Pith. sign in

REVIEW 3 major objections 4 minor 45 references

This paper claims that a tree of agents in a fully decentralized system can simultaneously minimize inefficiency, average discomfort, and the spread of discomfort—fairness—at negligible extra communication cost, by rewriting unfairness in t

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review

2026-08-01 18:22 UTC pith:2MKEJSW6

load-bearing objection Useful engineering extension of I-EPOS with a variance-based fairness term, held back by an unvalidated proxy and weak empirical baselines; worth refereeing, not yet a proven trilemma. the 3 major comments →

arxiv 2607.17311 v1 pith:2MKEJSW6 submitted 2026-07-19 cs.MA cs.AIcs.CYcs.DCcs.SYeess.SY

The Optimization Trilemma: Efficiency, Comfort and Fairness in Decentralized Multi-agent Coordination

Jovan Nikolic , Maciej Krzysztof Zuziak , Evangelos Pournaras This is my paper
classification cs.MA cs.AIcs.CYcs.DCcs.SYeess.SY
keywords decentralized optimizationmulti-agent coordinationfairnessdiscomfort costmulti-objective optimizationcombinatorial optimizationcollective learningPareto frontier
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper sets out to show that fairness can be added as a third objective to fully decentralized multi-agent coordination without a central planner and with negligible extra messaging. Its key move is to rewrite the global unfairness term—the standard deviation of individual discomfort costs—as a function of two aggregates agents already exchange: the sum of plan costs and the sum of squared plan costs. Embedding that term in the scalarized objective of a tree-based collective-learning protocol, the authors report that efficiency, comfort, and fairness all converge within a few dozen iterations on synthetic, smart-grid, and bike-sharing datasets. If the claim holds, operators of self-organizing systems gain a cheap lever to keep a few participants from absorbing most of the burden, which should reduce dropout and polarization.

Core claim

The central discovery is Lemma 1: the unfairness cost U, defined as the standard deviation of the discomfort costs of all agents' selected plans, can be rewritten as sqrt((1/N)K_a - ((1/N)k_a)^2), where k_a is the sum of plan costs and K_a is the sum of squared plan costs over the whole agent set. Because agents in a tree already maintain k_a for comfort optimization, adding K_a is a small local computation that can travel with existing aggregate messages. The paper integrates this fairness term into a scalarized objective alongside efficiency and comfort and reports that, on one synthetic and two real-world datasets, all three objectives converge within fewer than 35 iterations; the Pareto-

What carries the argument

The load-bearing object is the variance identity of Lemma 1. It reduces the global standard deviation of discomfort costs to three numbers—the agent count N, the aggregated plan cost k_a, and the aggregated squared plan cost K_a—so that each agent can estimate system-wide unfairness from information that is already flowing up and down the coordination tree. The accompanying Corollary 1 gives the identity a statistical reading: the term is the biased sample variance and converges almost surely to the true variance under IID sampling. The same pair of aggregates also expresses Jain's fairness index, showing the mechanism generalizes beyond standard deviation.

Load-bearing premise

The load-bearing premise is that minimizing a previous-iteration, locally computed stand-in for the global standard deviation of discomfort costs reliably pushes the true system-wide unfairness down; if that proxy and the true value diverge, the fairness guarantee collapses.

What would settle it

Compute the exact global standard deviation of discomfort costs at every iteration from a central observer while the decentralized algorithm runs. The central claim fails if any step lowers the proxy built from the root's previous-iteration aggregates while the true system-wide standard deviation rises, or if a fairness-weighted run converges to a higher exact standard deviation than the same run with the fairness weight set to zero.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

