Pith. sign in

REVIEW 3 major objections 5 minor 35 references

Stable and Budget-Feasible Coalition Formation for Clustered Federated Learning: A Hedonic Potential-Game Approach

T0 review · 3 major / 5 minor · reviewed 2026-07-30 · grok-4.5

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Symmetric pairwise transfers turn clustered federated learning into an exact potential game with stable, budget-feasible coalitions and tight welfare bounds.

desk verdict Solid, carefully scoped paper: classical potential-game machinery applied cleanly to budgeted FL coalitions, with tight PoS results and unusually honest small-n empirics. read the letter →

arxiv 2607.26788 v1 pith:AHGFQIXL submitted 2026-07-29 cs.GT cs.LG

Cengis Hasan This is my paper · ORCID
classification cs.GTcs.LG MSC 91A1291A8068T4291B32
keywords clusteredfederatedlearningcoalitionformationhedonicgamesNashstabilityindividualexactpotentialbudgetfeasibilitypriceof
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Clustered federated learning only works if people want to stay in their groups and the coordinator can afford the payouts. This paper separates learning benefit, costs, and money transfers, then shows that a simple rule—each participant’s utility is the sum of pairwise scores with coalition mates—makes the whole coalition game an exact potential game. That single structure guarantees a Nash-stable partition exists, better-response dynamics finish in finite steps, and destination-consent moves reach individual stability. Welfare splits into participant potential plus coordinator-retained slack, so controlling slack at the optimum yields additive and multiplicative price-of-stability bounds that are asymptotically tight; budget feasibility alone does not. Global potential maximization is weighted correlation clustering, and approximate clustering plus stabilization still carries an end-to-end welfare guarantee. On preregistered CIFAR-10 instances the pairwise mechanism hits the certified welfare optimum every time, while equal-surplus sharing often has no stable outcome.

What carries the argument

The exact potential P_v(Π) = sum over coalitions of pairwise edge values inside them. Every unilateral move changes a player’s utility and P_v by the same amount, which delivers existence, finite convergence, and the welfare decomposition SW = 2P_v + R_v that ties stability to retained budget slack.

What would settle it

Find a federated instance where true preferences have large non-pairwise effects, or where estimated pair values that look budget-feasible on the mechanism table violate the independent benchmark surplus, and check whether better-response still reaches a near-optimal stable partition or the welfare gap exceeds the slack bound.

Watch

Extended reading notes

Core claim

For any symmetric pairwise allocation, the induced hedonic game is an exact potential game whose potential equals half total participant utility; under weak budget feasibility the best potential-maximizing partition is Nash stable and loses at most the coordinator’s retained slack at the welfare optimum, with a multiplicative price of stability of at most 1/(1−δ) when relative slack is at most δ—and that bound is asymptotically tight.

Load-bearing premise

Participant payoffs must be exactly the sum of symmetric pairwise scores the coordinator posts, and the coordinator must estimate coalition surplus well enough to keep those scores inside the budget with controlled slack.

Editorial extensions

If this is right

  • Designers can post pairwise scores, run decentralized better-response, and still certify existence of a stable partition without solving a global combinatorial search first.
  • Retained coordinator slack and negative-edge mass become operational diagnostics that bound how far a stable outcome can sit from social welfare.
  • Exact budget balance yields a welfare-optimal stable partition only when surplus itself is pairwise-representable; otherwise some slack must be kept.
  • Pair-sign estimators matter more than magnitude: pairwise validation gain is far more reliable than gradient alignment for destination acceptance.
  • Approximation algorithms for weighted maximum-agreement correlation clustering, followed by better-response cleanup, inherit end-to-end welfare guarantees.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same potential-plus-slack template could transfer to other multi-agent clustering settings where a coordinator posts pairwise rewards under a hard budget—edge computing coalitions, spectrum sharing, or collaborative sensing.
  • Because equal-surplus sharing often has empty stable sets while pairwise structure does not, practitioners who ignore the potential form may see cycling even when money is available.
  • Scaling past exact enumeration will hinge on surplus oracles that keep retained slack submodular, otherwise the polynomial verification path closes.
  • Private-type elicitation is the natural next barrier: once costs or data quality are hidden, the complete-information allocation rule needs an incentive-compatible wrapper.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies coalition formation for clustered federated learning under monetary transfers and a coordinator budget. It separates learning benefit, costs, transfers, participant utilities, and retained coordinator surplus; posts symmetric pairwise utilities U_i^v(S)=sum_j v_ij; and shows the induced hedonic game is an exact potential game, so Nash-stable partitions exist, strict better responses terminate, and destination-consent dynamics reach individual stability. Weak budget feasibility yields an additive welfare gap controlled by retained slack at the social optimum and a multiplicative price-of-stability bound under relative slack (asymptotically tight); exact balance gives welfare-optimal stability only on pairwise-representable surplus, while budget feasibility alone permits unbounded loss. Global potential maximization is identified with weighted maximum-agreement correlation clustering, and approximation plus stabilization gives an end-to-end welfare bound. A preregistered n=4 CIFAR-10 study reports that the pairwise mechanism attains the certified estimated-table welfare optimum on all primary instances, while equal-surplus sharing has an empty Nash-stable set on three seeds.

