arXiv subjects

René Romen

Publications and source records attributed to René Romen.

6 recordsLinked to original sources

arXiv2026

Stability Under Valuation Updates in Coalition Formation

Coalition formation studies how to partition a set of agents into disjoint coalitions under consideration of their preferences. We study the classical objective of stability in a variant of additively separable hedonic games where agents can change their valuations. Our objective is to find a stable partition after each change. To minimize the reconfiguration cost, we search for nearby stable coalition structures. Our focus is on stability concepts based on single-agent deviations. We present a detailed picture of the complexity of finding nearby stable coalition structures in additively separable hedonic games, for both symmetric and non-symmetric valuations. Our results show that the problem is NP-complete for Nash stability, individual stability, contractual Nash stability, and contractual individual stability. We complement these results by presenting polynomial-time algorithms for contractual Nash stability and contractual individual stability under restricted symmetric valuations. Finally, we show that these algorithms guarantee a bounded average distance over long sequences of updates.

cs.GT↗

arXiv2025

The Power of Matching for Online Fractional Hedonic Games

We study coalition formation in the framework of fractional hedonic games (FHGs). The objective is to maximize social welfare in an online model where agents arrive one by one and must be assigned to coalitions immediately and irrevocably. A recurrent theme in online coalition formation is that online matching algorithms, where coalitions are restricted to size at most $2$, yield good competitive ratios. For example, computing maximal matchings achieves the optimal competitive ratio for general online FHGs. However, this ratio is bounded only if agents' valuations are themselves bounded. We identify optimal algorithms with constant competitive ratios in two related settings, independent of the range of agent valuations. First, under random agent arrival, we present an asymptotically optimal $(\frac{1}{3}-\frac 1n)$-competitive algorithm, where $n$ is the number of agents. This result builds on our identification of an optimal matching algorithm in a general model of online matching with edge weights and an unknown number of agents. In this setting, we also achieve an asymptotically optimal competitive ratio of $\frac{1}{3}-\frac 1n$. Second, when agents arrive in an arbitrary order but algorithms are allowed to irrevocably and entirely dissolve coalitions, we show that another matching-based algorithm achieves an optimal competitive ratio of $\frac{1}{6 + 4\sqrt{2}}$.

cs.GT↗

arXiv2025

Online Coalition Formation under Random Arrival or Coalition Dissolution

Coalition formation explores how to partition a set of $n$ agents into disjoint coalitions according to their preferences. We consider a cardinal utility model with an additively separable aggregation of preferences and study the online variant of coalition formation, where the agents arrive in sequence. The goal is to achieve competitive social welfare. In the basic model, agents arrive in an arbitrary order and have to be assigned to coalitions immediately and irrevocably. There, the natural greedy algorithm 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 $Θ\left(\frac{1}{n^2}\right)$. In contrast, an alternative algorithm, which is based on alternating between waiting and greedy phases, can achieve a competitive ratio of $Θ\left(\frac{1}{n}\right)$. Second, we relax the irrevocability of decisions by allowing the dissolution of coalitions into singleton coalitions. We achieve an asymptotically optimal competitive ratio of $Θ\left(\frac 1n\right)$ by drawing a close connection to a general model of online matching. Hence, in both models, we obtain a competitive ratio that removes the unavoidable utility dependencies in the basic model and essentially matches the best possible approximation ratio by polynomial-time algorithms.

cs.GT↗

arXiv2025

Stability in Online Coalition Formation

Coalition formation is concerned with the question of how to partition a set of agents into disjoint coalitions according to their preferences. Deviating from most of the previous work, we consider an online variant of the problem, where agents arrive in sequence. Whenever an agent arrives, they must be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve \emph{stable} coalition structures online and treat the most common stability concepts based on deviations by single agents and groups of agents. We present a comprehensive picture in additively separable hedonic games, leading to dichotomies, where positive results are obtained by deterministic algorithms and negative results even hold for randomized algorithms.

cs.GT↗

arXiv2024

Towards a Characterization of Random Serial Dictatorship

Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these axioms. Extending this characterization to arbitrary $n$ is a long-standing open problem. By weakening ex post efficiency and strategyproofness, we reduce the question of whether RSD is characterized by these axioms for fixed $n$ to determining whether a matrix has rank $n^2 n!^n$. We provide computer-generated counterexamples to show that two other approaches for proving the characterization (using deterministic extreme points or restricted domains of preferences) are inadequate.

econ.TH↗

arXiv2022

Relaxed Notions of Condorcet-Consistency and Efficiency for Strategyproof Social Decision Schemes

Social decision schemes (SDSs) map the preferences of a group of voters over some set of $m$ alternatives to a probability distribution over the alternatives. A seminal characterization of strategyproof SDSs by Gibbard implies that there are no strategyproof Condorcet extensions and that only random dictatorships satisfy ex post efficiency and strategyproofness. The latter is known as the random dictatorship theorem. We relax Condorcet-consistency and ex post efficiency by introducing a lower bound on the probability of Condorcet winners and an upper bound on the probability of Pareto-dominated alternatives, respectively. We then show that the SDS that assigns probabilities proportional to Copeland scores is the only anonymous, neutral, and strategyproof SDS that can guarantee the Condorcet winner a probability of at least 2/m. Moreover, no strategyproof SDS can exceed this bound, even when dropping anonymity and neutrality. Secondly, we prove a continuous strengthening of Gibbard's random dictatorship theorem: the less probability we put on Pareto-dominated alternatives, the closer to a random dictatorship is the resulting SDS. Finally, we show that the only anonymous, neutral, and strategyproof SDSs that maximize the probability of Condorcet winners while minimizing the probability of Pareto-dominated alternatives are mixtures of the uniform random dictatorship and the randomized Copeland rule.

econ.TH↗