Share X Bluesky LinkedIn Reddit HN

If this is right

  • Decentralized coordination algorithms that already exchange aggregated plan costs can add a fairness objective by tracking one extra aggregate—the sum of squared plan costs—with no new message types.
  • Fairness becomes a third tunable knob: changing the weight on the fairness term yields a visible Pareto trade-off against efficiency and comfort, so operators can choose how much imbalance they accept.
  • Because convergence happens in tens of iterations even with thousands of agents, fairness-aware coordination is plausible for real-time smart-grid scheduling and bike-sharing operations.
  • Spreading discomfort more evenly should reduce the dropout and polarization that occur when a few agents are repeatedly assigned costly plans, protecting the stability of the collaboration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The paper validates the proxy only empirically, on three datasets, with no bound on the gap between the locally computed proxy and the true global standard deviation; a formal approximation bound would turn the empirical finding into a guarantee.
  • Corollary 1's convergence relies on an IID assumption that the paper itself acknowledges is violated when agents couple their decisions; treating the formula as a tractable proxy is therefore an assumption, not a proven convergence result.
  • The same two-moment recipe likely transfers to other distributed settings where agents exchange aggregate statistics—federated learning, distributed resource markets—wherever a fairness metric can be written through sums and sums of squares.
  • A natural stress test is to break the balanced-tree assumption: in mesh or dynamically reconfiguring topologies, the root's previous-iteration aggregates may be a poorer stand-in, so the approach's reliability on those topologies remains open.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper proposes a fairness objective for decentralized multi-agent combinatorial optimization, defined as the standard deviation of agents' discomfort costs. It shows (Lemma 1) that this unfairness measure can be rewritten using only the aggregated plan cost and aggregated squared plan cost, quantities that are locally available in a tree-structured aggregation protocol. The fairness objective is then folded into a scalarized multi-objective optimization (Eq. 8) and combined with the I-EPOS collective learning algorithm (Section V), yielding a claimed simultaneous optimization of system-wide efficiency, individual comfort, and fairness with negligible extra communication. The experimental section evaluates the approach on one synthetic and two real-world datasets, reporting convergence, Pareto frontiers, and visualizations of discomfort distributions.

Significance. If the central claim holds, the paper offers a practical, low-overhead way to incorporate fairness into decentralized coordination at scale, which is a relevant and timely problem. The algebraic identity in Lemma 1 is clean and correct under the stated condition T_a=A, and the open-source implementation and experiments on up to 5600 agents are strengths. The Pareto-frontier analysis and the use of real-world datasets are also valuable. However, the load-bearing step—using a stale, approximate global variance in the local optimization (Eq. 9)—is not rigorously justified, and the empirical support lacks error bars and baselines. The result is consequently not yet established to the standard required for a strong journal claim.

major comments (3)
  1. [Section V-A, Eq. (9)] The local optimization step evaluates the fairness term using the root's previous-iteration aggregates k_r^(t-1) and K_r^(t-1) plus local deltas, rather than the true global unfairness of the state being constructed. During the bottom-up phase, non-root agents do not have exact T_a=A data, so the quantity under the square root is a proxy. The paper's own text in Section IV-A explicitly concedes that Corollary 1's i.i.d. assumption is not satisfied and calls the formula 'a tractable proxy.' No error bound or monotonicity argument is given, and no experiment measures how often locally accepted changes actually increase the true global U after all agent decisions are folded in. Since the paper's central novelty is decentralized fairness optimization, this proxy validity is the hinge of the trilemma claim. The authors should either provide a theoretical bound on the approximation error or em
  2. [Section VI-C, Figures 2-5] The experiments are said to repeat each setting 1000 times with different initial tree positions (Appendix B-E), yet Figures 2-5 show no error bars, confidence intervals, or statistical dispersion measures. The Pareto-frontier plots (Figures 4 and 5) appear to show a single run per parameter triplet, making it impossible to assess the variability of the claimed trade-offs. Moreover, there is no comparison against a centralized optimum, plain I-EPOS without the fairness term, or any existing fairness-aware multi-agent method. Without such baselines, the empirical support for 'the model can achieve fairer optimization outcomes' is weak. The authors should show distributions over repetitions and compare with at least a centralized solution and the α=0 baseline.
  3. [Section IV-A, Corollary 1] Corollary 1's asymptotic convergence relies on plan costs being i.i.d. samples, an assumption that the authors themselves state is 'not strictly satisfied in the decentralized setting where agents make coupled decisions.' The asymptotic result therefore does not justify the use of the formula as a finite-N proxy in the actual algorithm. What is needed is either a finite-sample bound, a worst-case characterization of the proxy's error, or a direct empirical demonstration that the proxy tracks the true global U across iterations. As written, the proof provides mathematical appearance but not support for the core algorithmic claim.
minor comments (4)
  1. [Section VI-B] The three objectives are scalarized with weights γ, α, β summing to 1, but the costs have very different orders of magnitude (as noted in Section VI-D). Without normalizing the objectives, the fairness term may be effectively ignored for most of the weight grid, which weakens the claim that the Pareto frontier reflects genuine trade-offs. The authors should discuss or implement normalization.
  2. [Figure 3] Figure 3 says 'only trees with 100 agents are visualized,' but the datasets contain 1000 or 5600 agents. Please clarify whether this is a subsampled tree or a separate configuration, and state how the 100-agent tree relates to the main experiments.
  3. [Appendix B-E] The threats-to-validity section only varies 'the initial relative positions of the agents in the hierarchy.' Other potentially influential factors—such as branching factor, number of plans, and initialization of the algorithm—are not controlled, though earlier work is cited. A sentence explaining why these factors are expected not to alter the conclusions would be helpful.
  4. [Notation] Equation (8) uses α, β, γ without subscripts, while Equation (9) uses α_a, β_a, γ_a. The relationship between global and per-agent weights should be stated explicitly. Also, in Table I, 'Efficnecy' is misspelled.

Circularity Check

0 steps flagged

No significant circularity: Lemma 1 is an in-paper algebraic identity and the fairness proxy in Eq. 9 is an acknowledged approximation, not a fitted prediction.

full rationale

The derivation chain runs as follows: U (Eq. 6) is defined as the standard deviation of per-agent discomfort costs; Lemma 1 rewrites it as sqrt((1/N)K_a - ((1/N)k_a)^2) by expanding the square and substituting k_a and K_a. The proof is self-contained algebra from the definitions, so no input is smuggled in. Corollary 1 is a standard SLLN statement, and the paper explicitly concedes in Section IV-A that the i.i.d. assumption 'may not be strictly satisfied' and that the formula is only 'a tractable proxy' — a validity caveat, not a circular reduction. Eq. 9 uses the root's previous-iteration aggregate sums k_r^(t-1), K_r^(t-1) plus local deltas; this is an approximation whose error is not bounded, but U-hat is not defined in terms of the final U and no parameter is fitted to the reported outcomes. The empirical sections show that increasing the weight α reduces U; because αU is part of the scalarized objective, this is an optimization check rather than an independent prediction, and the paper does not frame it as a prediction. Self-citations to I-EPOS [5], [10], AETOS [4], and [41] supply the tree-aggregation substrate and prior robustness evidence; they do not carry the fairness identity or the trilemma conclusion. No load-bearing step reduces to its own input, so the circularity score is 0.

Axiom & Free-Parameter Ledger

1 free parameters · 6 axioms · 0 invented entities

The derivation itself relies only on elementary statistics and the I-EPOS tree protocol. The main modeling choices are the scalarization weights, the variance as the fairness metric, and the i.i.d. assumption for the asymptotic claims. No new physical or conceptual entity is postulated.

free parameters (1)
  • objective weights γ, α, β = grid search 0-1 with step 0.01; γ+α+β=1
    Scalarization weights are chosen by the experimenter, not fitted to data. The Pareto-frontier results and the reported trade-offs depend directly on these weights.
axioms (6)
  • standard math Variance identity: (1/N)Σ(x_i − x̄)^2 = (1/N)Σx_i^2 − ((1/N)Σx_i)^2
    Used in Lemma 1 to rewrite unfairness in terms of aggregated plan cost and aggregated squared plan cost.
  • standard math Strong law of large numbers and continuous mapping theorem
    Used in Corollary 1 and Lemma 2 to justify convergence of the sample variance and Jain's index to their population values as N→∞.
  • domain assumption Agents are organized in a balanced tree and root aggregates are globally disseminated each iteration
    I-EPOS assumes a tree topology with bottom-up aggregation and top-down dissemination (Section V). This gives each agent access to root-level k_r and K_r from the previous iteration.
  • ad hoc to paper Plan costs are i.i.d. samples for the asymptotic convergence claims
    Corollary 1 and Lemma 2 assume i.i.d. samples; the authors explicitly acknowledge this is not strictly satisfied because agents' decisions are coupled (Section IV-A).
  • domain assumption The scalarized objective with fixed weights is an adequate decision rule for all agents
    Equation (8)/(9) assumes every agent minimizes a global linear combination of efficiency, discomfort, and unfairness; Section IV-B states agents may need extrinsic incentives to be altruistic.
  • domain assumption Discomfort costs are scalar and comparable across agents
    Fairness is defined as the standard deviation of scalar discomfort costs l(s_a), which requires a common scale across agents (Section III-A).

reviewed 2026-08-01 · how reviews work

0 comments
Cite this review

Pith. "Pith review of The Optimization Trilemma: Efficiency, Comfort and Fairness in Decentralized Multi-agent Coordination." pith.science (2026). https://pith.science/paper/2MKEJSW6

@misc{pith2026260717311,
  author       = {Pith},
  title        = {Pith review of: The Optimization Trilemma: Efficiency, Comfort and Fairness in Decentralized Multi-agent Coordination},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2MKEJSW6}},
  note         = {Machine review of arXiv:2607.17311}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

The problem of fair multi-agent coordination in decentralized settings is one of the most pressing challenges for building efficient collaborative systems. Resource allocation is based on optimized collective arrangements accounting for agents' needs. Such coordination should not only be computationally efficient but also account for fairness, i.e., equitable redistribution of costs incurred by all agents. Recent literature has proposed several algorithms that efficiently determine optimal plan combinations balancing system-wide efficiency and individual discomfort of agents in a centralized setting. However, these works do not address equitable resource optimization in fully decentralized scenarios, specifically, the optimized redistribution of discomfort among coordinating agents so that none experiences a discomfort level that could lead to loss of incentive or polarization that can disrupt planned operations. In this work, we study the problem of optimizing three objectives: (i) system-wide efficiency, (ii) individuals' comfort and (iii) fairness (i.e., balancing of incurred discomfort costs) in decentralized multi-agent coordination. We design a novel model to optimize those three orthogonal objectives, without any substantial increase in communication and computational overhead. Through experiments on two real-world datasets, we validate the model and demonstrate that it can achieve fairer optimization outcomes, while satisfying agents' preferences and system goals.

Figures

Figures reproduced from arXiv: 2607.17311 by Evangelos Pournaras, Jovan Nikolic, Maciej Krzysztof Zuziak.

Figure 1
Figure 1. Figure 1: Sequence diagram of the augmented I-EPOS protocol on a balanced tree topology during an iteration. In the bottom-up () [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Convergence of three objectives over I-EPOS runtime for [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Discomfort (local) cost within the tree topology at the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The feasible regions visualized for the (a) synthetic, (b) bicycle and (c) energy datasets. Inefficiency (global), discomfort [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Feasible regions of the three datasets with respect to [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 2 linked inside Pith

  1. [1]

    Will the real smart city please stand up? intelligent, progressive or entrepreneurial?

    R. G. Hollands, “Will the real smart city please stand up? intelligent, progressive or entrepreneurial?”City, vol. 12, no. 3, pp. 303–320, 2008

    2008

  2. [2]

    Deakin,Smart cities: governing, modelling and analysing the tran- sition

    M. Deakin,Smart cities: governing, modelling and analysing the tran- sition. Routledge, 2013

    2013

  3. [3]

    COHDA: A combi- natorial optimization heuristic for distributed agents,

    C. Hinrichs, S. Lehnhoff, and M. Sonnenschein, “COHDA: A combi- natorial optimization heuristic for distributed agents,” inInternational Conference on Agents and Artificial Intelligence. Springer, 2013, pp. 23–39

    2013

  4. [4]

    Multi-level reconfigurable self-organization in overlay services,

    E. Pournaras, “Multi-level reconfigurable self-organization in overlay services,” Master’s thesis, TU Delft, 2013

    2013

  5. [5]

    Decentralized collective learning for self-managed sharing economies,

    E. Pournaras, P. Pilgerstorfer, and T. Asikis, “Decentralized collective learning for self-managed sharing economies,”ACM Transactions of Autonomous and Adaptive Systems, 2018

    2018

  6. [6]

    Data collaboratives with the use of decentralised learning,

    M. K. Zuziak, O. Hinrichs, A. Abdrassulova, and S. Rinzivillo, “Data collaboratives with the use of decentralised learning,” in2023 ACM Conference on Fairness, Accountability, and Transparency. ACM, 2023, pp. 615–625

    2023

  7. [7]

    Cooperative flexibility exchange: fair and comfort-aware decentralized resource allocation,

    R. Khalid and E. Pournaras, “Cooperative flexibility exchange: fair and comfort-aware decentralized resource allocation,”EPJ Data Science, vol. 15, no. 1, p. 43, 2026

    2026

  8. [8]

    Inequity aversion and individual behavior in public good games: An experimental inves- tigation,

    A. Dannenberg, T. Riechmann, B. Sturm, and C. V ogt, “Inequity aversion and individual behavior in public good games: An experimental inves- tigation,”ZEW - Centre for European Economic Research Discussion Papers, no. 991555, 2007

    2007

  9. [9]

    Fairness and retaliation: The economics of reciprocity,

    E. Fehr and S. G ¨achter, “Fairness and retaliation: The economics of reciprocity,”The Journal of Economic Perspectives, vol. 14, no. 3, pp. 159–181, 2000

    2000

  10. [10]

    Collective learning: A 10-year odyssey to human- centered distributed intelligence,

    E. Pournaras, “Collective learning: A 10-year odyssey to human- centered distributed intelligence,” in2020 IEEE International Confer- ence on Autonomic Computing and Self-Organizing Systems (ACSOS). IEEE, 2020, pp. 205–214

    2020

  11. [11]

    Fairness in multi-agent sequential decision- making,

    C. Zhang and J. A. Shah, “Fairness in multi-agent sequential decision- making,” inAdvances in Neural Information Processing Systems, vol. 27. Curran Associates, Inc., 2014

    2014

  12. [12]

    Learning fairness in multi-agent systems,

    J. Jiang and Z. Lu, “Learning fairness in multi-agent systems,”Advances in Neural Information Processing Systems, vol. 32, 2019

    2019

  13. [13]

    DECAF: Learning to be fair in multi-agent resource allocation,

    A. Kumar and W. Yeoh, “DECAF: Learning to be fair in multi-agent resource allocation,”ArXiv, no. arXiv:2502.04281, 2025

    Pith/arXiv arXiv 2025

  14. [14]

    Multi-objective multi-agent bandits: From learning efficiency to fairness optimization,

    J. Wang and M. Xu, “Multi-objective multi-agent bandits: From learning efficiency to fairness optimization,”arXiv preprint arXiv:2605.06864, 2026

    Pith/arXiv arXiv 2026

  15. [15]

    Learning fair poli- cies in decentralized cooperative multi-agent reinforcement learning,

    M. Zimmer, C. Glanois, U. Siddique, and P. Weng, “Learning fair poli- cies in decentralized cooperative multi-agent reinforcement learning,” inInternational conference on machine learning. PMLR, 2021, pp. 12 967–12 978

    2021

  16. [16]

    Cooper- ation and fairness in multi-agent reinforcement learning,

    J. J. Aloor, S. N. Nayak, S. Dolan, and H. Balakrishnan, “Cooper- ation and fairness in multi-agent reinforcement learning,”Journal on Autonomous Transportation Systems, vol. 2, no. 2, pp. 1–25, 2024

    2024

  17. [17]

    Fairness in cooperative multi-objective multi-agent reinforcement learning using expected utility,

    F. Chouaki, A. Beynier, N. Maudet, and P. Viappiani, “Fairness in cooperative multi-objective multi-agent reinforcement learning using expected utility,” in25th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2026), 2026

    2026

  18. [18]

    An effective and distributed particle swarm optimization algorithm for flexible job- shop scheduling problem,

    M. Nouiri, A. Bekrar, A. Jemai, S. Niar, and A. C. Ammari, “An effective and distributed particle swarm optimization algorithm for flexible job- shop scheduling problem,”Journal of Intelligent Manufacturing, vol. 29, no. 3, pp. 603–615, 2018

    2018

  19. [19]

    Combining tabu search and genetic algorithm in a multi-agent system for solving flexible job shop problem,

    A. Azzouz, M. Ennigrou, B. Jlifi, and K. Ghedira, “Combining tabu search and genetic algorithm in a multi-agent system for solving flexible job shop problem,” inArtificial Intelligence (MICAI), 2012 11th Mexican International Conference on. IEEE, 2012, pp. 83–88

