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Optimizing over Serial Dictatorships

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Algorithmic Game Theory (SAGT 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14238))

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Abstract

Motivated by the success of the serial dictatorship mechanism in social choice settings, we explore its usefulness in tackling various combinatorial optimization problems. We do so by considering an abstract model, in which a set of agents are asked to act in a particular ordering, called the action sequence. Each agent acts in a way that gives her the maximum possible value, given the actions of the agents who preceded her in the action sequence. Our goal is to compute action sequences that yield approximately optimal total value to the agents (a.k.a., social welfare). We assume query access to the value \(v_i(S)\) that the agent i gets when she acts after the agents in the ordered set S.

We establish tight bounds on the social welfare that can be achieved using polynomially many queries. Even though these bounds show a marginally sublinear approximation of optimal social welfare in general, excellent approximations can be obtained when the valuations stem from an underlying combinatorial domain. Indicatively, when the valuations are defined using bipartite matching and satisfiability of Boolean expressions, simple query-efficient algorithms yield 2-approximations. Furthermore, we introduce and study the price of serial dictatorship, a notion that provides an optimistic measure of the quality of combinatorial optimization solutions generated by action sequences.

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Notes

  1. 1.

    Note that agents are myopic, i.e., they choose their best available action in a given round without thinking how their peers will behave in subsequent rounds.

  2. 2.

    Indeed, consider instances in which a special agent i has valuation \(v_i(S)=1\) if S contains all \(n-1\) other agents in a specific hidden order and all other agent valuations are zero. To compute the only action sequence with non-zero social welfare, an algorithm needs to “guess” the hidden order.

  3. 3.

    A clause is the disjunction of literals of the variables e.g., \(C_4 = x_1 \vee \overline{x_2} \vee \overline{x_4}\).

  4. 4.

    An OSI instance is defined with an n-node undirected graph G. Each node corresponds to an agent. For an agent \(i\in [n]\), the value \(v_i(S)\) for an action subsequence \(S\in \mathcal {S}_{-i}\) is 1 if the nodes in \(S\cup \{i\}\) form an independent set and 0 otherwise. It is not difficult to see that these valuations are monotone. Furthermore, the social welfare \(\textrm{SW}(\pi )\) of an action sequence \(\pi \) is equal to the length of the maximal prefix of \(\pi \) consisting of agents whose corresponding nodes form an independent set in G. Hence, the optimal social welfare among all action sequences is equal to the size of the maximum independent set. Now, notice that a simple algorithm that uses only \(O(n^2)\) queries can learn the underlying graph G, compute a maximum independent set in it, and, consequently, an action sequence with maximum social welfare. It just suffices to query the value \(v_i(j)\) for every pair of agents i and j. Then, the edge (i, j) exists in G if \(v_i(j)=0\) and does not exist if \(v_i(j)=1\).

References

  1. Abdulkadiroğlu, A., Sönmez, T.: Random serial dictatorship and the core from random endowments in house allocation problems. Econometrica 66(3), 689–701 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abraham, D.J., Cechlárová, K., Manlove, D.F., Mehlhorn, K.: Pareto optimality in house allocation problems. In: Proceedings of the 16th International Symposium on Algorithms and Computation (ISAAC), pp. 3–15 (2005)

    Google Scholar 

  3. Anshelevich, E., Dasgupta, A., Kleinberg, J.M., 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  MathSciNet  MATH  Google Scholar 

  4. Bertsimas, D., Farias, V.F., Trichakis, N.: The price of fairness. Oper. Res. 59(1), 17–31 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Beynier, A., Bouveret, S., Lemaître, M., Maudet, N., Rey, S., Shams, P.: Efficiency, sequenceability and deal-optimality in fair division of indivisible goods. In: Proceedings of the 18th International Conference on Autonomous Agents and MultiAgent Systems (AAMAS), pp. 900–908 (2019)

    Google Scholar 

  6. Bogomolnaia, A., Moulin, H.: A new solution to the random assignment problem. J. Econ. Theory 100(2), 295–328 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Borodin, A., Boyar, J., Larsen, K.S., Mirmohammadi, N.: Priority algorithms for graph optimization problems. Theor. Comput. Sci. 411(1), 239–258 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Borodin, A., Nielsen, M.N., Rackoff, C.: Incremental priority algorithms. Algorithmica 37(4), 295–326 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Bouveret, S., Lang, J.: A general elicitation-free protocol for allocating indivisible goods. In: Proceedings of the 22nd International Joint Conference on Artificial Intelligence (IJCAI), pp. 73–78 (2011)

