Martin Bullinger

AAAI Conference 2026 Conference Paper

Deviation Dynamics in Cardinal Hedonic Games

• Valentin Zech
• Martin Bullinger

Computing stable partitions in hedonic games is a challenging task because there exist games in which stable outcomes do not exist. Even more, these No-instances can often be leveraged to prove computational hardness results. We make this impression rigorous in a dynamic model of cardinal hedonic games by providing meta theorems. These imply hardness of deciding about the possible or necessary convergence of deviation dynamics based on the mere existence of No-instances. Our results hold for additively separable, fractional, and modified fractional hedonic games (ASHGs, FHGs, and MFHGs). Moreover, they encompass essentially all reasonable stability notions based on single-agent deviations. In addition, we propose dynamics as a method to find individually rational and contractually individual stable (CIS) partitions in ASHGs. In particular, we find that CIS dynamics from the singleton partition possibly converge after a linear number of deviations but may require an exponential number of deviations in the worst case.

AAMAS Conference 2025 Conference Paper

Selecting Interlacing Committees

• Chris Dong
• Martin Bullinger
• Tomasz Was
• Larry Birnbaum
• Edith Elkind

Polarization is a major concern for a well-functioning society. Often, mass polarization of a society is driven by polarizing political representation, even when the latter is easily preventable. The existing computational social choice methods for the task of committee selection are not designed to address this issue. We enrich the standard approach to committee selection by defining two quantitative measures that evaluate how well a given committee interconnects the voters. Maximizing these measures aims at avoiding polarizing committees. While the corresponding maximization problems are NP-complete in general, we obtain efficient algorithms for profiles in the voter-candidate interval domain. Moreover, we analyze the compatibility of our goals with other representation objectives, such as excellence, diversity, and proportionality. We identify tradeoffs between approximation guarantees, and describe algorithms that achieve simultaneous constant-factor approximations.

IJCAI Conference 2025 Conference Paper

Settling the Complexity of Popularity in Additively Separable and Fractional Hedonic Games

• Martin Bullinger
• Matan Gilboa

We study coalition formation in the framework of hedonic games. These games model the problem of partitioning a set of agents having a preference order over the coalitions they can be part of. A partition is called popular if it does not lose a majority vote among the agents against any other partition. Unfortunately, hedonic games need not admit popular partitions. We go further and settle the complexity of the existence problem concerning popularity in additively separable and fractional hedonic games by showing that it is Sigma_2^p-complete in both cases. We are thus the first work that proves a completeness result of popularity for the second level of the polynomial hierarchy.

JAIR Journal 2025 Journal Article

Stability in Online Coalition Formation

• Martin Bullinger
• René Romen

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 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.

AAMAS Conference 2025 Conference Paper

Towards Fair and Efficient Public Transportation: A Bus Stop Model

• Martin Bullinger
• Edith Elkind
• Mohamad Latifian

We consider a stylized formal model of public transportation, where a set of agents need to travel along a given road, and there is a bus that runs the length of this road. Each agent has a left terminal and a right terminal between which they wish to travel; they can walk all the way, or walk to/from the nearest stop and use the bus for the rest of their journey. The bus can make a fixed number of stops, and the planner needs to select locations for these stops. We study notions of efficiency and fairness for this setting. First, we give a polynomial-time algorithm for computing a solution that minimizes the total travel time; our approach can capture further extensions of the base model, such as more general cost functions or existing infrastructure. Second, we develop a polynomial-time algorithm that outputs solutions with provable fairness guarantees (such as a variant of the justified representation axiom or 2-approximate core). Our simulations indicate that our algorithm almost always outputs fair solutions, even for parameter regimes that do not admit theoretical guarantees.

AAMAS Conference 2025 Conference Paper

Welfare Approximation in Additively Separable Hedonic Games

• Martin Bullinger
• Vaggos Chatziafratis
• Parnian Shahkar

Partitioning a set of 𝑛 items or agents while maximizing the value of the partition is a fundamental algorithmic task. We study this problem in the specific setting of maximizing social welfare in additively separable hedonic games. Unfortunately, this task faces strong computational boundaries: Extending previous results, we show that approximating welfare by a factor of 𝑛1−𝜀 is NP-hard, even for severely restricted weights. However, we can obtain a randomized log𝑛-approximation on instances for which the sum of input valuations is nonnegative. Finally, we study two stochastic models of aversion-to-enemies games, where the weights are derived from Erdős-Rényi or multipartite graphs. We obtain constant-factor and logarithmic-factor approximations with high probability.

