Equilibria of Games in Networks for Local Tasks

Authors Simon Collet, Pierre Fraigniaud, Paolo Penna



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Author Details

Simon Collet
  • CNRS and University Paris Diderot, France
Pierre Fraigniaud
  • CNRS and University Paris Diderot, France
Paolo Penna
  • ETH Zurich, Switzerland

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Simon Collet, Pierre Fraigniaud, and Paolo Penna. Equilibria of Games in Networks for Local Tasks. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 6:1-6:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.OPODIS.2018.6

Abstract

Distributed tasks such as constructing a maximal independent set (MIS) in a network, or properly coloring the nodes or the edges of a network with reasonably few colors, are known to admit efficient distributed randomized algorithms. Those algorithms essentially proceed according to some simple generic rules, by letting each node choosing a temptative value at random, and checking whether this choice is consistent with the choices of the nodes in its vicinity. If this is the case, then the node outputs the chosen value, else it repeats the same process. Although such algorithms are, with high probability, running in a polylogarithmic number of rounds, they are not robust against actions performed by rational but selfish nodes. Indeed, such nodes may prefer specific individual outputs over others, e.g., because the formers suit better with some individual constraints. For instance, a node may prefer not being placed in a MIS as it is not willing to serve as a relay node. Similarly, a node may prefer not being assigned some radio frequencies (i.e., colors) as these frequencies would interfere with other devices running at that node. In this paper, we show that the probability distribution governing the choices of the output values in the generic algorithm can be tuned such that no nodes will rationally deviate from this distribution. More formally, and more generally, we prove that the large class of so-called LCL tasks, including MIS and coloring, admit simple "Luby's style" algorithms where the probability distribution governing the individual choices of the output values forms a Nash equilibrium. In fact, we establish the existence of a stronger form of equilibria, called symmetric trembling-hand perfect equilibria for those games.

Subject Classification

ACM Subject Classification
  • Theory of computation → Distributed algorithms
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Network games
Keywords
  • Local distributed computing
  • Locally checkable labelings

