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Computational social choice for coordination in agent networks

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Abstract

This paper presents some models and algorithms for social choice in agent networks. Agent networks are graphical models used to represent systems involving multiple, locally interacting, agents. They allow the representation of complex decision-making situations where the utility function of every agent depends on the actions of its neighbors. In this context, coordination requires some optimization method able to determine a combination of individual actions that maximizes social efficiency. We study here the maximization of different social welfare functions covering various attitudes ranging from utilitarianism to egalitarianism. For all these models we propose graph-based algorithms as well as MIP formulations to find optimal sets of actions. We also provide numerical tests to assess their practical efficiency.

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References

  1. Arrow, K.J., Sen, A.K., Suzumura, K., (eds.): Handbook of Social Choice and Welfare, vol. 2. Elsevier (2012)

  2. Ausiello, G.: Complexity and approximation: Combinatorial optimization problems and their approximability properties. Springer Science & Business Media (1999)

  3. Bacchus, F., Grove, A.: Graphical models for preference and utility. In: Proceedings of the Eleventh conference on Uncertainty in artificial intelligence, pp. 3–10. Morgan Kaufmann Publishers Inc. (1995)

  4. Bertele, U., Brioschi, F.: Nonserial dynamic programming. Academic Press Inc. (1972)

  5. Bodlaender, H.L.: A partial k-arboretum of graphs with bounded treewidth. Theor. Comput. Sci. 209(1-2), 1–45 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Braziunas, D., Boutilier, C.: Local utility elicitation in GAI models. In: Proceedings of the Twenty-first Conference on Uncertainty in Artificial Intelligence (UAI-05), pp. 42–49 (2005)

  7. Chapman, A.C., Farinelli, A., Munoz, E., Cote, de, Rogers, A., Jennings, N.R.: A distributed algorithm for optimising over pure strategy Nash equilibria. In: AAAI (2010)

  8. Daskalakis, C., Papadimitriou, C.H.: Computing pure Nash equilibria in graphical games via Markov random fields. In: ACM-EC, pp. 91–99 (2006)

  9. Dechter, R., Pearl, J.: Tree clustering for constraint networks. Artif. Intell. 38(3), 353–366 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  10. Diakonikolas, I., Yannakakis, M.: Small approximate pareto sets for biobjective shortest paths and other problems. SIAM J. Comput. 39(4), 1340–1371 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Elkind, E., Goldberg, L.A., Goldberg, P.W.: Computing good Nash equilibria in graphical games (2007)

  12. Fishburn, P.C.: Interdependence and additivity in multivariate, unidimensional expected utility theory. Int. Econ. Rev. 8, 335–342 (1967)

    Article  MATH  Google Scholar 

  13. Gao, Y.: Treewidth of Erdos-rényi random graphs, random intersection graphs, and scale-free random graphs. Discrete Applied Mathematics (2011)

  14. Gonzales, C., Perny, P., Queiroz, S.: GAI-networks: optimization, ranking and collective choice in combinatorial domains. Found. Comput. Decis. Sci. 33, 3–24 (2008)

    MathSciNet  MATH  Google Scholar 

  15. Inc. Gurobi Optimization. Gurobi optimizer reference manual (2015)

  16. Ismaili, A., Bampis, E., Maudet, N., Perny, P.: A study on the stability and efficiency of graphical games with unbounded treewidth. In: proceedings of AAMAS (2013)

  17. Jensen, F., Jensen, F.V., Dittmer, S.L.: From influence diagrams to junction trees. In: Proceedings of the Tenth international conference on Uncertainty in artificial intelligence, pp. 367–373. Morgan Kaufmann Publishers Inc. (1994)

  18. Jiang, A.X., Safari, M.A.: Pure Nash equilibria: complete characterization of hard and easy graphical games. In: AAMAS, pp. 199–206 (2010)