Significance. If the results hold as stated, the paper cleanly couples clustered-FL value to affordable transfers and classical hedonic stability, with a single exact potential driving existence, finite improvement, and individual stability under destination consent. The welfare decomposition SW=2P_v+R_v and the slack-based PoS bounds (with matching tightness examples and the negative-edge construction) are the right efficiency language for this design class, and the correlation-clustering reduction usefully imports approximation algorithms into stable post-processing. Strengths that raise confidence include short classical proofs with correct local-vs-global caveats (Remark 5.7), explicit impossibility under budget feasibility alone (Prop. 5.14), polynomial oracle verification when retained slack is submodular, and unusually disciplined empirics: preregistration, sealed provenance, exact estimated-table certification at n=4, bootstrap uncertainty, and honest lean-regime and benchmark-budget failures. The main limitation on impact is scope: complete-information posted pairwise utilities rather than IC elicitation, and experimental scale confined to four participants.

major comments (3)
  1. [§5.3, Remark 5.7; §7; Theorem 6.5] Remark 5.7 and Theorems 5.8/5.12 vs. §7: the additive and relative-slack PoS guarantees are for a global potential maximizer Π_P, whereas decentralized strict better response is only guaranteed to reach a local Nash-stable partition. At n=4 the dynamics hit the certified optimum, but the manuscript’s central applied claim—that affordable stable coalitions with welfare near optimum are reached by decentralized adjustment—needs an explicit statement that the PoS theorems are existence/price-of-stability results, not dynamics guarantees, except along the approximation-plus-stabilization path of Theorem 6.5 (which still requires a nontrivial agreement initialization and does not bound the number of improvement steps).
  2. [§6.1, Prop. 6.1, Cor. 6.2] Section 6.1, Proposition 6.1 and the discussion after Corollary 6.2: feasibility of V(W) and the design LP (40) have exponentially many coalition constraints; polynomial oracle time holds when r_v is submodular (e.g., submodular W and nonnegative pair rewards). The paper correctly notes that submodular W is implausible precisely in the increasing-returns regimes that motivate clustering. For the design contribution to support the FL motivation, the manuscript should either supply a concrete structured surplus/estimator class usable when W is not submodular, or clearly demote (40) to an offline complete-information benchmark and state what can be certified with pairwise or sparse coalition queries alone.
  3. [§8.2–8.3, Table 1, Figure 4] Section 8.2–8.3 and Table 1: at the primary cell (λ,γ)=(10,1) the mechanism matches the certified optimum on all five seeds, but the optimum is all-singletons on seeds 202–204 and only one productive pair on 201 and 205; at the lean co-primary (2,1) two seeds fail singleton pre-screening and the feasible seeds have empirical PoS up to about 1.29 with large relative slack. The headline “reaches the certified optimum” should be qualified in the abstract/conclusion by calibration dependence and by how often nontrivial coalitions are actually optimal, so readers do not over-read the benign cell as generic coalition-formation success.
minor comments (5)
  1. [Abstract; §1; §9] Abstract and §1 use “mechanism” language; §9 correctly narrows this to complete-information incentive allocation without IC elicitation. Move a one-sentence scope statement into the introduction so the contribution boundary is visible before the related-work comparison.
  2. [§5.1, Eqs. (19)–(22)] Equation (19) assigns the full pair value v_ij to both endpoints (hence the factor 2 in budget constraints). A brief remark contrasting this with splitting a single pair surplus would prevent misreading relative to standard transferable-utility edge weights.
  3. [§8.2, Figure 3] Figure 3 and convergence statistics (mean 1.53 moves, at most four) are useful; state explicitly in the caption or text that these counts are only for n=4 exhaustive instances and do not suggest a general rate.
  4. [Throughout; Declarations] Typographical inconsistencies: “CIF AR-10” vs “CIFAR-10”, and “F unding” in Declarations. Normalize throughout.
  5. [§6.2] Section 6.2 still reads partly as a prospectus (“The journal version will study…”). Since this appears to be the journal manuscript, rephrase as open problems or future work.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: potential, slack, and welfare bounds are derived from posted pairwise utilities, not defined into the target.

