Abstract
How and why people form ties is a critical issue for understanding the fabric of social networks. In contrast to most existing work, we are interested in settings where agents are neither so myopic as to consider only the benefit they derive from their immediate neighbors, nor do they consider the effects on the entire network when forming connections. Instead, we consider games on networks where a node tries to maximize its utility taking into account the benefit it gets from the nodes it is directly connected to (called direct benefit), as well as the benefit it gets from the nodes it is acquainted with via a two-hop connection (called two-hop benefit). We call such games Two-Hop Games. The decision to consider only two hops stems from the observation that human agents rarely consider “contacts of a contact of a contact” (3-hop contacts) or further while forming their relationships. We consider several versions of Two-Hop games which are extensions of well-studied games. While the addition of two-hop benefit changes the properties of these games significantly, we prove that in many important cases good equilibrium solutions still exist, and bound the change in the price of anarchy due to two-hop benefit both theoretically and in simulation.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abraham, D.J., Levavi, A., Manlove, D.F., O’Malley, G.: The stable roommates problem with globally ranked pairs. Internet Math. 5(4), 493–515 (2008)
Abramson, G., Kuperman, M.: Social games in a social network. Phys. Rev. E 63(3), 030901 (2001)
Alon, N., Demaine, E.D., Hajiaghayi, M.T., Leighton, T.: Basic network creation games. SIAM J. Discret. Math. 27(2), 656–668 (2013)
Anshelevich, E., Das, S., Naamad, Y.: Anarchy, stability, and utopia: creating better matchings. In: SAGT (2009)
Anshelevich, E., Hoefer, M.: Contribution games in networks. Algorithmica 63(1-2), 51–90 (2012)
Baiou, M., Balinski, M.: Many-to-many matching: stable polyandrous polygamy (or polygamous polyandry). Discret. Appl. Math. 101(13), 1–12 (2000)
Bei, Xi., Chen, W., Teng, S., Zhang, J., Zhu, J.: Bounded budget betweenness centrality game for strategic network formations. Theor. Comput. Sci. 412(52), 7147–7168 (2011)
Bramoullé, Y., Kranton, R.: Public goods in networks. J. Econ. Theory 135(1), 478–494 (2007)
Brandes, U., Hoefer, M., Nick, B.: Network creation games with disconnected equilibria. In: WINE (2008)
Buehler, R., Goldman, Z., Liben-Nowell, D., Pei, Y., Quadri, J., Sharp, A., Taggart, S., Wexler, T., Woods, K.: The price of civil society. WINE (2011)
Chung, K.S.: On the existence of stable roommate matchings. Games Econ. Behav. 33(2), 206–230 (2000)
Corbo, J., Calvó-Armengol, A., Parkes, D.: The importance of network topology in local contribution games. WINE (2007)
Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: Proceedings of PODC, pp. 99–107. ACM (2005)
Demaine, E., Hajiaghayi, M., Mahini, H., Zadimoghaddam, M.: The price of anarchy in network creation games. In: Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing, pp. 292–298. ACM (2007)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a network creation game. In: Proceedings of PODC, pp. 347–351. ACM (2003)
Gale, D., Shapley, L.S.: College admissions and the stability of marriage. Am. Math. Mon., 9–15 (1962)
Galeotti, A., Goyal, S., Jackson, M.O., Vega-Redondo, F., Yariv, L.: Network games. Rev. Econ. Stud. 77(1), 218–244 (2010)
Gusfield, D., Irving, R.W.: The stable marriage problem: structure and algorithms (1989)
Hoefer, M., Krysta, P.: Geometric network design with selfish agents. In: Computing and Combinatorics, pp. 167–178. Springer (2005)
Hoefer, M., Skopalik, A.: Social context in potential games. In: WINE (2012)
Jackson, M.O., Wolinsky, A.: A strategic model of social and economic networks. J. Econ. Theory 71(1), 44–74 (1996)
Laoutaris, N., Poplawski, L., Rajaraman, R., Sundaram, R., Teng, S.: Bounded budget connection (bbc) games or how to make friends and influence people, on a budget. In: Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing, pp. 165–174. ACM (2008)
Manlove, D.: Algorithmics of matching under preferences. World Scientific Publishing (2013)
Osborne, M.J., Rubinstein, A.: A course in game theory. MIT press (1994)
Roth, A.E., Sotomayor, M.A.O.: Two-sided matching: a study in game-theoretic modeling and analysis, vol. 18. Cambridge University Press (1992)
Sethuraman, J., Teo, C.P., Qian, L.: Many-to-one stable matching: geometry and fairness. Math. Oper. Res. 31(3), 581–596 (2006)
Sotomayor, M.: Three remarks on the many-to-many stable matching problem. Math. Social Sci. 38(1), 55–70 (1999)
Acknowledgments
We thank Martin Hoefer for many useful discussions about Two-Hop games. This work was supported in part by NSF awards CCF- 0914782, CCF-1101495, and CNS-1017932.
Author information
Authors and Affiliations
Corresponding author
Additional information
Preliminary version of this paper appeared in Symposium on Algorithmic Game Theory, 2013
Rights and permissions
About this article
Cite this article
Anshelevich, E., Bhardwaj, O. & Usher, M. Friend of My Friend: Network Formation with Two-Hop Benefit. Theory Comput Syst 57, 711–752 (2015). https://doi.org/10.1007/s00224-014-9582-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00224-014-9582-4