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Swap dynamics in single-peaked housing markets

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Abstract

This paper focuses on the problem of fairly and efficiently allocating resources to agents. We consider a specific setting, usually referred to as a housing market, where each agent must receive exactly one resource (and initially owns one). In this framework, in the domain of linear preferences, the Top Trading Cycle (TTC) algorithm is the only procedure satisfying Pareto-optimality, individual rationality and strategy-proofness. Under the restriction of single-peaked preferences, Crawler enjoys the same properties. These two centralized procedures might however involve long trading cycles. In this paper we focus instead on procedures involving the shortest cycles: bilateral swap-deals. In such swap dynamics, the agents perform pairwise mutually improving deals until reaching a swap-stable allocation (no improving swap-deal is possible). We prove that in the single-peaked domain every swap-stable allocation is Pareto-optimal, showing the efficiency of the swap dynamics. In fact, this domain turns out to be maximal when it comes to guaranteeing this property. Besides, both the outcome of TTC and Crawler can always be reached by sequences of swaps. However, some Pareto-optimal allocations are not reachable through improving swap-deals. We further analyze the outcome of swap dynamics through social welfare notions, in our context the average or minimum rank of the resources obtained by agents in the final allocation. We start by providing a worst-case analysis of these procedures. Finally, we present an extensive experimental study in which different versions of swap dynamics are compared to other existing allocation procedures. We show that they exhibit good results on average in this domain, under different cultures for generating synthetic data.

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Notes

  1. In principle, it is possible to distribute the execution of central procedures, by letting all agents broadcast, compute locally their own version of the central algorithm, and coordinate. This might however induce a significant cost.

  2. Note that the algorithm can equivalently be executed from the last agent to the first one.

  3. The underlined allocation will only be relevant in forthcoming proofs.

  4. Again, the underlined allocation will only be relevant in a later proof.

  5. The Kendall’s tau distance between two preference order \(\succ _i\) and \(\succ _{i'}\) over \(\mathcal {R}\) is the number of pairs \((r, r') \in \mathcal {R}^2\) such that \(\succ _i\) and \(\succ _{i'}\) do not rank r and \(r'\) in the same order. The Spearman distance between two preference order \(\succ _i\) and \(\succ _{i'}\) over \(\mathcal {R}\) is defined as \(\sum _{r \in \mathcal {R}} |rank_{a_i}(r) - rank_{a_{i'}}(r)|\). In both cases, the diversity index of a profile L is the sum of the distance between every pair of preference orders \((\succ _i, \succ _{i'})\) of L.

References

  1. Abbassi, Z., Lakshmanan, L. V., & Xie, M. (2013). Fair recommendations for online barter exchange networks. In: Proceedings of the 16th International Workshop on the Web and Databases (WebDB), pp 43–48.

  2. Ackermann, H., Goldberg, P. W., Mirrokni, V. S., Röglin, H., & Vöcking, B. (2011). Uncoordinated two-sided matching markets. SIAM Journal on Computing, 40(1), 92–106.

    Article  MathSciNet  Google Scholar 

  3. Anshelevich, E., Das, S., & Naamad, Y. (2013). Anarchy, stability, and utopia: creating better matchings. Autonomous Agents and Multi-Agent Systems, 26(1), 120–140.

    Article  Google Scholar 

  4. Arrow, K. J. (1951). Social choice and individual values. Wiley.

    MATH  Google Scholar 

  5. Aziz, H. (2020). Developments in multi-agent fair allocation. In: Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI), pp 13563–13568.

  6. Aziz, H., Gaspers, S., Mackenzie, S., & Walsh, T. (2015). Fair assignment of indivisible objects under ordinal preferences. Artificial Intelligence, 227, 71–92.

    Article  MathSciNet  Google Scholar 

  7. Aziz, H., Biró, P., Lang, J., Lesca, J., & Monnot J. (2016). Optimal reallocation under additive and ordinal preferences. In Proceedings of the 15th International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), pp. 402–410.