full rationale

The central chain is classical and self-contained. Symmetric pairwise utilities (19) induce potential P_v by direct unilateral-deviation algebra (Thm 5.3); existence/FIP follow from finite exact-potential maximization (Cor 5.4–5.5). Welfare identity SW = 2P_v + R_v (34) is accounting from the definitions of U^v, r_v, and W, then used to bound the best potential maximizer versus SW★ (Thm 5.8, Cor 5.12) with an explicit tightness construction (Prop 5.13)—not a fit renamed as prediction. Correlation-clustering equivalence (Prop 6.3) is the constant-shift identity A_v = C_v + P_v. Empirics certify stability/welfare on estimated value tables at n=4 and separately bootstrap uncertainty; ‘certified’ is scoped as table-exact. The conference precursor is disclosed as corrected, not invoked as a uniqueness lemma that forces the present results. No step reduces the claimed prediction to its own inputs by construction.

Assumptions & free parameters 4 free parameters · 8 assumptions · 3 invented entities

Central stability theorems rest on standard potential-game and hedonic machinery plus the paper’s modeling choices that utilities equal symmetric pairwise scores and the coordinator posts a weakly budget-feasible v from known/estimated W. Efficiency claims add nonnegativity of retained slack and optional relative-slack or exact pairwise representability of W. Empirics add hand-chosen economic calibrations (λ,γ), benefit map, and n=4 Dirichlet heterogeneous CIFAR-10 instances. No new physical entities; the ‘invented’ objects are modeling constructs (pairwise v, slack r_v, agreement A_v).

