Hedonic Games with Graph-restricted Communication

We study hedonic coalition formation games in which cooperation among the players is restricted by a graph structure: a subset of players can form a coalition if and only if they are connected in the given graph. We investigate the complexity of finding stable outcomes in such games, for several notions of stability. In particular, we provide an efficient algorithm that finds an individually stable partition for an arbitrary hedonic game on an acyclic graph. We also introduce a new stability concept -in-neighbor stability- which is tailored for our setting. We show that the problem of finding an in-neighbor stable outcome admits a polynomial-time algorithm if the underlying graph is a path, but is NP-hard for arbitrary trees even for additively separable hedonic games; for symmetric additively separable games we obtain a PLS-hardness result

Relaxed Core Stability for Hedonic Games with Size-Dependent Utilities

We study relationships between different relaxed notions of core stability in hedonic games. In particular, we study (i) q-size core stable outcomes in which no deviating coalition of size at most q exists and (ii) k-improvement core stable outcomes in which no coalition can improve by a factor of more than k. For a large class of hedonic games, including fractional and additively separable hedonic games, we derive upper bounds on the maximum factor by which a coalition of a certain size can improve in a q-size core stable outcome. We further provide asymptotically tight lower bounds for a large class of hedonic games. Finally, our bounds allow us to confirm two conjectures by Fanelli et al. [Angelo Fanelli et al., 2021][IJCAI\u2721] for symmetric fractional hedonic games (S-FHGs): (i) every q-size core stable outcome in an S-FHG is also q/(q-1)-improvement core stable and (ii) the price of anarchy of q-size stability in S-FHGs is precisely 2q/q-1

Novel Hedonic Games and Stability Notions

We present here work on matching problems, namely hedonic games, also known as coalition formation games. We introduce two classes of hedonic games, Super Altruistic Hedonic Games (SAHGs) and Anchored Team Formation Games (ATFGs), and investigate the computational complexity of finding optimal partitions of agents into coalitions, or finding - or determining the existence of - stable coalition structures. We introduce a new stability notion for hedonic games and examine its relation to core and Nash stability for several classes of hedonic games

On a Simple Hedonic Game with Graph-Restricted Communication

International audienceWe study a hedonic game for which the feasible coalitions are prescribed by a graph representing the agents' social relations. A group of agents can form a feasible coalition if and only if their corresponding vertices can be spanned with a star. This requirement guarantees that agents are connected, close to each other, and one central agent can coordinate the actions of the group. In our game everyone strives to join the largest feasible coalition. We study the existence and computational complexity of both Nash stable and core stable partitions. Then, we provide tight or asymptotically tight bounds on their quality, with respect to both the price of anarchy and stability, under two natural social functions, namely, the number of agents who are not in a singleton coalition, and the number of coalitions. We also derive refined bounds for games in which the social graph is restricted to be claw-free. Finally, we investigate the complexity of computing socially optimal partitions as well as extreme Nash stable ones

Coalition Formation For Distributed Constraint Optimization Problems

This dissertation presents our research on coalition formation for Distributed Constraint Optimization Problems (DCOP). In a DCOP, a problem is broken up into many disjoint sub-problems, each controlled by an autonomous agent and together the system of agents have a joint goal of maximizing a global utility function. In particular, we study the use of coalitions for solving distributed k-coloring problems using iterative approximate algorithms, which do not guarantee optimal results, but provide fast and economic solutions in resource constrained environments. The challenge in forming coalitions using iterative approximate algorithms is in identifying constraint dependencies between agents that allow for effective coalitions to form. We first present the Virtual Structure Reduction (VSR) Algorithm and its integration with a modified version of an iterative approximate solver. The VSR algorithm is the first distributed approach for finding structural relationships, called strict frozen pairs, between agents that allows for effective coalition formation. Using coalition structures allows for both more efficient search and higher overall utility in the solutions. Secondly, we relax the assumption of strict frozen pairs and allow coalitions to form under a probabilistic relationship. We identify probabilistic frozen pairs by calculating the propensity between two agents, or the joint probability of two agents in a k-coloring problem having the same value in all satisfiable instances. Using propensity, we form coalitions in sparse graphs where strict frozen pairs may not exist, but there is still benefit to forming coalitions. Lastly, we present a cooperative game theoretic approach where agents search for Nash stable coalitions under the conditions of additively separable and symmetric value functions

Online Coalition Formation under Random Arrival or Coalition Dissolution

Coalition formation considers the question of how to partition a set of $n$ agents into disjoint coalitions according to their preferences. We consider a cardinal utility model with additively separable aggregation of preferences and study the online variant of coalition formation, where the agents arrive in sequence and whenever an agent arrives, they have to be assigned to a coalition immediately. The goal is to maximize social welfare. In a purely deterministic model, the greedy algorithm, where an agent is assigned to the coalition with the largest gain, is known to achieve an optimal competitive ratio, which heavily relies on the range of utilities. We complement this result by considering two related models. First, we study a model where agents arrive in a random order. We find that the competitive ratio of the greedy algorithm is $\Theta\left(\frac{1}{n^2}\right)$, whereas an alternative algorithm, which is based on alternating between waiting and greedy phases, can achieve a competitive ratio of $\Theta\left(\frac{1}{n}\right)$. Second, we relax the irrevocability of decisions by allowing to dissolve coalitions into singleton coalitions, presenting a matching-based algorithm that once again achieves a competitive ratio of $\Theta\left(\frac{1}{n}\right)$. Hence, compared to the base model, we present two ways to achieve a competitive ratio that precisely gets rid of utility dependencies. Our results also give novel insights in weighted online matching.Comment: Appears in the 31st Annual European Symposium on Algorithms (ESA 2023

Internal Hierarchy and Stable Coalition Structures

When an agent decides whether to join a coalition or not, she must consider both i) the expected strength of the coalition and ii) her position in the vertical structure within the coalition. We establish that there exists a positive relationship between the degree of inequality in remuneration across ranks within coalitions and the number of coalitions to be formed. When coalition size is unrestricted, in all stable systems the endogenous coalitions must be mixed and balanced in terms of members' abilities, with no segregation. When coalitions must have a fixed finite size, stable systems display segregation by clusters while maintaining the aforesaid feature within clusters.Stable Systems, Abilities, Hierarchy, Cyclic Partition