arXiv subjects

Warut Suksompong

Publications and source records attributed to Warut Suksompong.

At least 73 records · Page 4Linked to original sources

arXiv2021

On the Complexity of Fair House Allocation

We study fairness in house allocation, where $m$ houses are to be allocated among $n$ agents so that every agent receives one house. We show that maximizing the number of envy-free agents is hard to approximate to within a factor of $n^{1-γ}$ for any constant $γ>0$, and that the exact version is NP-hard even for binary utilities. Moreover, we prove that deciding whether a proportional allocation exists is computationally hard, whereas the corresponding problem for equitability can be solved efficiently.

cs.GT↗

arXiv2021

Graphical Cake Cutting via Maximin Share

We study the recently introduced cake-cutting setting in which the cake is represented by an undirected graph. This generalizes the canonical interval cake and allows for modeling the division of road networks. We show that when the graph is a forest, an allocation satisfying the well-known criterion of maximin share fairness always exists. Our result holds even when separation constraints are imposed, in which case no multiplicative approximation of proportionality can be guaranteed. Furthermore, while maximin share fairness is not always achievable for general graphs, we prove that ordinal relaxations can be attained.

cs.GT↗

arXiv2021

Fairly Allocating Many Goods with Few Queries

We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic utilities, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We show that the logarithmic query complexity bound also holds for three agents with additive utilities, and that a polylogarithmic bound holds for three agents with monotonic utilities. These results suggest that it is possible to fairly allocate goods in practice even when the number of goods is extremely large. By contrast, we prove that computing an allocation satisfying envy-freeness and another of its relaxations, envy-freeness up to any good (EFX), requires a linear number of queries even when there are only two agents with identical additive utilities.

cs.GT↗

arXiv2021

The Price of Fairness for Indivisible Goods

We investigate the efficiency of fair allocations of indivisible goods using the well-studied price of fairness concept. Previous work has focused on classical fairness notions such as envy-freeness, proportionality, and equitability. However, these notions cannot always be satisfied for indivisible goods, leading to certain instances being ignored in the analysis. In this paper, we focus instead on notions with guaranteed existence, including envy-freeness up to one good (EF1), balancedness, maximum Nash welfare (MNW), and leximin. We also introduce the concept of strong price of fairness, which captures the efficiency loss in the worst fair allocation as opposed to that in the best fair allocation as in the price of fairness. We mostly provide tight or asymptotically tight bounds on the worst-case efficiency loss for allocations satisfying these notions, for both the price of fairness and the strong price of fairness.

cs.GT↗

arXiv2021

Weighted Envy-Freeness in Indivisible Item Allocation

We introduce and analyze new envy-based fairness concepts for agents with weights that quantify their entitlements in the allocation of indivisible items. We propose two variants of weighted envy-freeness up to one item (WEF1): strong, where envy can be eliminated by removing an item from the envied agent's bundle, and weak, where envy can be eliminated either by removing an item (as in the strong version) or by replicating an item from the envied agent's bundle in the envying agent's bundle. We show that for additive valuations, an allocation that is both Pareto optimal and strongly WEF1 always exists and can be computed in pseudo-polynomial time; moreover, an allocation that maximizes the weighted Nash social welfare may not be strongly WEF1, but always satisfies the weak version of the property. Moreover, we establish that a generalization of the round-robin picking sequence algorithm produces in polynomial time a strongly WEF1 allocation for an arbitrary number of agents; for two agents, we can efficiently achieve both strong WEF1 and Pareto optimality by adapting the adjusted winner procedure. Our work highlights several aspects in which weighted fair division is richer and more challenging than its unweighted counterpart.

cs.AI↗

arXiv2020

Almost Envy-Freeness in Group Resource Allocation

We study the problem of fairly allocating indivisible goods between groups of agents using the recently introduced relaxations of envy-freeness. We consider the existence of fair allocations under different assumptions on the valuations of the agents. In particular, our results cover cases of arbitrary monotonic, responsive, and additive valuations, while for the case of binary valuations we fully characterize the cardinalities of two groups of agents for which a fair allocation can be guaranteed with respect to both envy-freeness up to one good (EF1) and envy-freeness up to any good (EFX). Moreover, we introduce a new model where the agents are not partitioned into groups in advance, but instead the partition can be chosen in conjunction with the allocation of the goods. In this model, we show that for agents with arbitrary monotonic valuations, there is always a partition of the agents into two groups of any given sizes along with an EF1 allocation of the goods. We also provide an extension of this result to any number of groups.

