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Bargaining in Networks with Socially-Aware Agents

  • Konstantinos Georgiou
  • Somnath KunduEmail author
Conference paper
Part of the Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering book series (LNICST, volume 277)

Abstract

We introduce and characterize new stability notions in bargaining games over networks. Similar results were already known for networks induced by simple graphs, and for bargaining games whose underlying combinatorial optimization problems are packing-type. Our results are threefold. First, we study bargaining games whose underlying combinatorial optimization problems are covering-type. Second, we extend the study of stability notions when the networks are induced by hypergraphs, and we further extend the results to fully weighted instances where the objects that are negotiated have non-uniform value among the agents. Third, we introduce and characterize new stability notions that are naturally derived by polyhedral combinatorics and duality theory for Linear Programming. Interestingly, these new stability notions admit intuitive interpretations touching on socially-aware agents. Overall, our contributions are meant to identify natural and desirable bargaining outcomes as well as to characterize powerful positions in bargaining networks.

Keywords

Bargaining Stable outcomes Hypergraphs Linear Programming 

References

  1. 1.
    Azar, Y., Birnbaum, B., Celis, L.E., Devanur, N.R., Peres, Y.: Convergence of local dynamics to balanced outcomes in exchange networks. In: 50th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2009, Atlanta, Georgia, USA, 25–27 October 2009, pp. 293–302. IEEE Computer Society (2009)Google Scholar
  2. 2.
    Bateni, M.H., Hajiaghayi, M.T., Immorlica, N., Mahini, H.: The cooperative game theory foundations of network bargaining games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6198, pp. 67–78. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-14165-2_7CrossRefGoogle Scholar
  3. 3.
    Bayati, M., Borgs, C., Chayes, J., Kanoria, Y., Montanari, A.: Bargaining dynamics in exchange networks. J. Econ. Theory 156, 417–454 (2015)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bock, A., Chandrasekaran, K., Könemann, J., Peis, B., Sanità, L.: Finding small stabilizers for unstable graphs. Math. Program. 154(1–2), 173–196 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Celis, L.E., Devanur, N.R., Peres, Y.: Local dynamics in bargaining networks via random-turn games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 133–144. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-17572-5_11CrossRefGoogle Scholar
  6. 6.
    Chakraborty, T., Kearns, M.: Bargaining solutions in a social network. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 548–555. Springer, Heidelberg (2008).  https://doi.org/10.1007/978-3-540-92185-1_61CrossRefGoogle Scholar
  7. 7.
    Chakraborty, T., Kearns, M., Khanna, S.: Network bargaining: algorithms and structural results. In: Proceedings 10th ACM Conference on Electronic Commerce, EC 2009, Stanford, California, USA, 6–10 July 2009, pp. 159–168 (2009)Google Scholar
  8. 8.
    Chalkiadakis, G., Elkind, E., Wooldridge, M.: Computational Aspects of Cooperative Game Theory. Morgan & Claypool Publishers, San Rafael (2011)CrossRefGoogle Scholar
  9. 9.
    Chan, T.-H.H., Chen, F., Ning, L.: Optimizing social welfare for network bargaining games in the face of unstability, greed and spite. In: Epstein, L., Ferragina, P. (eds.) ESA 2012. LNCS, vol. 7501, pp. 265–276. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-33090-2_24CrossRefGoogle Scholar
  10. 10.
    Chvátal, V.: Edmonds polytopes and a hierarchy of combinatorial problems. Discrete Math. 306(10–11), 886–904 (2006)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Cook, K.S., Emerson, R.M., Gillmore, M.R., Yamagishi, T.: Distribution of power in exchange networks: theory and experimental results. Am. J. Sociol. 89, 275–305 (1983)CrossRefGoogle Scholar