  8. Bade, S. (2019). Matching with single-peaked preferences. Journal of Economic Theory, 180, 81–99.

    Article  MathSciNet  Google Scholar 

  9. Ballester, M. A., & Haeringer, G. (2011). A characterization of the single-peaked domain. Social Choice and Welfare, 36(2), 305–322.

    Article  MathSciNet  Google Scholar 

  10. Bentert M, Chen J, Froese V, & Woeginger GJ. (2019). Good things come to those who swap objects on paths. CoRR abs/1905.04219.

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

  12. Beynier, A., Maudet, N., Rey, S., & Shams, P. (2020). An optimal procedure to check pareto-optimality in house markets with single-peaked preferences. ArXiv, 2002, 11660.

    Google Scholar 

  13. Black, D. (1948). On the rationale of group decision-making. Journal of Political Economy, 56(1), 23–34.

    Article  Google Scholar 

  14. Van den Bos, K., Lind, E. A., Vermunt, R., & Wilke, H. A. (1997). How do I judge my outcome when I do not know the outcome of others? the psychology of the fair process effect. Journal of Personality and Social Psychology, 72(5), 1034.

    Article  Google Scholar 

  15. Bouveret, S., Endriss, U., & Lang, J. (2010). Fair division under ordinal preferences: Computing envy-free allocations of indivisible goods. In: Proceedings of the 19th European Conference on Artificial Intelligence (ECAI), pp 387–392.

  16. Bouveret, S., Chevaleyre, Y., & Maudet, N. (2016). Fair allocation of indivisible goods. In V. Conitzer, U. Endriss, J. Lang, & A. D. E. Procaccia (Eds.), Brandt F (pp. 284–310). Cambridge University Press: Handbook of Computational Social Choice.

  17. Brams, S. J., Edelman, P. H., & Fishburn, P. C. (2003). Fair division of indivisible items. Theory and Decision, 55(2), 147–180.

    Article  MathSciNet  Google Scholar 

  18. Brandt F, & Wilczynski A. (2019). On the convergence of swap dynamics to pareto-optimal matchings. In: Proceedings of the 15th International Workshop on Internet and Network Economics (WINE), pp. 100–113.

  19. Chevaleyre, Y., Dunne, P. E., Endriss, U., Lang, J., Lemaître, M., Maudet, N., et al. (2006). Issues in multiagent resource allocation. Informatica, 30(1).

  20. Chevaleyre, Y., Endriss, U., Estivie, S., & Maudet N. (2007). Reaching envy-free states in distributed negotiation settings. In: Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI), vol 7, pp 1239–1244.

  21. Chevaleyre, Y., Endriss, U., & Maudet, N. (2010). Simple negotiation schemes for agents with simple preferences: Sufficiency, necessity and maximality. Autonomous Agents and Multi-Agent Systems, 20(2), 234–259.

    Article  Google Scholar 

  22. Chevaleyre, Y., Endriss, U., & Maudet, N. (2017). Distributed fair allocation of indivisible goods. Artificial Intelligence, 242, 1–22.

    Article  MathSciNet  Google Scholar 

  23. Conitzer, V. (2009). Eliciting single-peaked preferences using comparison queries. Journal of Artificial Intelligence Research, 35, 161–191.

    Article  MathSciNet  Google Scholar 

  24. Damamme A, Beynier A, Chevaleyre Y, & Maudet N. (2015). The power of swap deals in distributed resource allocation. In:Proceedings of the 14th International Joint Conference on Autonomous Agents and Multi-Agent Systems (AAMAS), pp 625–633.

  25. DeMarzo, P. M., Vayanos, D., & Zwiebel, J. (2003). Persuasion bias, social influence, and unidimensional opinions. The Quarterly Journal of Economics, 118(3), 909–968.

    Article  Google Scholar 

  26. Dunne, P., Wooldridge, M., & Laurence, M. (2005). The complexity of contract negotiation. Artificial Intelligence, 164(1), 23–46.

    Article  MathSciNet  Google Scholar 

  27. Egan, P. J. (2014). “do something” politics and double-peaked policy preferences. The Journal of Politics, 76(2), 333–349.

    Article  Google Scholar 

  28. Elkind E, Lackner M, & Peters D. (2017). Structured preferences. In: E U (ed) Trends in Computational Social Choice, Lulu.com, pp 187–207.