free parameters (4)
  • benefit scale λ and cost scale γ = primary (10,1); lean (2,1); grid λ∈{2,5,10,20,50}, γ∈{0.5,1,2}
    Primary calibration (λ,γ)=(10,1) and lean (2,1) convert accuracy into surplus units; sensitivity grid chosen by authors. Welfare levels and feasibility screens depend on these scales.
  • Q_ref in benefit map B_λ = 0.10
    Reference accuracy 0.10 in (50) shifts positive-part validation benefit; hand-set, not estimated from a stated principle.
  • pair bounds v_ij, v̄_ij and design weights ω_ij = β=50 arm; PVG vs GA estimators; bounds from validation/policy
    Feasible polytope V(W) and allocation LP (40) depend on chosen box bounds and objective weights; PVG/GA estimators and β=50 transfer-scale arm set effective magnitudes.
  • Dirichlet concentration and size/comms ranges = α=0.3; five seeds 201–205
    Heterogeneity protocol (concentration 0.3, m_i∈[800,3200], p_i∈[0.60,0.95], R=20, lr=0.05) defines the empirical W tables on which stability/welfare are certified.
assumptions (8)
  • standard math Finite exact potential games have pure Nash equilibria and the finite improvement property (Monderer–Shapley).
    Used for Cor 5.4–5.5 after Thm 5.3 establishes the potential.
  • domain assumption Hedonic preferences: U_i depends only on own coalition membership; no cross-coalition externalities.
    §4.2; rules out shared capacity and competition that would require partition-function games.
  • ad hoc to paper Utilities are exactly symmetric pairwise: U_i^v(S)=sum_{j≠i in S} v_ij with v_ij=v_ji.
    §5.1 eq (19); this is the design class that yields the potential and acceptance rule, not derived from FL first principles.
  • domain assumption Weak budget feasibility: sum_i U_i(S) ≤ W(S) for every nonempty S (nonnegative coordinator slack).
    Def 4.2; load-bearing for efficiency theorems and retained-surplus interpretation.
  • domain assumption Pre-screened population W({i})≥0 and outside option normalized U_i({i})=0.
    Assumption 4.1 and §4.1; IR follows from Nash stability via singleton deviation.
  • domain assumption Coordinator knows or estimates B(S), C_0(S), d_i(S); complete-information posted allocation, not strategy-proof elicitation.
    §9 explicitly limits the mechanism-design claim.
  • standard math Submodular set-function minimization in strongly polynomial oracle time when r_v is submodular.
    Prop 6.1 citing Schrijver; only for the poly-time verification regime.
  • domain assumption Safe aggregation and coalition-specific training induce well-defined expected benefits B(S) without assuming merge-improves-loss.
    §3.2–3.3 eqs (8)–(9); statistical model behind empirical W.
invented entities (3)
  • Symmetric pairwise surplus allocation v and potential P_v independent evidence
    purpose: Convert coalition surplus into hedonic utilities that guarantee an exact potential and stable partitions.
    Standard mathematically once postulated; novelty is coupling to FL W and budget slack, not a new physical object.
  • Coordinator retained slack r_v(S) / R_v(Π) independent evidence
    purpose: Account welfare SW=2P_v+R_v and bound price of stability.
    Definitional accounting residual from W minus paid pairwise utility; falsifiable as measured leftover surplus in deployments.
  • Pairwise validation gain (PVG) pair-score estimator independent evidence
    purpose: Estimate signs/magnitudes of v_ij from coalition validation runs versus gradient alignment.
    Operational estimator introduced for experiments; compared to disjoint high-replication benchmark on CIFAR-10.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stable and Budget-Feasible Coalition Formation for Clustered Federated Learning: A Hedonic Potential-Game Approach." pith.science (2026). https://pith.science/paper/AHGFQIXL

@misc{pith2026260726788,
  author       = {Pith},
  title        = {Pith review of: Stable and Budget-Feasible Coalition Formation for Clustered Federated Learning: A Hedonic Potential-Game Approach},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AHGFQIXL}},
  note         = {Machine review of arXiv:2607.26788}
}
read the original abstract

Clustered federated learning benefits from organizing heterogeneous participants into coalitions that train coalition-specific models, but such clustering is sustainable only if participants prefer their assigned coalition and the required transfers are affordable. We develop a transferable-surplus model separating learning benefit, system cost, participant cost, and monetary transfers; an allocation rule converts coalition surplus into hedonic preferences, and weak budget feasibility guarantees nonnegative retained coordinator surplus. For symmetric pairwise allocations the induced game is an exact potential game: a Nash-stable partition exists, every strict better-response process converges, and with destination consent accepted better responses reach an individually stable partition. We characterize feasibility of bounded pair incentives and verify the exponentially many budget constraints in polynomial oracle time when retained slack is submodular. Decomposing welfare into participant potential and retained slack yields additive and multiplicative price-of-stability guarantees, the latter asymptotically tight; exact balance gives welfare-optimal stability only on the pairwise-representable class, and budget feasibility alone permits unbounded welfare loss. Global potential maximization equals weighted maximum-agreement correlation clustering, and approximation followed by stabilization satisfies an end-to-end welfare bound governed by retained slack and negative-edge mass, attained by an explicit construction. In a preregistered five-seed CIFAR-10 study the mechanism reaches the certified estimated-table welfare optimum on every primary instance, equal-surplus sharing has no Nash-stable outcome on three, and pairwise validation gain gives far more reliable pair signs than gradient alignment.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

35 extracted references · 6 canonical work pages

  1. [1]

    In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, pp

    McMahan, H.B., Moore, E., Ramage, D., Hampson, S., Arcas, B.A.: Communication-efficient learning of deep networks from decentralized data. In: Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, pp. 1273–1282 (2017)

    2017

  2. [2]

    IEEE Signal Processing Magazine37(3), 50–60 (2020) https://doi.org/10.1109/MSP.2020.2975749