  12. 12.
    Deng, X., Fang, Q.: Algorithmic cooperative game theory. In: Chinchuluun, A., Pardalos, P.M., Migdalas, A., Pitsoulis, L. (eds.) Pareto Optimality, Game Theory and Equilibria. SOIA, vol. 17, pp. 159–185. Springer, New York (2008).  https://doi.org/10.1007/978-0-387-77247-9_7CrossRefGoogle Scholar
  13. 13.
    Deng, X., Ibaraki, T., Nagamochi, H.: Algorithmic aspects of the core of combinatorial optimization games. Math. Oper. Res. 24(3), 751–766 (1999)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Draief, M., Vojnovic, M.: Bargaining dynamics in exchange networks. CoRR, abs/1202.1089 (2012)Google Scholar
  15. 15.
    Farczadi, L., Georgiou, K., Könemann, J.: Network bargaining with general capacities. In: Bodlaender, H.L., Italiano, G.F. (eds.) ESA 2013. LNCS, vol. 8125, pp. 433–444. Springer, Heidelberg (2013).  https://doi.org/10.1007/978-3-642-40450-4_37CrossRefGoogle Scholar
  16. 16.
    Georgiou, K., Karakostas, G., Könemann, J., Stamirowska, Z.: Social exchange networks with distant bargaining. Theoret. Comput. Sci. 554, 263–274 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Gomory, R.E.: Solving linear programming problems in integers. In: Bellman, R., Hall Jr., M. (eds.) Combinatorial Analysis, pp. 211–215, Providence, RI. Symposia in Applied Mathematics X. American Mathematical Society (1960)Google Scholar
  18. 18.
    Granot, D., Granot, F.: On some network flow games. Math. Oper. Res. 17(4), 792–841 (1992)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Hajiaghayi, M., Mahini, H.: Bargaining networks. In: Kao, M.Y. (ed.) Encyclopedia of Algorithms, pp. 1–5. Springer, Boston (2014).  https://doi.org/10.1007/978-3-642-27848-8CrossRefGoogle Scholar
  20. 20.
    Ito, T., Kakimura, N., Kamiyama, N., Kobayashi, Y., Okamoto, Y.: Efficient stabilization of cooperative matching games. Theoret. Comput. Sci. 677, 69–82 (2017)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kanoria, Y., Bayati, M., Borgs, C., Chayes, J.T., Montanari, A.: A natural dynamics for bargaining on exchange networks. CoRR, abs/0911.1767 (2009)Google Scholar
  22. 22.
    Kleinberg, J.M., Tardos, É.: Balanced outcomes in social exchange networks. In: Proceedings of the ACM Symposium on Theory of Computing, pp. 295–304 (2008)Google Scholar
  23. 23.
    Lasserre, J.B.: An explicit exact SDP relaxation for nonlinear 0-1 programs. In: Aardal, K., Gerards, B. (eds.) IPCO 2001. LNCS, vol. 2081, pp. 293–303. Springer, Heidelberg (2001).  https://doi.org/10.1007/3-540-45535-3_23CrossRefGoogle Scholar
  24. 24.
    Lovász, L., Schrijver, A.: Cones of matrices and set-functions and 0-1 optimization. SIAM J. Optim. 1(2), 166–190 (1991)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Nash, J.: The bargaining problem. Econometrica 18, 155–162 (1950)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Nemhauser, G.L., Wolsey, L.A.: Integer and Combinatorial Optimization. Wiley, Hoboken (1988)CrossRefGoogle Scholar
  27. 27.
    Rochford, S.C.: Symmetrically pairwise-bargained allocations in an assignment market. J. Econ. Theory 34(2), 262–281 (1984)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Shapley, L.S., Shubik, M.: The assignment game: the core. Int. J. Game Theory 1(1), 111–130 (1971)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Sherali, H.D., Adams, W.P.: A hierarchy of relaxations between the continuous and convex hull representations for zero-one programming problems. SIAM J. Discrete Math. 3(3), 411–430 (1990)MathSciNetCrossRefGoogle Scholar
  30. 30.
    Willer, D.: Network Exchange Theory. Praeger Publishers, Westport (1999)Google Scholar

Copyright information

© ICST Institute for Computer Sciences, Social Informatics and Telecommunications Engineering 2019

Authors and Affiliations

  1. 1.Department of MathematicsRyerson UniversityTorontoCanada

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