AAAI Conference 2024 Conference Paper

Participation Incentives in Approval-Based Committee Elections

• Martin Bullinger
• Chris Dong
• Patrick Lederer
• Clara Mehler

In approval-based committee (ABC) voting, the goal is to choose a subset of predefined size of the candidates based on the voters’ approval preferences over the candidates. While this problem has attracted significant attention in recent years, the incentives for voters to participate in an election for a given ABC voting rule have been neglected so far. This paper is thus the first to explicitly study this property, typically called participation, for ABC voting rules. In particular, we show that all ABC scoring rules even satisfy group participation, whereas most sequential rules severely fail participation. We furthermore explore several escape routes to the impossibility for sequential ABC voting rules: we prove for many sequential rules that (i) they satisfy participation on laminar profiles, (ii) voters who approve none of the elected candidates cannot benefit by abstaining, and (iii) it is NP-hard for a voter to decide whether she benefits from abstaining

AAMAS Conference 2024 Conference Paper

Robust Popular Matchings

• Martin Bullinger
• Rohith Reddy Gangam
• Parnian Shahkar

We study popularity for matchings under preferences. This solution concept captures matchings that do not lose against any other matching in a majority vote by the agents. A popular matching is said to be robust if it is popular among multiple instances. We present a polynomial-time algorithm for deciding whether there exists a robust popular matching if instances only differ with respect to the preferences of a single agent while obtaining NP-completeness if two instances differ only by a downward shift of one alternative by four agents. Moreover, we find a complexity dichotomy based on preference completeness for the case where instances differ by making some options unavailable.

AIJ Journal 2024 Journal Article

Stability based on single-agent deviations in additively separable hedonic games

• Felix Brandt
• Martin Bullinger
• Leo Tappe

AAAI Conference 2024 Conference Paper

Stability in Online Coalition Formation

• Martin Bullinger
• René Romen

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 and whenever an agent arrives, they have to be assigned to a coalition immediately and irrevocably. The scarce existing literature on online coalition formation has focused on the objective of maximizing social welfare, a demanding requirement, even in the offline setting. Instead, we seek to achieve stable coalition structures in an online setting, and focus on stability concepts based on deviations by single 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.

TCS Journal 2024 Journal Article

Topological distance games

• Martin Bullinger
• Warut Suksompong

AAAI Conference 2023 Conference Paper

Causes of Stability in Dynamic Coalition Formation

• Niclas Boehmer
• Martin Bullinger
• Anna Maria Kerkmann

We study the formation of stable outcomes via simple dynamics in cardinal hedonic games, where the utilities of agents change over time depending on the history of the coalition formation process. Specifically, we analyze situations where members of a coalition decrease their utility for a leaving agent (resent) or increase their utility for a joining agent (appreciation). We show that in contrast to classical dynamics, for resentful or appreciative agents, dynamics are guaranteed to converge under mild conditions for various stability concepts. Thereby, we establish that both resent and appreciation are strong stability-driving forces.

AAAI Conference 2023 Conference Paper

Topological Distance Games

• Martin Bullinger
• Warut Suksompong

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs—for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.

MFCS Conference 2022 Conference Paper

Boundaries to Single-Agent Stability in Additively Separable Hedonic Games

• Martin Bullinger

Coalition formation considers the question of how to partition a set of agents into coalitions with respect to their preferences. Additively separable hedonic games (ASHGs) are a dominant model where cardinal single-agent values are aggregated into preferences by taking sums. Output partitions are typically measured by means of stability, and we follow this approach by considering stability based on single-agent movements (to join other coalitions), where a coalition is defined as stable if there exists no beneficial single-agent deviation. Permissible deviations should always lead to an improvement for the deviator, but they may also be constrained by demanding the consent of agents involved in the deviations, i. e. , by agents in the abandoned or welcoming coalition. Most of the existing research focuses on the unanimous consent of one or both of these coalitions, but more recent research relaxes this to majority-based consent. Our contribution is twofold. First, we settle the computational complexity of the existence of contractually Nash stable partitions, where deviations are constrained by the unanimous consent of the abandoned coalition. This resolves the complexity of the last classical stability notion for ASHGs. Second, we identify clear boundaries to the tractability of stable partitions under majority-based stability concepts by proving elaborate hardness results for restricted classes of ASHGs. Slight further restrictions lead to positive results.