cs.GT↗

arXiv2020

Consensus Halving for Sets of Items

Consensus halving refers to the problem of dividing a resource into two parts so that every agent values both parts equally. Prior work has shown that when the resource is represented by an interval, a consensus halving with at most $n$ cuts always exists, but is hard to compute even for agents with simple valuation functions. In this paper, we study consensus halving in a natural setting where the resource consists of a set of items without a linear ordering. When agents have additive utilities, we present a polynomial-time algorithm that computes a consensus halving with at most $n$ cuts, and show that $n$ cuts are almost surely necessary when the agents' utilities are drawn from probabilistic distributions. On the other hand, we show that for a simple class of monotonic utilities, the problem already becomes PPAD-hard. Furthermore, we compare and contrast consensus halving with the more general problem of consensus $k$-splitting, where we wish to divide the resource into $k$ parts in possibly unequal ratios, and provide some consequences of our results on the problem of computing small agreeable sets.

cs.GT↗

arXiv2020

On the Number of Almost Envy-Free Allocations

Envy-freeness is a standard benchmark of fairness in resource allocation. Since it cannot always be satisfied when the resource consists of indivisible items even when there are two agents, the relaxations envy-freeness up to one item (EF1) and envy-freeness up to any item (EFX) are often considered. We establish tight lower bounds on the number of allocations satisfying each of these benchmarks in the case of two agents. In particular, while there can be as few as two EFX allocations for any number of items, the number of EF1 allocations is always exponential in the number of items. Our results apply a version of the vertex isoperimetric inequality on the hypercube and help explain the large gap in terms of robustness between the two notions.

cs.GT↗

arXiv2020

Truthful Fair Division without Free Disposal

We study the problem of fairly dividing a heterogeneous resource, commonly known as cake cutting and chore division, in the presence of strategic agents. While a number of results in this setting have been established in previous works, they rely crucially on the free disposal assumption, meaning that the mechanism is allowed to throw away part of the resource at no cost. In the present work, we remove this assumption and focus on mechanisms that always allocate the entire resource. We exhibit a truthful and envy-free mechanism for cake cutting and chore division for two agents with piecewise uniform valuations, and we complement our result by showing that such a mechanism does not exist when certain additional constraints are imposed on the mechanisms. Moreover, we provide bounds on the efficiency of mechanisms satisfying various properties, and give truthful mechanisms for multiple agents with restricted classes of valuations.

cs.GT↗

arXiv2020

Closing Gaps in Asymptotic Fair Division

We study a resource allocation setting where $m$ discrete items are to be divided among $n$ agents with additive utilities, and the agents' utilities for individual items are drawn at random from a probability distribution. Since common fairness notions like envy-freeness and proportionality cannot always be satisfied in this setting, an important question is when allocations satisfying these notions exist. In this paper, we close several gaps in the line of work on asymptotic fair division. First, we prove that the classical round-robin algorithm is likely to produce an envy-free allocation provided that $m=Ω(n\log n/\log\log n)$, matching the lower bound from prior work. We then show that a proportional allocation exists with high probability as long as $m\geq n$, while an allocation satisfying envy-freeness up to any item (EFX) is likely to be present for any relation between $m$ and $n$. Finally, we consider a related setting where each agent is assigned exactly one item and the remaining items are left unassigned, and show that the transition from non-existence to existence with respect to envy-free assignments occurs at $m=en$.

cs.GT↗

arXiv2020

On the Structure of Stable Tournament Solutions

A fundamental property of choice functions is stability, which, loosely speaking, prescribes that choice sets are invariant under adding and removing unchosen alternatives. We provide several structural insights that improve our understanding of stable choice functions. In particular, (i) we show that every stable choice function is generated by a unique simple choice function, which never excludes more than one alternative, (ii) we completely characterize which simple choice functions give rise to stable choice functions, and (iii) we prove a strong relationship between stability and a new property of tournament solutions called local reversal symmetry. Based on these findings, we provide the first concrete tournament---consisting of 24 alternatives---in which the tournament equilibrium set fails to be stable. Furthermore, we prove that there is no more discriminating stable tournament solution than the bipartisan set and that the bipartisan set is the unique most discriminating tournament solution which satisfies standard properties proposed in the literature.

econ.TH↗

arXiv2020

How to Cut a Cake Fairly: A Generalization to Groups

A fundamental result in cake cutting states that for any number of players with arbitrary preferences over a cake, there exists a division of the cake such that every player receives a single contiguous piece and no player is left envious. We generalize this result by showing that it is possible to partition the players into groups of any desired sizes and divide the cake among the groups, so that each group receives a single contiguous piece and no player finds the piece of another group better than that of the player's own group.

