Not obviously manipulable allotment rules
Abstract: In the problem of allocating a single non-disposable commodity among agents whose preferences are single-peaked, we study a weakening of strategy-proofness called not obvious manipulability (NOM). If agents are cognitively limited, then NOM is sufficient to describe their strategic behavior. We characterize a large family of own-peak-only rules that satisfy efficiency, NOM, and a minimal fairness condition. We call these rules "simple". In economies with excess demand, simple rules fully satiate agents whose peak amount is less than or equal to equal division and assign, to each remaining agent, an amount between equal division and his peak. In economies with excess supply, simple rules are defined symmetrically. These rules can be thought of as a two-step procedure that involves solving a claims problem. We also show that the single-plateaued domain is maximal for the characterizing properties of simple rules. Therefore, even though replacing strategy-proofness with NOM greatly expands the family of admissible rules, the maximal domain of preferences involved remains basically unaltered.
- Arribillaga, R. P. and A. G. Bonifacio (2024): “Obvious manipulations of tops-only voting rules,” Games and Economic Behavior, 143, 12–24.
- Arribillaga, R. P. and E. Risma (2023): “Obvious manipulations in matching with and without contracts,” arXiv preprint arXiv:2306.17773.
- Aziz, H. and A. Lam (2021): “Obvious manipulability of voting rules,” in International Conference on Algorithmic Decision Theory, Springer, 179–193.
- Barberà, S., M. O. Jackson, and A. Neme (1997): “Strategy-proof allotment rules,” Games and Economic Behavior, 18, 1–21.
- Barbera, S. and B. Peleg (1990): “Strategy-proof voting schemes with continuous preferences,” Social Choice and Welfare, 7, 31–38.
- Brams, S. J., M. A. Jones, and C. Klamler (2008): “Proportional pie-cutting,” International Journal of Game Theory, 36, 353–367.
- Brams, S. J., M. A. Jones, C. Klamler, et al. (2006): “Better ways to cut a cake,” Notices of the AMS, 53, 1314–1321.
- Ching, S. (1994): “An alternative characterization of the uniform rule,” Social Choice and Welfare, 11, 131–136.
- Ching, S. and S. Serizawa (1998): “A maximal domain for the existence of strategy-proof rules,” Journal of Economic Theory, 78, 157–166.
- Massó, J. and A. Neme (2001): “Maximal domain of preferences in the division problem,” Games and Economic Behavior, 37, 367–387.
- Ortega, J. and E. Segal-Halevi (2022): “Obvious manipulations in cake-cutting,” Social Choice and Welfare, 1–20.
- Psomas, A. and P. Verma (2022): “Fair and efficient allocations without obvious manipulations,” arXiv preprint arXiv:2206.11143.
- Thomson, W. (2024): “Fully allocating a commodity among agents with single-peaked preferences,” Tech. rep., Working paper.
- Troyan, P. and T. Morrill (2020): “Obvious manipulations,” Journal of Economic Theory, 185, 104970.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.