Coalition Structure Generation in Multi-Agent Systems

Coalition structure generation addresses the problem of organising autonomous agents into disjoint groups so as to maximise collective objectives under computational constraints. As the number of agents grows, the space of possible partitions expands exponentially, posing significant challenges for optimal decision-making. Traditional approaches assume deterministic settings with static valuations and rely on exact algorithms, such as dynamic programming or branch-and-bound, which suffer from prohibitive runtimes. Recent advances have broadened the scope to include online arrival of agents, uncertainty in agent availability and externalities between coalitions, yielding richer models such as additively separable hedonic games and partition function games. Emerging techniques balance optimality and tractability through anytime and approximation algorithms, enabling progressively better solutions under time limits. Practical applications span sensor networks, robotic swarms, distributed resource allocation and strategic task assignment in commercial and defence systems. The field continues to deepen its theoretical foundations while driving real-world deployments that demand scalable, robust coalition formation in dynamic, multi-goal environments.

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Stability in Online Coalition Formation has mapped the landscape of online variants where agents arrive sequentially and must be irrevocably assigned to coalitions. Focusing on additively separable hedonic preferences, deterministic algorithms achieve stable structures under both individual and group deviation notions, while fundamental lower bounds show the limits of randomisation.

An Anytime Algorithm for Optimal Simultaneous Coalition Structure Generation and Assignment extends classical generation methods by integrating coalition formation with task allocation. The proposed algorithm delivers interim solutions with quality guarantees, benchmarks favourably against industry solvers and demonstrates real-time applicability in strategy-game scenarios, highlighting the importance of coupling formation and goal assignment in cooperative environments.

Optimal Coalition Structures for Probabilistically Monotone Partition Function Games introduces uncertainty into external-effect models by defining probabilistically monotone value functions. Through a constructive greedy approach, it proves that exact optima can be found in these uncertain settings and analyses the algorithm’s time complexity, opening new avenues for robust coalition design under stochastic participation.

Coalition Structure Generation in Multi-Agent Systems publication trend

The graph below shows the total number of articles in coalition structure generation in multi-agent systems across all publications each year (not limited to Nature Index journals).

Technical terms

Coalition structure: A partition of the agent set into exhaustive, disjoint coalitions.

Social welfare: The sum of coalition values, reflecting the overall effectiveness of the partition.

Additively separable hedonic game: A preference model where each agent’s utility for a coalition equals the sum of pairwise valuations of its members.

Anytime algorithm: An algorithm that can be halted at any time to yield a valid solution with bounded suboptimality.

Partition function game: A cooperative game in which a coalition’s value depends on the configuration of all other coalitions, capturing externalities.

References

1. Stability in Online Coalition Formation. Journal of Artificial Intelligence Research (2025).
2. An anytime algorithm for optimal simultaneous coalition structure generation and assignment. Autonomous Agents and Multi-Agent Systems (2020).
3. Optimal coalition structures for probabilistically monotone partition function games. Autonomous Agents and Multi-Agent Systems (2022).