JAIR Journal 2022 Journal Article

Finding and Recognizing Popular Coalition Structures

• Felix Brandt
• Martin Bullinger

An important aspect of multi-agent systems concerns the formation of coalitions that are stable or optimal in some well-defined way. The notion of popularity has recently received a lot of attention in this context. A partition is popular if there is no other partition in which more agents are better off than worse off. In this paper, we study popularity, strong popularity, and mixed popularity (which is particularly attractive because existence is guaranteed by the Minimax Theorem) in a variety of coalition formation settings. Extending previous work on marriage games, we show that mixed popular partitions in roommate games can be found efficiently via linear programming and a separation oracle. This approach is quite universal, leading to efficient algorithms for verifying whether a given partition is popular and for finding strongly popular partitions (resolving an open problem). By contrast, we prove that both problems become computationally intractable when moving from coalitions of size 2 to coalitions of size 3, even when preferences are strict and globally ranked. Moreover, we show that finding popular, strongly popular, and mixed popular partitions in symmetric additively separable hedonic games and symmetric fractional hedonic games is NP-hard. Together, these results indicate strong boundaries to the tractability of popularity in both ordinal and cardinal models of hedonic games.

IJCAI Conference 2022 Conference Paper

Network Creation with Homophilic Agents

• Martin Bullinger
• Pascal Lenzner
• Anna Melnichenko

Network Creation Games are an important framework for understanding the formation of real-world networks. These games usually assume a set of indistinguishable agents strategically buying edges at a uniform price leading to a network among them. However, in real life, agents are heterogeneous and their relationships often display a bias towards similar agents, say of the same ethnic group. This homophilic behavior on the agent level can then lead to the emergent global phenomenon of social segregation. We study Network Creation Games with multiple types of homophilic agents and non-uniform edge cost, introducing two models focusing on the perception of same-type and different-type neighboring agents, respectively. Despite their different initial conditions, both our theoretical and experimental analysis show that both the composition and segregation strength of the resulting stable networks are almost identical, indicating a robust structure of social networks under homophily.

JAIR Journal 2022 Journal Article

On the Indecisiveness of Kelly-Strategyproof Social Choice Functions

• Felix Brandt
• Martin Bullinger
• Patrick Lederer

Social choice functions (SCFs) map the preferences of a group of agents over some set of alternatives to a non-empty subset of alternatives. The Gibbard-Satterthwaite theorem has shown that only extremely restrictive SCFs are strategyproof when there are more than two alternatives. For set-valued SCFs, or so-called social choice correspondences, the situation is less clear. There are miscellaneous -- mostly negative -- results using a variety of strategyproofness notions and additional requirements. The simple and intuitive notion of Kelly-strategyproofness has turned out to be particularly compelling because it is weak enough to still allow for positive results. For example, the Pareto rule is strategyproof even when preferences are weak, and a number of attractive SCFs (such as the top cycle, the uncovered set, and the essential set) are strategyproof for strict preferences. In this paper, we show that, for weak preferences, only indecisive SCFs can satisfy strategyproofness. In particular, (i) every strategyproof rank-based SCF violates Pareto-optimality, (ii) every strategyproof support-based SCF (which generalize Fishburn's C2 SCFs) that satisfies Pareto-optimality returns at least one most preferred alternative of every voter, and (iii) every strategyproof non-imposing SCF returns the Condorcet loser in at least one profile. We also discuss the consequences of these results for randomized social choice.

AAAI Conference 2022 Conference Paper

Single-Agent Dynamics in Additively Separable Hedonic Games

• Felix Brandt
• Martin Bullinger
• Leo Tappe

The formation of stable coalitions is a central concern in multiagent systems. A considerable stream of research defines stability via the absence of beneficial deviations by single agents. Such deviations require an agent to improve her utility by joining another coalition while possibly imposing further restrictions on the consent of the agents in the welcoming as well as the abandoned coalition. While most of the literature focuses on unanimous consent, we also study consent decided by majority vote, and introduce two new stability notions that can be seen as local variants of popularity. We investigate these notions in additively separable hedonic games by pinpointing boundaries to computational complexity depending on the type of consent and restrictions on the utility functions. The latter restrictions shed new light on well-studied classes of games based on the appreciation of friends or the aversion to enemies. Many of our positive results follow from the Deviation Lemma, a general combinatorial observation, which can be leveraged to prove the convergence of simple and natural single-agent dynamics under fairly general conditions.

AAMAS Conference 2021 Conference Paper

Computing Desirable Outcomes in Specific Multi-Agent Scenarios

• Martin Bullinger

Coalition formation and Schelling segregation are important scenarios in algorithmic game theory. While the former considers the strategic behavior of agents gathering in coalitions, the latter is a setting in which agents of two groups seek to surround themselves with like-minded agents. In each case, the quality of outcomes can be measured in form of axioms of optimality and stability. The thesis investigates how to compute such desirable outcomes efficiently and how to deal with computational intractability by means of approximation algorithms, randomization, or domain restrictions.