  29. Endriss, U., & Maudet, N. (2005). On the communication complexity of multilateral trading. Autonomous Agents and Multi-Agent Systems, 11(1), 91–107.

    Google Scholar 

  30. Endriss U, Maudet N, Sadri F, & Toni F. (2006). Negotiating socially optimal allocations of resources. Journal of Artificial Intelligence Research.

  31. Garfinkel, R. S. (1971). An improved algorithm for the bottleneck assignment problem. Operations Research, 19(7), 1747–1751.

    Article  Google Scholar 

  32. Gourvès L, Lesca J, & Wilczynski A. (2017). Object allocation via swaps along a social network. In: Proceedings of the 26th International Joint Conference on Artificial Intelligence (IJCAI), pp 213–219.

  33. Hashemi V, & Endriss U. (2014). Measuring diversity of preferences in a group. In: Proceedings of the 21st European Conference on Artificial Intelligence, pp 423–428.

  34. Hougaard, J. L., Moreno-Ternero, J. D., & Østerdal, L. P. (2014). Assigning agents to a line. Games and Economic Behavior, 87, 539–553.

    Article  MathSciNet  Google Scholar 

  35. Huang S, & Xiao M. (2019). Object reachability via swaps along a line. In: Proceedings of the 33rd AAAI Conference on Artificial Intelligence (AAAI), vol 33, pp 2037–2044.

  36. Kasajima, Y. (2013). Probabilistic assignment of indivisible goods with single-peaked preferences. Social Choice and Welfare, 41(1), 203–215.

    Article  MathSciNet  Google Scholar 

  37. Kondratev, A.Y., & Nesterov, A. S. (2019). Minimal envy and popular matchings. arXiv preprint arXiv:1902.08003.

  38. Koutsoupias, E., & Papadimitriou, C. (1999). Worst-case equilibria. In: Meinel, C.., Tison, S. (eds) Proceedings of the 16th International Symposium on Theoretical Aspects of Computer Science (STACS), pp. 404–413.

  39. Lee, J. S., Filatova, T., Ligmann-Zielinska, A., Hassani-Mahmooei, B., Stonedahl, F., & Lorscheid, I., et al. (2015). The complexities of agent-based modeling output analysis. Journal of Artificial Societies and Social Simulation, 18(4).

  40. Leventhal, G. S. (1980). What should be done with equity theory Social exchange (pp. 27–55). Berlin: Springer.

    Google Scholar 

  41. List, C., Luskin, R. C., Fishkin, J. S., & McLean, I. (2013). Deliberation, single-peakedness, and the possibility of meaningful democracy: evidence from deliberative polls. The Journal of Politics, 75(1), 80–95.

    Article  Google Scholar 

  42. Liu P. (2018). A large class of strategy-proof exchange rules with single-peaked preferences. Research Collection School of Economics, mimeo.

  43. Ma, J. (1994). Strategy-proofness and the strict core in a market with indivisibilities. International Journal of Game Theory, 23(1), 75–83.

    Article  MathSciNet  Google Scholar 

  44. Mattei N, & Walsh T. (2013). Preflib: A library for preferences http://www. preflib. org. In: Proceedings of the 3rd International Conference on Algorithmic Decision Theory (ADT), Springer, pp 259–270.

  45. Moulin, H. (1991). Axioms of cooperative decision making (Vol. 15). Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  46. Moulin, H. (2019). Fair division in the age of internet. Annual Review of Economics, 11, 407–441.

    Article  Google Scholar 

  47. Nguyen, N. T., Nguyen, T. T., Roos, M., & Rothe, J. (2014). Computational complexity and approximability of social welfare optimization in multiagent resource allocation. Autonomous Agents and Multi-agent Systems, 28(2), 256–289.

    Article  Google Scholar 

  48. Pazner, E. A., & Schmeidler, D. (1978). Egalitarian equivalent allocations: A new concept of economic equity. The Quarterly Journal of Economics, 92(4), 671–687.

