Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash 102 tok/s
Gemini 2.5 Pro 51 tok/s Pro
GPT-5 Medium 30 tok/s
GPT-5 High 27 tok/s Pro
GPT-4o 110 tok/s
GPT OSS 120B 475 tok/s Pro
Kimi K2 203 tok/s Pro
2000 character limit reached

Fair Division with Market Values (2410.23137v1)

Published 30 Oct 2024 in cs.GT and cs.AI

Abstract: We introduce a model of fair division with market values, where indivisible goods must be partitioned among agents with (additive) subjective valuations, and each good additionally has a market value. The market valuation can be viewed as a separate additive valuation that holds identically across all the agents. We seek allocations that are simultaneously fair with respect to the subjective valuations and with respect to the market valuation. We show that an allocation that satisfies stochastically-dominant envy-freeness up to one good (SD-EF1) with respect to both the subjective valuations and the market valuation does not always exist, but the weaker guarantee of EF1 with respect to the subjective valuations along with SD-EF1 with respect to the market valuation can be guaranteed. We also study a number of other guarantees such as Pareto optimality, EFX, and MMS. In addition, we explore non-additive valuations and extend our model to cake-cutting. Along the way, we identify several tantalizing open questions.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (38)
  1. H. Akrami and J. Garg. Breaking the 3/4 barrier for approximate maximin share. In Proceedings of the 35th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 74–91, 2024.
  2. N. Alon. Splitting necklaces. Advances in Mathematics, 63(3):247–253, 1987.
  3. H. Aziz and S. Mackenzie. A discrete and bounded envy-free cake cutting protocol for any number of agents. In 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS), pages 416–427. IEEE, 2016.
  4. Best of both worlds: Ex ante and ex post fairness in resource allocation. Operations Research, 72(4):1674–1688, 2024.
  5. Two-person cake cutting: The optimal number of cuts. The Mathematical Intelligencer, 36(3):23–35, 2014.
  6. Two applications of a theorem of Dvoretsky, Wald, and Wolfovitz to cake division. Theory and Decision, 43:203–207, 1997.
  7. Finding fair and efficient allocations. In Proceedings of the 19th ACM Conference on Economics and Computation (EC), pages 557–574, 2018.
  8. Finding fair allocations under budget constraints. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI), pages 5481–5489, 2023.
  9. A. Biswas and S. Barman. Fair division under cardinality constraints. In Proceedings of the 37th International Joint Conference on Artificial Intelligence (IJCAI), pages 91–97, 2018.
  10. A. Bogomolnaia and H. Moulin. A new solution to the random assignment problem. Journal of Economic theory, 100(2):295–328, 2001.
  11. N𝑁Nitalic_N-person cake-cutting: There may be no perfect division. American Mathematical Monthly, 120(1):35–47, 2013.
  12. Fair division with allocator’s preference. In Proceedings of the 19th Conference on Web and Internet Economics (WINE), pages 77–94, 2023.
  13. E. Budish. The combinatorial assignment problem: Approximate competitive equilibrium from equal incomes. Journal of Political Economy, 119(6):1061–1103, 2011.
  14. The unreasonable fairness of maximum Nash welfare. ACM Transactions on Economics and Computation, 7(3): Article 12, 2019.
  15. A little charity guarantees almost envy-freeness. SIAM Journal on Computing, 50(4):1336–1358, 2021.
  16. Optimal envy-free cake cutting. In Proceedings of the 25th AAAI Conference on Artificial Intelligence (AAAI), pages 626–631, 2011.
  17. Fair public decision making. In Proceedings of the 18th ACM Conference on Economics and Computation (EC), pages 629–646, 2017.
  18. M. Dall’Aglio. Fair division of goods in the shadow of market values. European Journal of Operational Research, 307(2):785–801, 2023.
  19. On fair division under heterogeneous matroid constraints. Journal of Artificial Intelligence Research, 76:567–611, 2023.
  20. L. Dubins and E. Spanier. How to cut a cake fairly. The American Mathematical Monthly, 68(1):1–17, 1961a.
  21. How to cut a cake fairly. American Mathematical Monthly, 68(1):1–17, 1961b.
  22. Equitable allocations of indivisible goods. In Proceedings of the 28th International Joint Conference on Artificial Intelligence (IJCAI), page 280–286, 2019.
  23. Two-sided matching meets fair division. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI), pages 203–209, 2021.
  24. Fair division with two-sided preferences. In Proceedings of the 32nd International Joint Conference on Artificial Intelligence (IJCAI), pages 2756–2764, 2023.
  25. J. Kagan. Equitable Distribution: Definition, State Laws, Exempt Property. https://www.investopedia.com/terms/e/equitable-division.asp, 2021a.
  26. J. Kagan. Assessor: Meaning, Certification, Why They Matter. https://www.investopedia.com/terms/a/assessor.asp, 2021b.
  27. Almost envy-freeness in group resource allocation. Theoretical Computer Science, 841:110–123, 2020.
  28. On approximately fair allocations of indivisible goods. In Proceedings of the 6th ACM Conference on Economics and Computation (EC), pages 125–131, 2004.
  29. A. Murhekar and J. Garg. On fair and efficient allocations of indivisible goods. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI), pages 5595–5602, 2021.
  30. Fairrec: Two-sided fairness for personalized recommendations in two-sided platforms. In Proceedings of the 29th International World Wide Web Conference (TheWebConf), pages 1194–1204, 2020.
  31. A. D. Procaccia and J. Wang. A lower bound for equitable cake cutting. In Proceedings of the 18th ACM Conference on Economics and Computation (EC), pages 479–495, 2017.
  32. J. Reijnierse and J. A. M. Potters. On finding an envy-free Pareto-optimal division. Mathematical Programming, 83:291–311, 1998.
  33. R. L. Schilling and D. Stoyan. Continuity assumptions in cake-cutting. arXiv:1611.04988, 2016.
  34. E. Segal-Halevi and B. R. Sziklai. Monotonicity and competitive equilibrium in cake-cutting. Economic Theory, 68(2):363–401, 2019.
  35. Fair cake-cutting algorithms with real land-value data. Autonomous Agents and Multi-Agent Systems, 35:1–28, 2021.
  36. H. Steinhaus. The problem of fair division. Econometrica, 16:101–104, 1948.
  37. W. Suksompong. Constraints in fair division. ACM SIGecom Exchanges, 19(2):46–61, 2021.
  38. D. Weller. Fair division of a measurable space. Journal of Mathematical Economics, 14(1):5–17, 1985.
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 10 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets