Pith. sign in

REVIEW 4 major objections 4 minor 44 references

Token pricing can force every federated client to choose the server's desired privacy level.

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 ↗

A token system where tokens expire and global models cost tokens forces strategic federated learning clients to adopt the server's acceptable privacy level.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection A clean little mechanism-design result that mostly delivers on its claims, but the headline no-cost-knowledge selling point rests on an untested assumption that needs an empirical check. the 4 major comments →

arxiv 2508.07138 v1 pith:SZJV4U5Y submitted 2025-08-10 cs.LG cs.GT

Strategic Incentivization for Locally Differentially Private Federated Learning

Yashwant Krishna Pagoti , Arunesh Sinha , Shamik Sural This is my paper
classification cs.LG cs.GT
keywords federated learninglocal differential privacyincentive mechanismgame theoryNash equilibriumtoken-based schemeprivacy-accuracy trade-offmechanism design
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 reading

This paper attempts to show that a token-based incentive scheme can resolve the privacy–accuracy tension in locally differentially private federated learning without the server knowing any client's privacy cost. Its central claim is that, under a simple pricing rule, any participating client's best choice is exactly the server's acceptable privacy level $\epsilon_a$, and all clients choosing $\epsilon_a$ forms a Nash equilibrium. Clients who choose stricter privacy earn too few tokens and get evicted; clients who choose looser privacy pay a higher privacy cost with no compensating gain in model value. If the claim holds, a server only needs to pick $\epsilon_a$ empirically and set token prices and expiry accordingly, and the clients' self-interest does the rest.

Core claim

The paper's discovery is a mechanism-design result: the server publishes a strictly increasing token reward $f(\epsilon)$, charges $C$ tokens for the global model, and expires tokens after $n$ rounds, setting $f(\epsilon_a)=C/n$. Any $\epsilon<\epsilon_a$ yields too few tokens and forced eviction; any $\epsilon>\epsilon_a$ costs more privacy with, by assumption, no gain in model value $V_i(t)$. Lemma 1 concludes every participating client chooses $\epsilon=\epsilon_a$, and all-$\epsilon_a$ is a Nash equilibrium. The server's only remaining choice is the smallest $\epsilon_a$ that avoids training collapse, found empirically (collapse at $\epsilon=25,17$, not at $15$ on MNIST). Grouping client

What carries the argument

The token freshness scheme with forced eviction: tokens awarded by a strictly monotone reward function $f(\epsilon)$ expire after $n$ rounds and the global model costs $C$ tokens, with $f(\epsilon_a)=C/n$. This makes "not enough tokens" a binding constraint that rules out $\epsilon<\epsilon_a$ and converts the privacy-cost monotonicity into a Nash equilibrium at $\epsilon_a$. The improved group variant replaces the participation interval $n$ with the group rotation period $G$, making the value gain over $G$ rounds large enough to keep clients participating.

Load-bearing premise

The argument assumes a single client's noise level does not change the value of the global model for any client, so no one gains by sending less noisy gradients.

What would settle it

Run federated learning with 3 clients on a disjoint split of MNIST, set all clients at $\epsilon_a=15$, then let one client unilaterally switch to $\epsilon=25$ while keeping token prices and expiry fixed. If the global model's accuracy over the next rounds improves (or stays equal) and that client's utility gain from $V_i(t)$ exceeds the extra privacy cost, then all-clients-$\epsilon_a$ is not a Nash equilibrium and Lemma 1 fails.

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

If this is right

  • A server can implement the mechanism without knowing clients' privacy costs; only an empirical choice of $\epsilon_a$ and the token parameters are required.
  • All participating clients converge to the same privacy level $\epsilon_a$, giving the server uniform-quality updates and avoiding the scattered participation seen in the non-strategic baseline.
  • Choosing $n=1$ (token expiry every round) is optimal when all clients participate every round; grouping clients into $G$ groups makes clients willing to participate longer because the value gain is measured over $G$ rounds.
  • If $\epsilon_a$ is set below the empirical collapse threshold, training persists for all rounds; above it, clients are evicted and accuracy collapses.
  • The grouping mechanism prevents collapse in cases where individual participation fails, as shown for $\epsilon=20$ with MNIST and $\epsilon=25$ with CIFAR10.