    Li, T., Sahu, A.K., Talwalkar, A., Smith, V.: Federated learning: Challenges, methods, and future directions. IEEE Signal Processing Magazine37(3), 50–60 (2020) https://doi.org/10.1109/MSP.2020.2975749

    arXiv 2020

  3. [3]

    Foundations and Trends in Machine Learning14(1–2), 1–210 (2021) https://doi.org/10.1561/2200000083

    Kairouz, P., McMahan, H.B.,et al.: Advances and open problems in federated learning. Foundations and Trends in Machine Learning14(1–2), 1–210 (2021) https://doi.org/10.1561/2200000083

    doi:10.1561/2200000083 2021

  4. [4]

    Games and Economic Behavior38(2), 201–230 (2002) https://doi.org/10.1006/ game.2001.0877

    Bogomolnaia, A., Jackson, M.O.: The stability of hedonic coalition structures. Games and Economic Behavior38(2), 201–230 (2002) https://doi.org/10.1006/ game.2001.0877

    arXiv 2002

  5. [5]

    International Game Theory Review8(4), 613–641 (2006) https://doi.org/10.1142/S0219198906001144

    Hajdukov´ a, J.: Coalition formation games: A survey. International Game Theory Review8(4), 613–641 (2006) https://doi.org/10.1142/S0219198906001144

    work page doi:10.1142/s0219198906001144 2006

  6. [6]

    In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (2012)

    Aziz, H., Brandl, F.: Existence of stability in hedonic coalition formation games. In: Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems (2012)

    2012

  7. [7]

    arXiv:2101.09673 (2021)

    Hasan, C.: Incentive Mechanism Design for Federated Learning: Hedonic Game Approach. arXiv:2101.09673 (2021)

    arXiv 2021

  8. [8]

    IEEE Transactions on Wireless Communications20(8), 4874–4887 (2021) https://doi.org/10.1109/TWC.2021.3062708

    Le, T.H.T., Tran, N.H., Tun, Y.K., Nguyen, M.N.H., Pandey, S.R., Han, Z., Hong, C.S.: An incentive mechanism for federated learning in wireless cellular networks: An auction approach. IEEE Transactions on Wireless Communications20(8), 4874–4887 (2021) https://doi.org/10.1109/TWC.2021.3062708

    arXiv 2021

Show all 35 references
  1. [9]

    In: 2020 18th International Sympo- sium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, pp

    Ding, N., Fang, Z., Huang, J.: Incentive mechanism design for federated learning with multi-dimensional private information. In: 2020 18th International Sympo- sium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks, pp. 1–8 (2020)

    2020

  2. [10]

    IEEE Networking Letters2(1), 23–27 (2020) https://doi.org/ 27 10.1109/LNET.2019.2947144

    Sarikaya, Y., Ercetin, O.: Motivating workers in federated learning: A stackelberg game perspective. IEEE Networking Letters2(1), 23–27 (2020) https://doi.org/ 27 10.1109/LNET.2019.2947144

    2020

  3. [11]

    In: IEEE INFOCOM 2020 - IEEE Confer- ence on Computer Communications, pp

    Zhan, Y., Zhang, J.: An incentive mechanism design for efficient edge learning by deep reinforcement learning approach. In: IEEE INFOCOM 2020 - IEEE Confer- ence on Computer Communications, pp. 2489–2498 (2020). https://doi.org/10. 1109/INFOCOM41043.2020.9155268

    2020

  4. [12]

    IEEE Access8, 187317–187325 (2020) https:// doi.org/10.1109/ACCESS.2020.3030888

    Kim, S.: Incentive design and differential privacy based federated learning: A mechanism design perspective. IEEE Access8, 187317–187325 (2020) https:// doi.org/10.1109/ACCESS.2020.3030888

    2020

  5. [13]

    IEEE Transactions on Cognitive Communications and Networking8(3), 1566–1593 (2022) https://doi.org/10.1109/TCCN.2022.3177522

    Tu, X., Zhu, K., Luong, N.C., Niyato, D., Zhang, Y., Li, J.: Incentive mechanisms for federated learning: From economic and game theoretic perspective. IEEE Transactions on Cognitive Communications and Networking8(3), 1566–1593 (2022) https://doi.org/10.1109/TCCN.2022.3177522

