Bicriteria Fair Allocation
Keywords: envy-free allocation, strategy proofness
TL;DR: We study a new model for envy-free allocations where each agent has two valuations.
Abstract: Fair allocation of goods to agents has been extensively studied because of their applications in several socio-economic contexts, from division of inheritance to recommendation systems.
In a common setting, we have $n$ agents and $m$ items, and each agent has an individual valuation for each of the goods.
However, in many situations agents may have more than one valuation - for example when a recommendation platform must allocate ad slots in order to satisfy both visibility and marketing goals.
To deal with this and other general scenarios, in this paper we study a novel bicriteria fair allocation framework: a generalization of standard fair allocation settings where each agent has a common public valuation and an individual valuation for each good.
The goal is to find an allocation that, for two integers $\gamma,\delta\geq 0$, is envy-free-up-to-publicly-$\gamma$-and-privately-$\delta$-goods (EF-$(\gamma,\delta$)): each agent becomes non-envious of each other w.r.t. the public (resp. her private) valuation, after deleting at most $\gamma$ (resp. $\delta$) goods from the bundle of each other.
We first provide a polynomial-time algorithm that is EF-(1,1) when private valuations are known to the system. Then, we focus on the realistic case in which agents can misreport their private valuations to the system, and we provide a randomized polynomial-time algorithm that returns EF-($1,\delta$) allocations with high probability, where $\delta=O(\alpha\sqrt{\log(n)m/n})$ and $\alpha$ is the maximum private valuation for any item.
Submission Number: 2
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