Object Allocation via Swaps along a Social Network

Gourvès, Laurent; Lesca, Julien; Wilczynski, Anaëlle

doi:10.24963/ijcai.2017/31

Cited by 38 publications

(69 citation statements)

References 7 publications

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“…[14] analyses optimality in the setting where pairs of agents exchange items or services. The influence of neighbourhood structures in terms of item exchange and its influence on convergence to stable and optimal allocations is studied in [20,13]. Exchange dynamics with restricted preferences orderings are considered in [40,17].…”

Section: Allocation Of Indivisible Goodsmentioning

confidence: 99%

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Das

Ramanujam

Simon

2019

Electron. Proc. Theor. Comput. Sci.

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Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a new one. This induces a natural graph structure that we call the improvement graph on the strategy space of these systems. We suggest that the monadic fixedpoint logic with counting, an extension of monadic first-order logic on graphs with fixed-point and counting quantifiers, is a natural specification language on improvement graphs, and thus for a class of properties that can be interpreted across these domains. The logic has an efficient model checking algorithm (in the size of the improvement graph).

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Section: Allocation Of Indivisible Goodsmentioning

confidence: 99%

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Das

Ramanujam

Simon

2019

Electron. Proc. Theor. Comput. Sci.

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“…Damamme et al (2015) firstly proved that the problem is NP-hard even to decide whether any one of a subset of objects is reachable for each agent. Gourvès, Lesca, and Wilczynski (2017) further showed that OBJECT REACHABILITY is polynomially solvable under star-structures and NP-complete under tree-structures. For the network being a path, they solved the special case where the given agent is an endpoint (a leaf) in the path and left it unsolved for the general case.…”

Section: Introductionmentioning

confidence: 99%

“…A swap between two agents is allowed when they are mutually beneficial from the exchange. This natural rule for HOUSING MARKET has been studied in the literature (Damamme et al 2015;Gourvès, Lesca, and Wilczynski 2017).…”

Section: Introductionmentioning

confidence: 99%

“…However, some agents often do not know each other and do not have the capacity to exchange even they can mutually get benefits. So Gourvès, Lesca, and Wilczynski (2017) studied HOUSING MARKET where the agents are embedded in a social network to denote the ability to exchange objects between them. In fact, recently it is a hot topic to study resources allocation problems over social networks and analyze the influences of networks.…”

Section: Introductionmentioning

confidence: 99%

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Object Reachability via Swaps along a Line

Huang

Xiao

2019

AAAI

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The HOUSING MARKET problem is a widely studied resources allocation problem. In this problem, each agent can only receive a single object and has preferences over all objects. Starting from an initial endowment, we want to reach a certain assignment via a sequence of rational trades. We consider the problem whether an object is reachable for a given agent under a social network, where a trade between two agents is allowed if they are neighbors in the network and no participant has a deficit from the trade. Assume that the preferences of the agents are strict (no tie is allowed). This problem is polynomially solvable in a star-network and NPcomplete in a tree-network. It is left as a challenging open problem whether the problem is polynomially solvable when the network is a path. We answer this open problem positively by giving a polynomial-time algorithm. Furthermore, we show that the problem on a path will become NP-hard when the preferences of the agents are weak (ties are allowed).

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“…Several recent papers combine graphs and fair division of indivisible items by assuming that agents are located in the vertices of a graph. For instance, Chevaleyre et al (2007) and Gourvès et al (2017) consider the case where each agent has an initial endowment of goods and can trade with her neighbors in the graph. The authors study outcomes that can be achieved by a sequence of mutually beneficial deals.…”

Section: Introductionmentioning

confidence: 99%

Chore division on a graph

Bouveret

Cechlárová

Lesca

2019

Auton Agent Multi-Agent Syst

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The paper considers fair allocation of indivisible nondisposable items that generate disutility (chores). We assume that these items are placed in the vertices of a graph and each agent's share has to form a connected subgraph of this graph. Although a similar model has been investigated before for goods, we show that the goods and chores settings are inherently different. In particular, it is impossible to derive the solution of the chores instance from the solution of its naturally associated fair division instance. We consider three common fair division solution concepts, namely proportionality, envy-freeness and equitability, and two individual disutility aggregation functions: additive and maximum based. We show that deciding the existence of a fair allocation is hard even if the underlying graph is a path or a star. We also present some efficiently solvable special cases for these graph topologies.

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Object Allocation via Swaps along a Social Network

Cited by 38 publications

References 7 publications

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Reasoning about Social Choice and Games in Monadic Fixed-Point Logic

Object Reachability via Swaps along a Line

Chore division on a graph

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