    2022

  6. [14]

    Knowledge-Based Systems315, 113212 (2025) https://doi.org/10.1016/j.knosys

    Wu, X., Lin, Y., Zhong, H., Tao, J., Gu, Y., Shen, S., Yu, S.: A diversity-aware incentive mechanism for cross-silo federated learning with budget constraint. Knowledge-Based Systems315, 113212 (2025) https://doi.org/10.1016/j.knosys. 2025.113212

    2025

  7. [15]

    Proceedings of the AAAI Conference on Artificial Intelligence35(6), 5303–5311 (2021) https://doi.org/10.1609/aaai.v35i6.16669

    Donahue, K., Kleinberg, J.: Model-sharing games: Analyzing federated learning under voluntary participation. Proceedings of the AAAI Conference on Artificial Intelligence35(6), 5303–5311 (2021) https://doi.org/10.1609/aaai.v35i6.16669

    2021 doi

  8. [16]

    In: Proceedings of the 38th International Conference on Machine Learning, pp

    Blum, A., Haghtalab, N., Phillips, R.L., Shao, H.: One for one, or all for all: Equilibria and optimality of collaboration in federated learning. In: Proceedings of the 38th International Conference on Machine Learning, pp. 1005–1014 (2021)

    2021

  9. [17]

    In: Advances in Neural Information Processing Systems, vol

    Chaudhury, B.R., Li, L., Kang, M., Li, B., Mehta, R.: Fairness in federated learn- ing via core-stability. In: Advances in Neural Information Processing Systems, vol. 35 (2022). https://proceedings.neurips.cc/paper files/paper/2022/hash/ 25e92e33ac8c35fd49f394c37f21b6da-Abstra...

    2022

  10. [18]

    In: Advances in Neural Information Processing Systems, vol

    Chen, M., Wu, X., Tang, X., He, T., Ong, Y.-S., Liu, Q., Lao, Q., Yu, H.: Free-rider and conflict aware collaboration formation for cross-silo fed- erated learning. In: Advances in Neural Information Processing Systems, vol. 37 (2024). https://proceedings.neurips.cc/paper file...

    2024

  11. [19]

    In: 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pp

    Singer, Y.: Budget feasible mechanisms. In: 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, pp. 765–774 (2010)

    2010

  12. [20]

    In: Advances in Neural Information Process- ing Systems, vol

    Ghosh, A., Chung, J., Yin, D., Ramchandran, K.: An efficient framework for clustered federated learning. In: Advances in Neural Information Process- ing Systems, vol. 33 (2020). https://proceedings.neurips.cc/paper/2020/hash/ e32cc80bf07915058ce90722ee17bb71-Abstract.html 28

    2020

  13. [21]

    IEEE Transactions on Neural Networks and Learning Systems32(8), 3710–3722 (2021) https://doi.org/10.1109/TNNLS.2020.3015958

    Sattler, F., M¨ uller, K.-R., Samek, W.: Clustered federated learning: Model- agnostic distributed multitask optimization under privacy constraints. IEEE Transactions on Neural Networks and Learning Systems32(8), 3710–3722 (2021) https://doi.org/10.1109/TNNLS.2020.3015958

    2021

  14. [22]

    In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D

    Aziz, H., Savani, R.: Hedonic games. In: Brandt, F., Conitzer, V., Endriss, U., Lang, J., Procaccia, A.D. (eds.) Handbook of Computational Social Choice. Cambridge University Press, ??? (2016). Chap. 15

    2016

  15. [23]

    ACM Transactions on Economics and Computation11(1–2), 4–1465 (2023) https://doi.org/10.1145/3588753

    Brandt, F., Bullinger, M., Wilczynski, A.: Reaching individually stable coalition structures. ACM Transactions on Economics and Computation11(1–2), 4–1465 (2023) https://doi.org/10.1145/3588753

    2023 doi

  16. [24]

    Journal of Artificial Intelligence Research62, 315–371 (2018) https://doi.org/10.1613/ jair.1.11211