    Google Scholar 

  10. Caragiannis, I., Filos-Ratsikas, A., Frederiksen, S.K.S., Hansen, K.A., Tan, Z.: Truthful facility assignment with resource augmentation: an exact analysis of serial dictatorship. In: Proceedings of the 12th Conference on Web and Internet Economics (WINE), pp. 236–250 (2016)

    Google Scholar 

  11. Caragiannis, I., Kaklamanis, C., Kanellopoulos, P., Kyropoulou, M.: The efficiency of fair division. Theory Comput. Syst. 50(4), 589–610 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Chen, J., Friesen, D., Zheng, H.: Tight bound on Johnson’s algorithm for max-sat. In: Proceedings of the 12th Annual IEEE Conference on Computational Complexity (CCC), pp. 274–281 (1997)

    Google Scholar 

  13. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 3rd edn. The MIT Press, Cambridge (2009)

    MATH  Google Scholar 

  14. Davis, S., Impagliazzo, R.: Models of greedy algorithms for graph problems. In: Proceedings of the 15th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pp. 381–390 (2004)

    Google Scholar 

  15. Deligkas, A., Mertzios, G.B., Spirakis, P.G.: The computational complexity of weighted greedy matching. In: Proceedings of the 31st AAAI Conference on Artificial Intelligence (AAAI), pp. 466–472 (2017)

    Google Scholar 

  16. Filos-Ratsikas, A., Frederiksen, S.K.S., Zhang, J.: Social welfare in one-sided matchings: random priority and beyond. In: Proceedings of the 7th International Symposium on Algorithmic Game Theory (SAGT), pp. 1–12 (2014)

    Google Scholar 

  17. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness (Series of Books in the Mathematical Sciences). W. H. Freeman (1979)

    Google Scholar 

  18. Gourvès, L., Lesca, J., Wilczynski, A.: On fairness via picking sequences in allocation of indivisible goods. In: Proceedings of the 7th International Conference on Algorithmic Decision Theory (ADT), pp. 258–272 (2021)

    Google Scholar 

  19. Johnson, D.S.: Approximation algorithms for combinatorial problems. J. Comput. Syst. Sci. 9(3), 256–278 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  20. Kalinowski, T., Narodytska, N., Walsh, T.: A social welfare optimal sequential allocation procedure. In: Proceedings of the 24th International Joint Conference on Artificial Intelligence (IJCAI), pp. 227–233 (2013)

    Google Scholar 

  21. Krysta, P., Manlove, D.F., Rastegari, B., Zhang, J.: Size versus truthfulness in the house allocation problem. Algorithmica 81(9), 3422–3463 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lehmann, B., Lehmann, D., Nisan, N.: Combinatorial auctions with decreasing marginal utilities. Games Econom. Behav. 55(2), 270–296 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. Manlove, D.F.: Algorithmics of Matching Under Preferences. World Scientific (2013)

    Google Scholar 

  24. Poloczek, M., Schnitger, G., Williamson, D., Zuylen, A.: Greedy algorithms for the maximum satisfiability problem: simple algorithms and inapproximability bounds. SIAM J. Comput. 46, 1029–1061 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  25. Roth, A.E., Sotomayor, M.A.O.: Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  26. Svensson, L.G.: Strategy-proof allocation of indivisible goods. Soc. Choice Welfare 16(4), 557–567 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yao, A.C.C.: Probabilistic computations: toward a unified measure of complexity. In: Proceedings and the 18th Annual Symposium on Foundations of Computer Science (FOCS), pp. 222–227 (1977)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Aarhus University, Åbogade 34, 8200, Aarhus N, Denmark

    Ioannis Caragiannis & Nidhi Rathi

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  1. Ioannis Caragiannis
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  2. Nidhi Rathi
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Correspondence to Ioannis Caragiannis .

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Editors and Affiliations

  1. Royal Holloway University of London, Egham, UK

    Argyrios Deligkas

  2. University of Edinburgh, Edinburgh, UK

    Aris Filos-Ratsikas

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Caragiannis, I., Rathi, N. (2023). Optimizing over Serial Dictatorships. In: Deligkas, A., Filos-Ratsikas, A. (eds) Algorithmic Game Theory. SAGT 2023. Lecture Notes in Computer Science, vol 14238. Springer, Cham. https://doi.org/10.1007/978-3-031-43254-5_19

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  • DOI: https://doi.org/10.1007/978-3-031-43254-5_19

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