–301 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  39. Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. International Journal of Game Theory 2, 65–67 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  40. Tardos, E., Wexler, T.: Network Formation Games and the Potential Function Method. In: Algorithmic Game Theory. Cambridge University Press (2007)

    Google Scholar 

  41. Vöcking, B.: In: Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V. (eds.) Algorithmic Game Theory: Selfish Load Balancing, ch. 20. Cambridge University Press (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Computer Science and Engineering, The Hebrew University, Jerusalem, Israel

    Guy Avni & Orna Kupferman

  2. School of Computer Science, The Interdisciplinary Center, Herzliya, Israel

    Tami Tamir

Authors
  1. Guy Avni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Orna Kupferman
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tami Tamir
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. CNRS,, New York University &amp, USA

    Stéphane Demri

  2. Department of Computer Science, University of New Mexico, 87131-0001, Albuquerque, NM, USA

    Deepak Kapur

  3. Max Planck Institute for Informatics, Campus E1 4, 66123, Saarbrücken, Germany

    Christoph Weidenbach

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Avni, G., Kupferman, O., Tamir, T. (2014). From Reachability to Temporal Specifications in Cost-Sharing Games. In: Demri, S., Kapur, D., Weidenbach, C. (eds) Automated Reasoning. IJCAR 2014. Lecture Notes in Computer Science(), vol 8562. Springer, Cham. https://doi.org/10.1007/978-3-319-08587-6_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-08587-6_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08586-9

  • Online ISBN: 978-3-319-08587-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation