Saturday 01 February 2025
The quest for fairness in coalition formation has long been a topic of interest in the field of artificial intelligence and game theory. In recent years, researchers have made significant progress in understanding the concept of core stability, which refers to the idea that a coalition structure is stable if no group of agents can improve their utility by deviating from it.
In a new paper published recently, a team of researchers has shed light on the relationship between different relaxed notions of core stability in hedonic games. Hedonic games are a type of game where players form coalitions to maximize their individual utilities. The researchers have identified a general upper bound for the price of anarchy, which measures how much the worst-case coalition structure deviates from the optimal one.
The study focuses on two types of hedonic games: fractional and additively separable hedonic games. In fractional games, each agent has a utility function that depends on the size of their coalition, while in additively separable games, utilities are based on the number of agents in a coalition. The researchers show that for these games, every q-size core stable outcome is (m, f(q, m))-core stable, where f(q, m) is an upper bound that depends on the size of the game and the size of the coalitions.
The implications of this result are significant. It means that in fractional and additively separable hedonic games, it is possible to design algorithms that can find a core stable coalition structure efficiently, even for large numbers of agents. This has important practical applications, such as in network formation problems or committee selection.
The researchers also explore the relationship between different relaxed notions of core stability, including q-size core stability and k-improvement core stability. They show that for fractional hedonic games, every q-size core stable outcome is qq−1-improvement core stable, which provides a tighter bound on the price of anarchy.
One of the key challenges in studying hedonic games is that they can exhibit complex behavior, making it difficult to design efficient algorithms for finding core stable coalition structures. The researchers’ results provide a significant step forward in understanding these games and developing more effective algorithms.
The paper’s findings have important implications for fields such as artificial intelligence, operations research, and computer science. They highlight the importance of considering different relaxed notions of core stability when designing algorithms for hedonic games, and demonstrate the potential for efficient coalition formation in large-scale systems.
Cite this article: “Stability Bounds in Hedonic Games: A Step Forward in Coalition Formation”, The Science Archive, 2025.
Coalition Formation, Hedonic Games, Core Stability, Artificial Intelligence, Game Theory, Algorithm Design, Network Formation, Committee Selection, Price Of Anarchy, Operations Research
Reference: Tom Demeulemeester, Jannik Peters, “Quantifying Core Stability Relaxations in Hedonic Games” (2024).