econ.TH↗

arXiv2020

Contiguous Cake Cutting: Hardness Results and Approximation Algorithms

We study the fair allocation of a cake, which serves as a metaphor for a divisible resource, under the requirement that each agent should receive a contiguous piece of the cake. While it is known that no finite envy-free algorithm exists in this setting, we exhibit efficient algorithms that produce allocations with low envy among the agents. We then establish NP-hardness results for various decision problems on the existence of envy-free allocations, such as when we fix the ordering of the agents or constrain the positions of certain cuts. In addition, we consider a discretized setting where indivisible items lie on a line and show a number of hardness results extending and strengthening those from prior work. Finally, we investigate connections between approximate and exact envy-freeness, as well as between continuous and discrete cake cutting.

cs.GT↗

arXiv2019

Refining Tournament Solutions via Margin of Victory

Tournament solutions are frequently used to select winners from a set of alternatives based on pairwise comparisons between alternatives. Prior work has shown that several common tournament solutions tend to select large winner sets and therefore have low discriminative power. In this paper, we propose a general framework for refining tournament solutions. In order to distinguish between winning alternatives, and also between non-winning ones, we introduce the notion of margin of victory (MoV) for tournament solutions. MoV is a robustness measure for individual alternatives: For winners, the MoV captures the distance from dropping out of the winner set, and for non-winners, the distance from entering the set. In each case, distance is measured in terms of which pairwise comparisons would have to be reversed in order to achieve the desired outcome. For common tournament solutions, including the top cycle, the uncovered set, and the Banks set, we determine the complexity of computing the MoV and provide worst-case bounds on the MoV for both winners and non-winners. Our results can also be viewed from the perspective of bribery and manipulation.

cs.GT↗

arXiv2019

Dividing a Graphical Cake

We consider the classical cake-cutting problem where we wish to fairly divide a heterogeneous resource, often modeled as a cake, among interested agents. Work on the subject typically assumes that the cake is represented by an interval. In this paper, we introduce a generalized setting where the cake can be in the form of the set of edges of an undirected graph. This allows us to model the division of road or cable networks. Unlike in the canonical setting, common fairness criteria such as proportionality cannot always be satisfied in our setting if each agent must receive a connected subgraph. We determine the optimal approximation of proportionality that can be obtained for any number of agents with arbitrary valuations, and exhibit tight guarantees for each graph in the case of two agents. In addition, when more than one connected piece per agent is allowed, we establish the best egalitarian welfare guarantee for each total number of connected pieces. We also study a number of variants and extensions, including when approximate equitability is considered, or when the item to be divided is undesirable (also known as chore division).

cs.GT↗

arXiv2019

Envy-Freeness in House Allocation Problems

We consider the house allocation problem, where $m$ houses are to be assigned to $n$ agents so that each agent gets exactly one house. We present a polynomial-time algorithm that determines whether an envy-free assignment exists, and if so, computes one such assignment. We also show that an envy-free assignment exists with high probability if the number of houses exceeds the number of agents by a logarithmic factor.

cs.GT↗

arXiv2019

Democratic Fair Allocation of Indivisible Goods

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group's share is fair. Under this strict requirement, fair allocations exist only for small groups. We introduce the concept of democratic fairness, which aims to satisfy a certain fraction of the agents in each group. This concept is better suited to large groups such as cities or countries. We present protocols for democratic fair allocation among two or more arbitrarily large groups of agents with monotonic, additive, or binary valuations. For two groups with arbitrary monotonic valuations, we give an efficient protocol that guarantees envy-freeness up to one good for at least $1/2$ of the agents in each group, and prove that the $1/2$ fraction is optimal. We also present other protocols that make weaker fairness guarantees to more agents in each group, or to more groups. Our protocols combine techniques from different fields, including combinatorial game theory, cake cutting, and voting.

cs.GT↗

arXiv2019

Schelling Games on Graphs

We consider strategic games that are inspired by Schelling's model of residential segregation. In our model, the agents are partitioned into k types and need to select locations on an undirected graph. Agents can be either stubborn, in which case they will always choose their preferred location, or strategic, in which case they aim to maximize the fraction of agents of their own type in their neighborhood. We investigate the existence of equilibria in these games, study the complexity of finding an equilibrium outcome or an outcome with high social welfare, and also provide upper and lower bounds on the price of anarchy and stability. Some of our results extend to the setting where the preferences of the agents over their neighbors are defined by a social network rather than a partition into types.

cs.GT↗