Sylvain Bouveret

Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity

We consider the problem of allocating fairly a set of indivisible goods among agents from the point of view of compact representation and computational complexity. We start by assuming that agents have dichotomous preferences expressed by propositional formulae. We express efficiency and envy-freeness in a logical setting, which reveals unexpected connections to nonmonotonic reasoning. Then we identify the complexity of determining whether there exists an efficient and envy-free allocation, for several notions of efficiency, when preferences are represented in a succinct way (as well as restrictions of this problem). We first study the problem under the assumption that preferences are dichotomous, and then in the general case.

Allocation of indivisible goods: a general model and some complexity results

Many industrial or research activities are so expensive that it is often benefitable for the involved agents to cofund the construction or the purchase of a common required resource. This resource will then be exploited in common, therefore in a shared way. The rules for resource sharing should take account of the possibly antagonistic preferences: each agent wants to maximize its own satisfaction, whereas, from the collective point of view, decisions which both are equitable and exploit the resource in an optimal way are looked for. We give in this article a formal model for indivisible goods resource sharing without monetary compensations and with arbitrary feasability constraints. We also give some complexity results about this model. The model is applied to a real-world case, namely satellite resource sharing.

Characterizing conflicts in fair division of indivisible goods using a scale of criteria

We investigate five different fairness criteria in a simple model of fair resource allocation of indivisible goods based on additive preferences. We show how these criteria are connected to each other, forming an ordered scale that can be used to characterize how conflicting the agents’ preferences are: for a given instance of a resource allocation problem, the less conflicting the agents’ preferences are, the more demanding criterion this instance is able to satisfy, and the more satisfactory the allocation can be. We analyze the computational properties of the five criteria, give some experimental results about them, and further investigate a slightly richer model with

Fair Division of a Graph

k

Towards matching improvement between spatio-temporal tasks and workers in mobile crowdsourcing market systems

k-additive preferences.

A generic architecture for spatial crowdsourcing

Picking sequences are a natural way of allocating indivisible items to agents in a decentralized manner: at each stage, a designated agent chooses an item among those that remain available. We address the computational issues of the manipulation of picking sequences by an agent or a coalition of agents. We show that a single agent can compute an optimal manipulation in polynomial time. Then we consider several notions of coalitional manipulation; for one of these notions, we show that computing an optimal manipulation is easy. We temper these results by giving a nontrivial upper bound on the impact of manipulation on the loss of social welfare.

Trajectory recommendation for task accomplishment in crowdsourcing – a model to favour different actors

We consider fair allocation of indivisible items under an additional constraint: there is an undirected graph describing the relationship between the items, and each agents share must form a connected subgraph of this graph. This framework captures, e.g., fair allocation of land plots, where the graph describes the accessibility relation among the plots. We focus on agents that have additive utilities for the items, and consider several common fair division solution concepts, such as proportionality, envy-freeness and maximin share guarantee. While finding good allocations according to these solution concepts is computationally hard in general, we design efficient algorithms for special cases wherethe underlying graph has simple structure, and/or the number of agents---or, less restrictively, the number of agent types---is small. In particular, despite non-existence results in the general case, we prove that for acyclic graphs a maximin share allocation always exists and can be found efficiently.

Heuristics for Task Recommendation in Spatiotemporal Crowdsourcing Systems

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector