Equilibria in sequential allocation
Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate th...
| Main Authors: | , , |
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| Format: | Conference item |
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Springer, Cham
2017
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| _version_ | 1797062781616259072 |
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| author | Aziz, H Goldberg, P Walsh, T |
| author_facet | Aziz, H Goldberg, P Walsh, T |
| author_sort | Aziz, H |
| collection | OXFORD |
| description | Sequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate that, even for two agents, better responses can cycle. We then present a linear-time algorithm that returns a profile (which we call the “bluff profile”) that is in pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the same as that of the truthful pro- file and the profile is in pure Nash equilibrium for all cardinal utilities consistent with the ordinal preferences. We show that the outcome of the bluff profile is Pareto optimal with respect to pairwise comparisons. In contrast, we show that an assignment may not be Pareto optimal with respect to pairwise comparisons even if it is a result of a preference profile that is in pure Nash equilibrium for all utilities consistent with ordinal preferences. Finally, we present a dynamic program to compute an optimal Stackelberg strategy for two agents, where the second agent has a constant number of distinct values for the items. |
| first_indexed | 2024-03-06T20:50:29Z |
| format | Conference item |
| id | oxford-uuid:37639fde-d18b-4552-8496-88e8f741a07b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T20:50:29Z |
| publishDate | 2017 |
| publisher | Springer, Cham |
| record_format | dspace |
| spelling | oxford-uuid:37639fde-d18b-4552-8496-88e8f741a07b2022-03-26T13:43:50ZEquilibria in sequential allocationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:37639fde-d18b-4552-8496-88e8f741a07bSymplectic Elements at OxfordSpringer, Cham2017Aziz, HGoldberg, PWalsh, TSequential allocation is a simple mechanism for sharing multiple indivisible items. We study strategic behavior in sequential allocation. In particular, we consider Nash dynamics, as well as the computation and Pareto optimality of pure equilibria, and Stackelberg strategies. We first demonstrate that, even for two agents, better responses can cycle. We then present a linear-time algorithm that returns a profile (which we call the “bluff profile”) that is in pure Nash equilibrium. Interestingly, the outcome of the bluff profile is the same as that of the truthful pro- file and the profile is in pure Nash equilibrium for all cardinal utilities consistent with the ordinal preferences. We show that the outcome of the bluff profile is Pareto optimal with respect to pairwise comparisons. In contrast, we show that an assignment may not be Pareto optimal with respect to pairwise comparisons even if it is a result of a preference profile that is in pure Nash equilibrium for all utilities consistent with ordinal preferences. Finally, we present a dynamic program to compute an optimal Stackelberg strategy for two agents, where the second agent has a constant number of distinct values for the items. |
| spellingShingle | Aziz, H Goldberg, P Walsh, T Equilibria in sequential allocation |
| title | Equilibria in sequential allocation |
| title_full | Equilibria in sequential allocation |
| title_fullStr | Equilibria in sequential allocation |
| title_full_unstemmed | Equilibria in sequential allocation |
| title_short | Equilibria in sequential allocation |
| title_sort | equilibria in sequential allocation |
| work_keys_str_mv | AT azizh equilibriainsequentialallocation AT goldbergp equilibriainsequentialallocation AT walsht equilibriainsequentialallocation |