Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Randomized Strategyproof Mechanisms with Best of Both Worlds Fairness and Efficiency

Ankang Sun, Bo Chen

TL;DR

This paper studies allocation of indivisible items under private valuations, showing that deterministic mechanisms cannot simultaneously achieve strategyproofness, fairness, and efficiency for chores and mixed-item settings. It then develops randomized mechanisms—RandChore for chores and RandMixed for two-agent mixed items—that achieve a strong best-of-both-worlds balance: strategyproofness in expectation with ex-ante fairness (EF, EQ, PROP) and ex-post fairness (EF1, PROP1, EQ1), alongside ex-ante and ex-post efficiency (UWM, EWM and PO), with competitive bounds such as a 2-approximation for egalitarian welfare. The constructions rely on restricted valuation domains (1-restricted additive for chores and M-restricted additive for mixed items) and careful partitioning plus randomized allocation steps to deter strategic misreporting while maintaining fairness across realizations. These results highlight how randomness can overcome deterministic impossibilities, yielding truthful, fair, and efficient allocations in scenarios with private preferences and indivisible resources, and they suggest directions for extending to more agents and goods in future work.

Abstract

We study the problem of mechanism design for allocating a set of indivisible items among agents with private preferences on items. We are interested in such a mechanism that is strategyproof (where agents' best strategy is to report their true preferences) and is expected to ensure fairness and efficiency to a certain degree. We first present an impossibility result that a deterministic mechanism does not exist that is strategyproof, fair and efficient for allocating indivisible chores. We then utilize randomness to overcome the strong impossibility. For allocating indivisible chores, we propose a randomized mechanism that is strategyproof in expectation as well as ex-ante and ex-post (best of both worlds) fair and efficient. For allocating mixed items, where an item can be a good (i.e., with a positive utility) for one agent but a chore (i.e., a with negative utility) for another, we propose a randomized mechanism that is strategyproof in expectation with best of both worlds fairness and efficiency when there are two agents.

Randomized Strategyproof Mechanisms with Best of Both Worlds Fairness and Efficiency

TL;DR

This paper studies allocation of indivisible items under private valuations, showing that deterministic mechanisms cannot simultaneously achieve strategyproofness, fairness, and efficiency for chores and mixed-item settings. It then develops randomized mechanisms—RandChore for chores and RandMixed for two-agent mixed items—that achieve a strong best-of-both-worlds balance: strategyproofness in expectation with ex-ante fairness (EF, EQ, PROP) and ex-post fairness (EF1, PROP1, EQ1), alongside ex-ante and ex-post efficiency (UWM, EWM and PO), with competitive bounds such as a 2-approximation for egalitarian welfare. The constructions rely on restricted valuation domains (1-restricted additive for chores and M-restricted additive for mixed items) and careful partitioning plus randomized allocation steps to deter strategic misreporting while maintaining fairness across realizations. These results highlight how randomness can overcome deterministic impossibilities, yielding truthful, fair, and efficient allocations in scenarios with private preferences and indivisible resources, and they suggest directions for extending to more agents and goods in future work.

Abstract

We study the problem of mechanism design for allocating a set of indivisible items among agents with private preferences on items. We are interested in such a mechanism that is strategyproof (where agents' best strategy is to report their true preferences) and is expected to ensure fairness and efficiency to a certain degree. We first present an impossibility result that a deterministic mechanism does not exist that is strategyproof, fair and efficient for allocating indivisible chores. We then utilize randomness to overcome the strong impossibility. For allocating indivisible chores, we propose a randomized mechanism that is strategyproof in expectation as well as ex-ante and ex-post (best of both worlds) fair and efficient. For allocating mixed items, where an item can be a good (i.e., with a positive utility) for one agent but a chore (i.e., a with negative utility) for another, we propose a randomized mechanism that is strategyproof in expectation with best of both worlds fairness and efficiency when there are two agents.
Paper Structure (25 sections, 17 theorems, 19 equations, 1 table, 2 algorithms)

This paper contains 25 sections, 17 theorems, 19 equations, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Main results
  3. Other related works
  4. Organization of the paper
  5. Preliminaries
  6. Fractional and randomized allocations
  7. Strategyproofness
  8. Efficiency, fairness and other distributional properties
  9. Impossibility results of deterministic mechanisms
  10. A randomized mechanism for indivisible chores
  11. A randomized mechanism for allocating mixed items
  12. Conclusions
  13. For Section \ref{['sec::deterministic']}
  14. Proof of Theorem \ref{['proposition::SEQ-pick']}
  15. For Section \ref{['Sec::chores']}
  16. ...and 10 more sections

Key Result

Theorem 3.1

For indivisible chores, no sequential picking mechanism can always return Pareto optimal allocations, even when agents' valuations have a binary margin.

Theorems & Definitions (28)

  • Definition 2.1: SP
  • Definition 2.2: SPIE
  • Definition 2.3: GSP
  • Definition 2.4: GSPIE
  • Definition 2.5: PO
  • Definition 2.6
  • Definition 2.7: EF and EF1
  • Definition 2.8: EQ and EQ1
  • Definition 2.9: PROP and PROP1
  • Theorem 3.1
  • ...and 18 more