    2012

  20. [20]

    A multi-agent genetic algorithm for community detection in complex networks,

    Z. Li and J. Liu, “A multi-agent genetic algorithm for community detection in complex networks,”Physica A: Statistical Mechanics and its Applications, vol. 449, pp. 336–347, 2016

    2016

  21. [21]

    A multi-agent based cooperative approach to scheduling and routing,

    S. Martin, D. Ouelhadj, P. Beullens, E. Ozcan, A. A. Juan, and E. K. Burke, “A multi-agent based cooperative approach to scheduling and routing,”European Journal of Operational Research, vol. 254, no. 1, pp. 169–178, 2016

    2016

  22. [22]

    Near-optimal decentralized power supply restoration in smart grids,

    P. Agrawal, A. Kumar, and P. Varakantham, “Near-optimal decentralized power supply restoration in smart grids,” inProceedings of the 2015 International Conference on Autonomous Agents and Multiagent Sys- tems. International Foundation for Autonomous Agents and Multiagent Systems, 2015, pp. 1275–1283

    2015

  23. [23]

    Measuring and controlling unfairness in decentralized planning of energy demand,

    E. Pournaras, M. Vasirani, R. E. Kooij, and K. Aberer, “Measuring and controlling unfairness in decentralized planning of energy demand,” in The 3rd IEEE International Energy Conference (EnergyCon” 14), no. EPFL-CONF-197293, 2014

    2014

  24. [24]

    Socio- technical smart grid optimization via decentralized charge control of electric vehicles,

    E. Pournaras, S. Jung, S. Yadhunathan, H. Zhang, and X. Fang, “Socio- technical smart grid optimization via decentralized charge control of electric vehicles,”Applied soft computing, vol. 82, p. 105573, 2019

    2019

  25. [25]

    Truth, justice, and cake cutting,

    Y . Chen, J. K. Lai, D. C. Parkes, and A. D. Procaccia, “Truth, justice, and cake cutting,”Games and Economic Behavior, vol. 77, no. 1, pp. 284–297, 2013

    2013

  26. [26]

    How to cut a cake fairly,

    L. E. Dubins and E. H. Spanier, “How to cut a cake fairly,”The American Mathematical Monthly, vol. 68, no. 1, pp. 1–17, 1961

    1961

  27. [27]

    Fairness in multi-agent systems,

    S. d. Jong, K. Tuyls, and K. Verbeeck, “Fairness in multi-agent systems,” The Knowledge Engineering Review, vol. 23, no. 2, pp. 153–180, 2008

    2008

  28. [28]

    Fairness, incentives, and contractual choices,

    E. Fehr and K. M. Schmidt, “Fairness, incentives, and contractual choices,”European Economic Review, vol. 44, no. 4, pp. 1057–1068, 2000

    2000

  29. [29]

    The logic of reciprocity: Trust, collective action, and law,

    D. Kahan, “The logic of reciprocity: Trust, collective action, and law,” Michigan Law Review, vol. 102, no. 1, pp. 71–103, 2003

    2003

  30. [30]

    The Origin and Scope of Hayek’s Idea of Spontaneous Order,

    L. Hunt, “The Origin and Scope of Hayek’s Idea of Spontaneous Order,” inLiberalism, Conservatism, and Hayek’s Idea of Spontaneous Order. Palgrave Macmillan US, 2007

    2007

  31. [31]

    Graph convolutional reinforce- ment learning,

    J. Jiang, C. Dun, T. Huang, and Z. Lu, “Graph convolutional reinforce- ment learning,” inInternational Conference on Learning Representa- tions, 2020

    2020

  32. [32]

    Traffic light control by multiagent reinforcement learning systems,

    B. Bakker, S. Whiteson, L. Kester, and F. C. A. Groen, “Traffic light control by multiagent reinforcement learning systems,” inInteractive Collaborative Information Systems, R. Babu ˇska and F. C. A. Groen, Eds. Springer Berlin Heidelberg, 2010, vol. 281, pp. 475–510, series Title: Studies in Computational Intelligence

    2010

  33. [33]

    Virtual machine resource allocation in cloud computing via multi-agent fuzzy control,