Where Pith is reading between the lines

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

  • The Nash-equilibrium claim rests on the assumption that one client's $\epsilon$ cannot change $V_i(t)$; with small client pools (3 or 10), a deviator's less noisy gradient is a substantial fraction of the aggregate, so a testable check is to measure whether global accuracy rises when a single client raises $\epsilon$ above $\epsilon_a$.
  • The mechanism assumes clients honestly report the $\epsilon$ they used; since tokens have no monetary value, the paper argues lying is not strategic, but a malicious client could over-report $\epsilon$ to earn tokens and still send a noisy gradient, which would break the pricing.
  • The empirical $\epsilon_a$ is dataset- and client-count-dependent (MNIST collapses at 17, CIFAR10 at 20), so the server's 'empirical choice' is not a fixed constant; a practical deployment would need an online rule to detect imminent collapse.
Share X Bluesky LinkedIn Reddit HN

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

4 major / 4 minor

Summary. The paper proposes a token-based incentive mechanism for cross-silo locally differentially private federated learning. A server publishes a token reward function f(epsilon) and charges C tokens for each global model update; tokens expire after n rounds. Lemma 1 claims that any participating client chooses the acceptable privacy level epsilon_a: a lower epsilon yields insufficient tokens and forced eviction, while a higher epsilon increases privacy cost without improving the global model's value. The server is thereby said to extract epsilon_a without knowing client costs. Experiments on MNIST and CIFAR10 study participation, accuracy, and training collapse, and compare against the SBTLF baseline.

Significance. If Lemma 1 held in practice, the mechanism would be an elegant non-monetary way to align client privacy choices with server accuracy goals in cross-silo FL, avoiding monetary payments and client cost knowledge. The token-expiry design is simple and the proof is clean under the stated assumption. However, the load-bearing assumption that a single client cannot affect the global model value is precisely where small-client FL is fragile, and the experimental evaluation does not independently validate it. The current evidence is not sufficient to establish the advertised cost-free extraction guarantee or the claimed improvement over the baseline.

major comments (4)
  1. [§IV-B, Lemma 1 in §IV-C2] The proof of Lemma 1 rules out unilateral deviations to epsilon > epsilon_a only by invoking the §IV-B assumption that Vi(t) does not change if a single client increases its epsilon. This assumption is not a theorem and is not tested. In the FedAvg update (Eq. 5) with K=3 or K=10 and disjoint/intermediary data (§V-B, Figs. 4–6), one client's gradient is a substantial fraction of the aggregate; a less-noisy update from a deviator can change the global model and hence Vi(t) for all clients. If that value gain exceeds ci(epsilon) - ci(epsilon_a), the deviation is strictly profitable and epsilon_a is not a Nash equilibrium. Since Lemma 1 is the basis for the claimed cost-free extraction of epsilon_a, this is a load-bearing gap. Please provide an explicit empirical check (e.g., measure the utility of a unilateral deviator in the K=3/K=10 setups) or a formal condition on K, gradient norms, and
  2. [§V-D, Eqs. (6)–(8), Figs. 3–5] The choice epsilon_a = 15 and the 'training collapse' results are not independent of the model. The utility in Fig. 3 is computed from the authors' chosen V(n) (Eq. 6) and c(epsilon) (Eq. 7), and the collapse in Figs. 4–5 is diagnosed by this same utility becoming negative ('this happens because their utility becomes negative'). Thus the finding that training does not collapse at epsilon = 15 is partly by construction: the authors picked epsilon_a from this utility curve and then used the same utility to define collapse. A de-circularized evaluation should report measured global-model accuracy over rounds for fixed epsilon values without filtering through V/c, and should include sensitivity analysis over V/c choices.
  3. [§V-E, Figs. 1 and 5] The headline comparison against the SBTLF baseline is confounded. The baseline run (Fig. 1b) uses intermediary data distribution (§V-C) and heterogeneous per-client epsilon values (25, 23, ..., 1), while the proposed-mechanism run (Fig. 5c) uses disjoint distribution with uniform epsilon = 15 (§V-D). Differences in accuracy and participation can therefore be attributed to data distribution and privacy-level assignment rather than to the mechanism itself. The comparison should be redone on the same data distribution and with matched privacy levels, or with the baseline using the same heterogeneous epsilon profile that the proposed mechanism is intended to replace.
  4. [§V-D, Eqs. (7)–(8)] Numerical values for key mechanism parameters are missing: cmin, cmax, epsilon_max, epsilon_min, C, and n are never specified, and G is also unspecified for the grouped mechanism. Eq. (7) and Eq. (8) are therefore not reproducible, and Fig. 3 cannot be regenerated from the information in the paper. The threshold epsilon_a = 15 depends on these values, so the central experimental claim cannot be checked. Please include the exact parameter settings used for all experiments.
minor comments (4)
  1. [§V-C] The text says 'the client with the highest privacy level (epsilon = 25)'. Higher epsilon means less privacy in LDP; the client with epsilon = 25 has the lowest privacy level. Please correct the terminology.
  2. [§III Step 4 vs §IV-A] Section III Step 4 states that 'the same client can use a different epsilon in the different rounds it participates,' while Section IV-A requires clients to commit to an epsilon 'same in every round.' These are inconsistent. Lemma 1's proof assumes a fixed epsilon; please clarify the action space.
  3. [§IV-C2] The Nash equilibrium proof considers only deviations to epsilon > epsilon_a. A deviation to non-participation is not analyzed; the statement 'no participation yields 0 rewards' is asserted but participation in the mechanism may yield negative utility for some clients. Please clarify whether participation is assumed or is itself an action in the game.
  4. [Appendix, CIFAR10] For CIFAR10, the text says at epsilon = 20 'utility drops below zero at the very end of the training process,' yet Figure 9(b) labels this case as 'collapse after most delay.' Please clarify whether a late negative-utility event is considered a collapse and how the threshold is defined.

