The DOI matches its Crossref record.
Graphs and Cooperation in Games
Abstract
Graph-theoretic ideas are used to analyze cooperation structures in games. Allocation rules, selecting a payoff for every possible cooperation structure, are studied for games in characteristic function form. Fair allocation rules are defined, and these are proven to be unique, closely related to the Shapley value, and stable for a wide class of games.
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“We introduce DAG-Shapley, exploiting DAG structure to achieve exact Shapley computation with enhanced efficiency through coalition space reduction and hierarchical memoization (Qian et al. 2024; Myerson 1977; Li and Shan 2020).”
From HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems (2025) · cites this paper as Myerson 1977
In the citing paper
“The DAG structure enforces strict information flow constraints through a formal access control mechanism (Myerson 1977).”
From HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems (2025) · cites this paper as Myerson 1977
In the citing paper
“The integration of Shapley value theory into this DAGbased framework provides a principled approach to contribution assessment that leverages the structured information flow (Myerson 1977).”
From HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems (2025) · cites this paper as Myerson 1977
In the citing paper
“For non-viable coalitions where Viable ( S ) is false, their value is zero ( v ( S ) = 0 ), enabling systematic elimination while preserving Shapley exactness (Myerson 1977).”
From HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems (2025) · cites this paper as Myerson 1977
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HiveMind: Contribution-Guided Online Prompt Optimization of LLM Multi-Agent Systems
Xia, Y., Wang, T., Zhang, S., Weng, Z., Cao, B., & Liew, S. C. (2025) · arXiv · doi:10.48550/arxiv.2512.06432
“…et al. 2025 C viable ← C viable ∪ { S } 13: end for 14: return C viable We introduce DAG-Shapley, exploiting DAG structure to achieve exact Shapley computation with enhanced efficiency through coalition space reduction and hierarchical memoization (Qian et al. 2024; Myerson 1977; Li and Shan 2020).”
Influential
Metadata
- Authors
- Myerson, R. B.
- Affiliations
- Northwestern University (US)
- Corresponding author
- Myerson, Roger B.
- ORCID
- Myerson, Roger B.
- Venue
- Mathematics of Operations Research
- Published
- 1977-08
- Volume
- 2
- Issue
- 3
- Pages
- 225-229
- ISSN
- 0364-765X (ISSN-L)
- 1526-5471
- OpenAlex
- W1975617599
- Cited by
- 1,446
- References
- 0
- Citations by year
- 2026: 45 · 2025: 55 · 2024: 56 · 2023: 48 · 2022: 59 · 2021: 56 · 2020: 53 · 2019: 59 · 2018: 66 · 2017: 81 · 2016: 63 · 2015: 69 · 2014: 72 · 2013: 83 · 2012: 53
- FWCI
- 12.43
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Mathematics of Operations Research (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Econstor (Econstor) (submittedVersion)
- Topics
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Game Theory and Voting Systems
- Social Sciences › Decision Sciences › Management Science and Operations Research › Game Theory and Applications
- Social Sciences › Sociology and Political Science › Evolutionary Game Theory and Cooperation
- Keywords
- cooperative structure, allocation rules, Shapley value, cooperative games
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