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References

  1. Ittai Abraham, Danny Dolev, and Joseph Y. Halpern. Distributed Protocols for Leader Election: A Game-Theoretic Perspective. In 27th International Symposium on Distributed Computing (DISC), pages 61-75, 2013. URL: http://dx.doi.org/10.1007/978-3-642-41527-2_5.
  2. Daron Acemoglu, Munther A Dahleh, Ilan Lobel, and Asuman Ozdaglar. Bayesian learning in social networks. The Review of Economic Studies, 78(4):1201-1236, 2011. Google Scholar
  3. Yehuda Afek, Yehonatan Ginzberg, Shir Landau Feibish, and Moshe Sulamy. Distributed computing building blocks for rational agents. In Symposium on Principles of Distributed Computing (PODC), pages 406-415. ACM, 2014. Google Scholar
  4. Yehuda Afek, Shaked Rafaeli, and Moshe Sulamy. Cheating by Duplication: Equilibrium Requires Global Knowledge. Technical report, arXiv, 2017. URL: http://arxiv.org/abs/1711.04728.
  5. Noga Alon, László Babai, and Alon Itai. A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem. J. Algorithms, 7(4):567-583, 1986. URL: http://dx.doi.org/10.1016/0196-6774(86)90019-2.
  6. Chen Avin, Avi Cohen, Pierre Fraigniaud, Zvi Lotker, and David Peleg. Preferential Attachment as a Unique Equilibrium. In The Web Conference (WWW), New-York, 2018. ACM. Google Scholar
  7. Leonid Barenboim and Michael Elkin. Distributed Graph Coloring: Fundamentals and Recent Developments. Synthesis Lectures on Distributed Computing Theory. Morgan & Claypool Publishers, 2013. Google Scholar
  8. A. Calvó-Armengol and J. de Martí Beltran. Information gathering in organizations: Equilibrium, welfare and optimal network structure. Journal of the European Economic Association, 7:116-161, 2009. Google Scholar
  9. A. Calvó-Armengol, J. de Martí Beltran, and Prat A. Communication and influence. Theoretical Economics, 10:649-690, 2015. Google Scholar
  10. Subir K Chakrabarti. Equilibrium in Behavior Strategies in Infinite Extensive Form Games with Imperfect Information. Economic Theory, 2(4):481-494, 1992. Google Scholar
  11. Ky Fan. Fixed-Point and Minimax Theorems in Locally Convex Topological Linear Spaces. PNAS, 38(2):121-126, 1952. Google Scholar
  12. Drew Fudenberg and David Levine. Subgame-Perfect Equilibria of Finite- and Infinite-Horizon Games. Journal of Economic Theory, 31(2):251-268, 1983. Google Scholar
  13. Andrea Galeotti, Christian Ghiglino, and Francesco Squintani. Strategic information transmission networks. J. Economic Theory, 148(5):1751-1769, 2013. Google Scholar
  14. Irving L. Glicksberg. A Further Generalization of the Kakutani Fixed Point Theorem with Application to Nash Equilibrium Points. Proceedings of the AMS, 3(1):170-174, 1952. Google Scholar
  15. J. Hagenbach and F. Koessler. Strategic communication networks. Review of Economic Studies, 77(3):1072-1099, 2011. Google Scholar
  16. Christopher Harris. Existence and Characterization of Perfect Equilibrium in Games of Perfect Information. Econometrica: Journal of the Econometric Society, 53(3):613-628, 1985. Google Scholar
  17. Matthew O. Jackson, Brian W. Rogers, and Yves Zenou. Networks: An Economic Perspective. Technical report, arXiv, 2016. Google Scholar
  18. Matthew O Jackson and Yves Zenou. Games on networks. In Handbook of game theory with economic applications, volume 4, pages 95-163. Elsevier, 2015. Google Scholar
  19. Fabian Kuhn, Thomas Moscibroda, and Roger Wattenhofer. Radio Network Clustering from Scratch. In 12th European Symposium on Algorithms (ESA), LNCS 3221, pages 460-471. Springer, 2004. Google Scholar
  20. Harold W. Kuhn. Extensive Games and the Problem of Information. In Contributions to the Theory of Games, volume II (Annals of Mathematics Studies, 28), pages 193-216. Princeton University Press, 1953. Google Scholar
  21. Nathan Linial. Locality in Distributed Graph Algorithms. SIAM J. Comput., 21(1):193-201, 1992. Google Scholar
  22. Michael Luby. A Simple Parallel Algorithm for the Maximal Independent Set Problem. SIAM J. Comput., 15(4):1036-1053, 1986. URL: http://dx.doi.org/10.1137/0215074.
  23. Thomas Moscibroda and Roger Wattenhofer. Maximal independent sets in radio networks. In 24th Symposium on Principles of Distributed Computing (PODC), pages 148-157. ACM, 2005. URL: http://dx.doi.org/10.1145/1073814.1073842.
  24. Moni Naor and Larry J. Stockmeyer. What Can be Computed Locally? SIAM J. Comput., 24(6):1259-1277, 1995. URL: http://dx.doi.org/10.1137/S0097539793254571.
  25. John F. Nash. Equilibrium Points in n-Person Games. Proceedings of the National Academy of Sciences, 36(1):48-49, 1950. Google Scholar
  26. David Peleg. Distributed Computing: A Locality-Sensitive Approach. Discrete Mathematics and Applications. SIAM, Philadelphia, 2000. Google Scholar
  27. Roy Radner. Collusive Behavior in non-Cooperative epsilon-Equilibria of Oligopolies with Long but Finite Lives. Journal of Economic Theory, 22:136-154, 1980. Google Scholar
  28. Reinhard Selten. Spieltheoretische Behandlung eines Oligopolmodells mit Nachfragetraheit. Z. Gesamte Staatwissenschaft, 12:301-324, 1965. Google Scholar
  29. Reinhard Selten. Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games. International journal of game theory, 4(1):25-55, 1975. Google Scholar
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