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Truthfulness, Proportional Fairness, and Efficiency
arXiv (Cornell University)
06 Jul 2012
Abstract
How does one allocate a collection of resources to a set of strategic agents
in a fair and efficient manner without using money? For in many scenarios it is
not feasible to use money to compensate agents for otherwise unsatisfactory
outcomes. This paper studies this question, looking at both fairness and
efficiency measures.
We employ the proportionally fair solution, which is a well-known fairness
concept for money-free settings. But although finding a proportionally fair
solution is computationally tractable, it cannot be implemented in a truthful
fashion. Consequently, we seek approximate solutions. We give several truthful
mechanisms which achieve proportional fairness in an approximate sense. We use
a strong notion of approximation, requiring the mechanism to give each agent a
good approximation of its proportionally fair utility. In particular, one of
our mechanisms provides a better and better approximation factor as the minimum
demand for every good increases. A motivating example is provided by the
massive privatization auction in the Czech republic in the early 90s.
With regard to efficiency, prior work has shown a lower bound of 0.5 on the
approximation factor of any swap-dictatorial mechanism approximating a social
welfare measure even for the two agents and multiple goods case. We surpass
this lower bound by designing a non-swap-dictatorial mechanism for this case.
Interestingly, the new mechanism builds on the notion of proportional fairness.
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Details
- Title
- Truthfulness, Proportional Fairness, and Efficiency
- Creators
- Richard ColeVasilis GkatzelisGagan Goel
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Computer Science (Computing)
- Other Identifier
- 991021868091604721