Cooperative and Competitive Multi-Agent Systems: From Optimization to Games
Bibliographic record
Abstract
Multi-agent systems can solve scientific issues related to complex systems that are difficult or impossible for a single agent to solve through mutual collaboration and cooperation optimization. In a multi-agent system, agents with a certain degree of autonomy generate complex interactions due to the correlation and coordination, which is manifested as cooperative/competitive behavior. This survey focuses on multi-agent cooperative optimization and cooperative/non-cooperative games. Starting from cooperative optimization, the studies on distributed optimization and federated optimization are summarized. The survey mainly focuses on distributed online optimization and its application in privacy protection, and overviews federated optimization from the perspective of privacy protection mechanisms. Then, cooperative games and non-cooperative games are introduced to expand the cooperative optimization problems from two aspects of minimizing global costs and minimizing individual costs, respectively. Multi-agent cooperative and non-cooperative behaviors are modeled by games from both static and dynamic aspects, according to whether each player can make decisions based on the information of other players. Finally, future directions for cooperative optimization, cooperative/non-cooperative games, and their applications are discussed.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".