  19. Kearns, M.: Graphical games. In: Algorithmic Game Theory. Cambridge University Press, Cambridge, UK (2007)

  20. Kearns, M.J., Littman, M.L., Singh, S.P.: Graphical models for game theory. In: UAI (2001)

  21. Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: STACS 99, pp. 404–413. Springer (1999)

  22. Kwisthout, J., Bodlaender, H.L., Gaag, L.C.V.D.: The necessity of bounded treewidth for efficient inference in bayesian networks. In: ECAI, vol. 215, pp. 237–242 (2010)

  23. Lesca, J., Minoux, M., Perny, P.: Compact versus Noncompact LP Formulations for minimizing Convex Choquet Integrals. Discret. Appl. Math. 161, 184–199 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  24. Lesca, J., Perny, P.: LP Solvable Models for Multiagent Fair Allocation problems. In: European Conference on Artificial Intelligence, pp. 387–392 (2010)

  25. Madsen, A.L., propagation, F.V., Jensen, LAZY: A junction tree inference algorithm based on lazy inference. Artif. Intell. 113(1–2), 203–245 (1999)

    Article  MATH  Google Scholar 

  26. Michel, G., Jean-Luc, M., Radko, M., Endre, P.: Aggregation Functions. Cambridge University Press (2009)

  27. Moulin, H.: Axioms of Cooperative Decision Making. Cambridge University Press (1991)

  28. Katta, G.M.: An algorithm for ranking all the assignments in order of increasing cost. Oper. Res. 16(3), 682–687 (1968)

    Article  Google Scholar 

  29. Nilsson, D.: An efficient algorithm for finding the M most probable configurations in probabilistic expert systems. Stat. Comput. 8(2), 159–173 (1998)

    Article  Google Scholar 

  30. Ogryczak, W., Sliwinski, T.: On solving linear programs with the ordered weighted averaging objective. Eur. J. Oper. Res. 148(1), 80–91 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  31. Olkin, I., Marshall, A.W.: Inequalities: Theory of majorization and its applications. Academic, New York (1979)

    MATH  Google Scholar 

  32. Papadimitriou, C.H., Yannakakis, M.: On the approximability of trade-offs and optimal access of web sources. In: Foundations of Computer Science, 2000. Proceedings. 41st Annual Symposium on, pp. 86–92. IEEE (2000)

  33. Roughgarden, T.: Routing games. Algorithmic Game Theory, 18 (2007)

  34. Roughgarden, T., Tardos, É.: How bad is selfish routing J. ACM (JACM) 49(2), 236–259 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  35. Salehi-Abari, A., Boutilier, C.: Empathetic social choice on social networks. In: Proceedings of the 2014 international conference on Autonomous agents and multi-agent systems, pages 693–700. International Foundation for Autonomous Agents and Multiagent Systems (2014)

  36. Schmeidler, D.: Subjective probability and expected utility without additivity. Econometrica 57(3), 571–587 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sen, A.K.: Social Choice Theory, vol. 3, pp. 1073–1181. Elsevier (1986)

  38. Shorrocks, A.F.: Ranking income distributions. Economica 50, 3–17 (1983)

    Article  Google Scholar 

  39. Weymark, J.A.: Generalized Gini inequality indices. Math. Soc. Sci. 1, 409–430 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  40. Yager, R.R.: On ordered weighted averaging aggregation operators in multicriteria decisionmaking. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Sorbonne Universités, Université Pierre et Marie Curie, Univ Paris 06, UMR 7606, LIP6, 75005, Paris, France

    Anisse Ismaili & Patrice Perny

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  1. Anisse Ismaili
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  2. Patrice Perny
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Correspondence to Patrice Perny.

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Ismaili, A., Perny, P. Computational social choice for coordination in agent networks. Ann Math Artif Intell 77, 335–359 (2016). https://doi.org/10.1007/s10472-015-9462-x

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  • DOI: https://doi.org/10.1007/s10472-015-9462-x

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