IJCAI Conference 2021 Conference Paper

Loyalty in Cardinal Hedonic Games

• Martin Bullinger
• Stefan Kober

A common theme of decision making in multi-agent systems is to assign utilities to alternatives, which individuals seek to maximize. This rationale is questionable in coalition formation where agents are affected by other members of their coalition. Based on the assumption that agents are benevolent towards other agents they like to form coalitions with, we propose loyalty in hedonic games, a binary relation dependent on agents' utilities. Given a hedonic game, we define a loyal variant where agents' utilities are defined by taking the minimum of their utility and the utilities of agents towards which they are loyal. This process can be iterated to obtain various degrees of loyalty, terminating in a locally egalitarian variant of the original game. We investigate axioms of group stability and efficiency for different degrees of loyalty. Specifically, we consider the problem of finding coalition structures in the core and of computing best coalitions, obtaining both positive and intractability results. In particular, the limit game possesses Pareto optimal coalition structures in the core.

AAMAS Conference 2021 Conference Paper

On the Indecisiveness of Kelly-Strategyproof Social Choice Functions

• Felix Brandt
• Martin Bullinger
• Patrick Lederer

Social choice functions (SCFs) map the preferences of a group of agents over some set of alternatives to a non-empty subset of alternatives. The Gibbard-Satterthwaite theorem has shown that only extremely unattractive single-valued SCFs are strategyproof when there are more than two alternatives. For set-valued SCFs, or so-called social choice correspondences, the situation is less clear. There are miscellaneous—mostly negative—results using a variety of strategyproofness notions and additional requirements. The simple and intuitive notion of Kelly-strategyproofness has turned out to be particularly compelling because it is weak enough to still allow for positive results. For example, the Pareto rule is strategyproof even when preferences are weak, and a number of attractive SCFs (such as the top cycle, the uncovered set, and the essential set) are strategyproof for strict preferences. In this paper, we show that, for weak preferences, only indecisive SCFs can satisfy strategyproofness. In particular, (i) every strategyproof rank-based SCF violates Pareto-optimality, (ii) every strategyproof support-based SCF (which generalize Fishburn’s C2 SCFs) that satisfies Paretooptimality returns at least one most preferred alternative of every voter, and (iii) every strategyproof non-imposing SCF returns a Condorcet loser in at least one profile.

AAAI Conference 2021 Conference Paper

Reaching Individually Stable Coalition Structures in Hedonic Games

• Felix Brandt
• Martin Bullinger
• Anaëlle Wilczynski

The formal study of coalition formation in multiagent systems is typically realized using so-called hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this paper, we study the convergence of simple dynamics leading to stable partitions in a variety of classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. We identify conditions for convergence, provide elaborate counterexamples of existence of individually stable partitions, and study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson (2002), Brandl, Brandt, and Strobel (2015), and Boehmer and Elkind (2020).

JAIR Journal 2021 Journal Article

Welfare Guarantees in Schelling Segregation

• Martin Bullinger
• Warut Suksompong
• Alexandros A. Voudouris

Schelling’s model is an influential model that reveals how individual perceptions and incentives can lead to residential segregation. Inspired by a recent stream of work, we study welfare guarantees and complexity in this model with respect to several welfare measures. First, we show that while maximizing the social welfare is NP-hard, computing an assignment of agents to the nodes of any topology graph with approximately half of the maximum welfare can be done in polynomial time. We then consider Pareto optimality, introduce two new optimality notions based on it, and establish mostly tight bounds on the worst-case welfare loss for assignments satisfying these notions as well as the complexity of computing such assignments. In addition, we show that for tree topologies, it is possible to decide whether there exists an assignment that gives every agent a positive utility in polynomial time; moreover, when every node in the topology has degree at least 2, such an assignment always exists and can be found efficiently.

AAAI Conference 2021 Conference Paper

Welfare Guarantees in Schelling Segregation

• Martin Bullinger
• Warut Suksompong
• Alexandros A. Voudouris

Schelling’s model is an influential model that reveals how individual perceptions and incentives can lead to racial segregation. Inspired by a recent stream of work, we study welfare guarantees and complexity in this model with respect to several welfare measures. First, we show that while maximizing the social welfare is NP-hard, computing an assignment with approximately half of the maximum welfare can be done in polynomial time. We then consider Pareto optimality and introduce two new optimality notions, and establish mostly tight bounds on the worst-case welfare loss for assignments satisfying these notions. In addition, we show that for trees, it is possible to decide whether there exists an assignment that gives every agent a positive utility in polynomial time; moreover, when every node in the topology has degree at least 2, such an assignment always exists and can be found efficiently.