    D. Minarolli and B. Freisleben, “Virtual machine resource allocation in cloud computing via multi-agent fuzzy control,” in2013 International Conference on Cloud and Green Computing, 2013, pp. 188–194

    2013

  34. [34]

    Fairness and load balancing in wireless LANs using association control,

    Y . Bejerano, S.-J. Han, and B. Laboratories, “Fairness and load balancing in wireless LANs using association control,”IEEE/ACM Transactions on Networking, vol. 15, 2007

    2007

  35. [35]

    Fairness in routing and load balancing,

    J. Kleinberg, Y . Rabani, and E. Tardos, “Fairness in routing and load balancing,”Journal of Computer and System Sciences, vol. 63, no. 1, pp. 2–20, 2001

    2001

  36. [36]

    Fair algorithms for multi-agent multi-armed bandits,

    S. Hossain, E. Micha, and N. Shah, “Fair algorithms for multi-agent multi-armed bandits,”Advances in Neural Information Processing Sys- tems, vol. 34, pp. 24 005–24 017, 2021

    2021

  37. [37]

    Appliance-level flexible scheduling for socio-technical smart grid optimization,

    F. Fanitabasi and E. Pournaras, “Appliance-level flexible scheduling for socio-technical smart grid optimization,”IEEE Access, vol. 8, pp. 119 880–119 898, 2020

    2020

  38. [38]

    A guide to formulating fairness in an optimization model,

    V . Xinying Chen, “A guide to formulating fairness in an optimization model,”Annals of Operations Research, vol. 326, no. 1, pp. 581–619, 2023

    2023

  39. [39]

    Optimal tradeoff between efficiency and Jain’s fairness index in resource allocation,

    A. B. Sediq, R. H. Gohary, and H. Yanikomeroglu, “Optimal tradeoff between efficiency and Jain’s fairness index in resource allocation,” in2012 IEEE 23rd International Symposium on Personal, Indoor and Mobile Radio Communications - (PIMRC), 2012, pp. 577–583, ISSN: 2166-9589

    2012

  40. [40]

    Self-regulating supply–demand systems,

    E. Pournaras, M. Yao, and D. Helbing, “Self-regulating supply–demand systems,”Future Generation Computer Systems, vol. 76, pp. 73–91, 2017

    2017

  41. [41]

    Structural self-adaptation for decentralized pervasive intelligence,

    J. Nikolic and E. Pournaras, “Structural self-adaptation for decentralized pervasive intelligence,” in2019 22nd Euromicro Conference on Digital System Design (DSD). IEEE, 2019, pp. 562–571. APPENDIXA OTHERFAIRNESSMEASURES A. Jain’s Fairness Index Raj Jain’s fairness index [39] was developed to determine fair resource allocation in shared systems. It can b...

    2019

  42. [43]

    The SW AP-15 generation scheme randomly selects 15 pairs of values of the original plan to swap, and their preference is adjusted to 1

  43. [44]

    Consequently, the mean and the standard deviation of the possible plans are constant for each agent

    Similarly, the SW AP-30 scheme randomly selects 30 pairs to swap, and their preference score is 1 30. Consequently, the mean and the standard deviation of the possible plans are constant for each agent. The preference scores are used for discomfort cost opti- mization, which entails selecting plans with high preference scores relative to the other efficin...

    2026

  44. [100]

    In other words, the first plan has the score of 0, the second one the score of 1 and so on

    Each possible plan is coupled with a score that indicates the index of the possible plan, and this score is used as the discomfort cost of the plan. In other words, the first plan has the score of 0, the second one the score of 1 and so on. It is used as a proof of concept since it is the most flexible dataset. D. Additional Experimental Details TABLE II:...

  45. [144]

    The first plan is the most preferred, as it is the only real-world plan and therefore has a preference score of1.0

    The first is the original disaggregated load; the next 3 are obtained by applying the SHUFFLE generation scheme to the original; the next 3 are obtained by applying the SW AP-15 generation scheme; and the final 3 are obtained by applying the SW AP-30 generation scheme. The first plan is the most preferred, as it is the only real-world plan and therefore h...

This paper was first reviewed by deepseek-v4-flash on August 1, 2026.