    Bil` o, V., Fanelli, A., Flammini, M., Monaco, G., Moscardelli, L.: Nash stable out- comes in fractional hedonic games: Existence, efficiency and computation. Journal of Artificial Intelligence Research62, 315–371 (2018) https://doi.org/10.1613/ jair.1.11211

    2018

  17. [25]

    In: Advances in Neural Information Processing Systems, vol

    Donahue, K., Kleinberg, J.M.: Optimality and stability in federated learning: A game-theoretic approach. In: Advances in Neural Information Processing Systems, vol. 34 (2021). https : / / proceedings . neurips . cc / paper / 2021 / hash / 09a5e2a11bea20817477e0b1dfe2cc21-Abstract.html

    2021

  18. [26]

    IEEE Transactions on Parallel and Distributed Systems 33(11), 2675–2686 (2022)

    Ng, J.S., Lim, W.Y.B., Xiong, Z., Cao, X., Jin, J., Niyato, D., Leung, C., Miao, C.: Reputation-aware hedonic coalition formation for efficient serverless hierar- chical federated learning. IEEE Transactions on Parallel and Distributed Systems 33(11), 2675–2686 (2022)

    2022

  19. [27]

    Proceedings of the AAAI Conference on Artificial Intelligence39(15), 15904–15912 (2025) https://doi.org/10.1609/aaai.v39i15

    Chen, X., Zhou, X., Zhang, S., Sun, M.: DualGFL: Federated learning with a dual- level coalition-auction game. Proceedings of the AAAI Conference on Artificial Intelligence39(15), 15904–15912 (2025) https://doi.org/10.1609/aaai.v39i15. 33746

    2025 doi

  20. [28]

    IEEE Internet of Things Journal12(9), 11258–11272 (2025) https://doi.org/10

    Liu, J., Li, X., Xu, Y., Lyu, C., Wang, Y., Liu, X.: Hedonic coalition formation game and contract-based federated learning in AA V-assisted internet of things. IEEE Internet of Things Journal12(9), 11258–11272 (2025) https://doi.org/10. 1109/JIOT.2025.3543917

    2025

  21. [29]

    Machine Learning56(1– 3), 89–113 (2004) https://doi.org/10.1023/B:MACH.0000033116.57574.95

    Bansal, N., Blum, A., Chawla, S.: Correlation clustering. Machine Learning56(1– 3), 89–113 (2004) https://doi.org/10.1023/B:MACH.0000033116.57574.95

    2004

  22. [30]

    In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp

    Swamy, C.: Correlation clustering: Maximizing agreements via semidefinite pro- gramming. In: Proceedings of the Fifteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 526–527 (2004)

    2004

  23. [31]

    Econo- metrica48(4), 987–1003 (1980) https://doi.org/10.2307/1912943 29

    Dr` eze, J.H., Greenberg, J.: Hedonic coalitions: Optimality and stability. Econo- metrica48(4), 987–1003 (1980) https://doi.org/10.2307/1912943 29

    1980 doi

  24. [32]

    Games and Economic Behavior 14(1), 124–143 (1996) https://doi.org/10.1006/game.1996.0044

    Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996) https://doi.org/10.1006/game.1996.0044

    1996

  25. [33]

    SIAM Journal on Computing38(4), 1602–1623 (2008) https://doi.org/10.1137/ 070680096

    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, ´E., Wexler, T., Rough- garden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing38(4), 1602–1623 (2008) https://doi.org/10.1137/ 070680096

    2008

  26. [34]

    Journal of Combinatorial Theory, Series B80(2), 346– 355 (2000) https://doi.org/10.1006/jctb.2000.1989

    Schrijver, A.: A combinatorial algorithm minimizing submodular functions in strongly polynomial time. Journal of Combinatorial Theory, Series B80(2), 346– 355 (2000) https://doi.org/10.1006/jctb.2000.1989

    2000

  27. [35]

    Artificial Intelligence195, 316–334 (2013) https://doi

    Aziz, H., Brandt, F., Seedig, H.G.: Computing desirable partitions in additively separable hedonic games. Artificial Intelligence195, 316–334 (2013) https://doi. org/10.1016/j.artint.2012.09.006 30

    2013 doi

Pith tools

Reviewed July 30, 2026 · model on record in the stance chip above.