    Article  Google Scholar 

  49. Peters D, & Lackner M. (2017). Preferences single-peaked on a circle. In: Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, AAAI Press, p 649–655.

  50. Puppe, C. (2018). The single-peaked domain revisited: A simple global characterization. Journal of Economic Theory, 176(C), 55–80.

    Article  MathSciNet  Google Scholar 

  51. Rawls, J. (1971). A theory of justice. Harvard University Press.

    Google Scholar 

  52. Rosenschein JS, & Zlotkin G. (1994). Rules of encounter: designing conventions for automated negotiation among computers. MIT press.

  53. Roth, A. E. (1982). Incentive compatibility in a market with indivisible goods. Economics letters, 9(2), 127–132.

    Article  MathSciNet  Google Scholar 

  54. Roth, A. E., & Vate, J. H. V. (1990). Random paths to stability in two-sided matching. Econometrica, 58, 1475–1480.

    Article  MathSciNet  Google Scholar 

  55. Roth, A. E., Sönmez, T., & Ünver, M. U. (2005). Pairwise kidney exchange. Journal of Economic theory, 125(2), 151–188.

    Article  MathSciNet  Google Scholar 

  56. Saffidine A, & Wilczynski A. (2018). Constrained swap dynamics over a social network in distributed resource reallocation. In: Proceedings of the 11th International Symposium on Algorithmic Game Theory (SAGT), pp 213–225.

  57. Sandholm T. (1998). Contract types for satisficing task allocation. In: Proceedings of the Spring Symposium of AAAI Conference on Artificial Intelligence (AAAI), pp 23–25.

  58. Sen, A. K. (1966). A possibility theorem on majority decisions. Econometrica, 34, 491–499.

    Article  Google Scholar 

  59. Shapley, L., & Scarf, H. (1974). On cores and indivisibility. Journal of Mathematical Economics, 1(1), 23–37.

    Article  MathSciNet  Google Scholar 

  60. Spector, D. (2000). Rational debate and one-dimensional conflict. The Quarterly Journal of Economics, 115(1), 181–200.

    Article  Google Scholar 

  61. Sprumont, Y. (1991). The division problem with single-peaked preferences: a characterization of the uniform allocation rule. Econometrica, 59, 509–519.

    Article  MathSciNet  Google Scholar 

  62. Sprumont, Y. (1996). Axiomatizing ordinal welfare egalitarianism when preferences may vary. Journal of Economic Theory, 68(1), 77–110.

    Article  MathSciNet  Google Scholar 

  63. Thibaut JW, & Walker L. (1975). Procedural justice: A psychological analysis. L. Erlbaum Associates.

  64. Thomson, W. (1983). Problems of fair division and the egalitarian solution. Journal of Economic Theory, 31(2), 211–226.

    Article  MathSciNet  Google Scholar 

  65. Thomson, W. (2016). Introduction to the theory of fair allocation. In V. Conitzer, U. Endriss, J. Lang, & A. D. Procaccia (Eds.), Brandt F (pp. 261–283). Cambridge University Press: Handbook of Computational Social Choice.

  66. Walsh, T. (2015). Generating single peaked votes. arXiv:1503.02766.

  67. Walsh, T. (2020). Fair division: The computer scientist’s perspective. In: Bessiere C (ed) Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence, IJCAI 2020, pp 4966–4972.

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Acknowledgements

We thank Sophie Bade, Yann Chevaleyre, Anastasia Damamme, and Julien Lesca, for discussions related to this topic as well as the anonymous reviewers for their comments and suggestions which significantly improved the paper.

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Authors and Affiliations

  1. Sorbonne Université, CNRS, LIP6, 75005, Paris, France

    Aurélie Beynier, Nicolas Maudet & Parham Shams

  2. Institute for Logic, Languages and Computation, University of Amsterdam, Amsterdam, The Netherlands

    Simon Rey

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  1. Aurélie Beynier
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Correspondence to Nicolas Maudet.

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Beynier, A., Maudet, N., Rey, S. et al. Swap dynamics in single-peaked housing markets. Auton Agent Multi-Agent Syst 35, 20 (2021). https://doi.org/10.1007/s10458-021-09503-z

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