Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2

Strategyproof Mechanisms for Additively Separable Hedonic Games and Fractional Hedonic Games

Additively separable hedonic games and fractional hedonic games have received considerable attention. They are coalition forming games of selfish agents based on their mutual preferences. Most of the work in the literature characterizes the existence and structure of stable outcomes (i.e., partitions in coalitions), assuming that preferences are given. However, there is little discussion on this assumption. In fact, agents receive different utilities if they belong to different partitions, and thus it is natural for them to declare their preferences strategically in order to maximize their benefit. In this paper we consider strategyproof mechanisms for additively separable hedonic games and fractional hedonic games, that is, partitioning methods without payments such that utility maximizing agents have no incentive to lie about their true preferences. We focus on social welfare maximization and provide several lower and upper bounds on the performance achievable by strategyproof mechanisms for general and specific additive functions. In most of the cases we provide tight or asymptotically tight results. All our mechanisms are simple and can be computed in polynomial time. Moreover, all the lower bounds are unconditional, that is, they do not rely on any computational or complexity assumptions

Group formation: The interaction of increasing returns and preferences' diversity

The chapter is organized as follows. Section 2 focuses on competition in a simple economy under increasing returns to scale and heterogeneous consumers. The concept of sustainable oligopoly is discussed and analyzed. Section 3 studies in a more general and abstract set up competition among groups in the absence of spillovers. Whereas Section 3 develops some insights of Section 2, it can be read first. Finally Section 4 analyzes public decisions in a simple public good economy through the previous approach, and addresses the interaction between free mobility and free entry under negative externalities.group formation

Mechanism Design for Team Formation

Team formation is a core problem in AI. Remarkably, little prior work has addressed the problem of mechanism design for team formation, accounting for the need to elicit agents' preferences over potential teammates. Coalition formation in the related hedonic games has received much attention, but only from the perspective of coalition stability, with little emphasis on the mechanism design objectives of true preference elicitation, social welfare, and equity. We present the first formal mechanism design framework for team formation, building on recent combinatorial matching market design literature. We exhibit four mechanisms for this problem, two novel, two simple extensions of known mechanisms from other domains. Two of these (one new, one known) have desirable theoretical properties. However, we use extensive experiments to show our second novel mechanism, despite having no theoretical guarantees, empirically achieves good incentive compatibility, welfare, and fairness.Comment: 12 page

Competitive Markets, Collective Decisions and Group Formation

We consider a general equilibrium model where groups operating in a competitive market environment can have several members and make efficient collective consumption decisions. Individuals have the option to leave the group and make it on their own or join another group. We study the effect of these outside options on group formation, group stability, equilibrium existence, and equilibrium efficiency.household behavior, household formation, collective decision making, general equilibrium

Formation of Segregated and Integrated Groups

A model of group formation is presented where the number of groups is fixed and a person can only join a group if the group’s members approve the person’s joining. Agents have either local status preferences (each agent wants to be the highest status agent in his group) or global status preferences (each agent wants to join the highest status group that she can join). For both preference types, conditions are provided which guarantee the existence of a segregated stable partition where similar people are grouped together and conditions are provided which guarantee the existence of an integrated stable partition where dissimilar people are grouped together. Additionally, in a dynamic framework we show that if a new empty group is added to a segregated stable partition, then integration may occur.Group Formation, Stable Partition, Segregation, Integration

Beyond revealed preference: choice-theoretic foundations for behavioral welfare economics

We propose a broad generalization of standard choice-theoretic welfare economics that encompasses a wide variety of nonstandard behavioral models. Our approach exploits the coherent aspects of choice that those positive models typically attempt to capture. It replaces the standard revealed preference relation with an unambiguous choice relation: roughly, x is (strictly) unambiguously chosen over y (written xP*y) iff y is never chosen when x is available. Under weak assumptions, P* is acyclic and therefore suitable for welfare analysis; it is also the most discerning welfare criterion that never overrules choice. The resulting framework generates natural counterparts for the standard tools of applied welfare economics and is easily applied in the context of specific behavioral theories, with novel implications. Though not universally discerning, it lends itself to principled refinements

On Coalition Formation with Heterogeneous Agents

We propose a framework to analyze coalition formation with heterogeneous agents. Existing literature defines stability conditions that do not ensure that, once an agent decides to sign an agreement, the enlarged coalition is feasible. Defining the concepts of refraction and exchanging, we set up conditions of existence and enlargement of a coalition with heterogeneous agents. We use the concept of exchanging agents to give necessary conditions for internal stability and show that refraction is a sufficient condition for the failure of an enlargement of the coalition. With heterogeneous agents we can get a situation where a group of members of an unstable coalition does not deviate, neither within the coalition nor within the extended coalition. Hence, the possibilities of agreement are richer than in the standard analysis with homogeneous agents. Examples of industrial economics are used for illustration, and an application to climate change negotiations is discussed in more detail.Heterogeneity, Coalition, Exchanging, Refraction, Global Externalities

Computational complexity of kk-stable matchings

We study deviations by a group of agents in the three main types of matching markets: the house allocation, the marriage, and the roommates models. For a given instance, we call a matching $k$-stable if no other matching exists that is more beneficial to at least $k$ out of the $n$ agents. The concept generalizes the recently studied majority stability. We prove that whereas the verification of $k$-stability for a given matching is polynomial-time solvable in all three models, the complexity of deciding whether a $k$-stable matching exists depends on $\frac{k}{n}$ and is characteristic to each model.Comment: SAGT 202