Circularity Check

0 steps flagged

No significant circularity: the equilibrium claim is a theorem under stated assumptions, not a reduction to the mechanism's definition.

full rationale

The paper's central derivation is Lemma 1, which argues that participating clients choose ϵa because (i) ϵ < ϵa yields insufficient tokens to buy the global model under the expiry rule, and (ii) ϵ > ϵa costs more privacy with no additional model value under the explicit assumption that a single client's ϵ does not affect Vi(t). Step (i) is a designed property of the mechanism (f(ϵa)=C/n and n-round expiry), but designing a mechanism so that a desired action is feasible is not circular: the equilibrium conclusion also requires step (ii), which is an empirical/behavioral assumption rather than an input equivalent to the conclusion. If that assumption fails, Lemma 1 is wrong, but that is a correctness risk, not circular reasoning. The paper's choice of ϵa=15 in experiments is presented as an empirical calibration using chosen V and c, not as a first-principles prediction; the server-side claim 'without any information about payoffs and costs' is thus overstated relative to the simulations, but the game-theoretic extraction result does not mathematically depend on the specific fitted value. There are no self-citations or imported uniqueness theorems. The experimental validation also fixes ϵ in the collapse experiments rather than letting clients choose, so it does not directly test the strategic claim; again, this is an experimental limitation, not circularity.

Axiom & Free-Parameter Ledger

6 free parameters · 5 axioms · 1 invented entities

The central claim rests on the server's ability to choose a workable threshold epsilon_a (a free parameter fitted in the experiments), on the non-maliciousness of clients, on the insensitivity of the global model to a single client's epsilon, and on diminishing returns. The token currency is an invented design element with no independent empirical handle.

free parameters (6)
  • epsilon_a (acceptable privacy level) = 15 (both MNIST and CIFAR10)
    Chosen empirically from utility curves computed with the authors' value and cost functions; the server is assumed to be able to find this minimum acceptable level, and in the experiments the authors know the cost function when choosing it.
  • C (token price for global model) = unspecified in experimental details
    Set by server; must be positive integer multiple of n. The actual value used in experiments is not reported, affecting reproducibility.
  • n (freshness window) = 1 (from analysis)
    Derived as optimal from diminishing returns assumption, not fitted.
  • value function parameters = V(n)=30(log(n+1))^2.8/(1+0.15(log(n+1))^1.5)
    Chosen empirically to exhibit diminishing returns; used to compute utility and select epsilon_a.
  • cost function parameters (cmin, cmax) = not specified
    Chosen empirically for experiments; used in utility plots to determine collapse thresholds.
  • reward function parameters (epsilon_min, epsilon_max) = not specified
    Chosen empirically to set the reward schedule; the cubic function is arbitrary.
axioms (5)
  • ad hoc to paper Clients are non-malicious and will not misreport their chosen epsilon to the server.
    Stated in Section III, Step 4: 'We consider the clients to behave non-maliciously in this context, since there is no monetary incentive.' The mechanism relies on this because the server cannot verify local noise levels.
  • ad hoc to paper A single client's epsilon choice does not affect the global model value Vi(t).
    Assumed in Section IV-B and used in Lemma 1 to rule out profitable deviations to higher epsilon; likely false with 3 or 10 clients.
  • domain assumption Global model value Vi(t) has diminishing returns and is non-decreasing.
    Used to justify n=1 as optimal in Section IV-C2 and to set the participation inequality.
  • domain assumption The server can enforce that clients use a global model from within the last n rounds and that tokens expire.
    Needed for the freshness scheme to work; no enforcement mechanism is described.
  • standard math Standard definitions of LDP and Nash equilibrium.
    Background from Section II.
invented entities (1)
  • Token currency no independent evidence
    purpose: Artificial incentive currency: rewarded based on epsilon, spent to buy global model.
    The tokens exist only within the proposed mechanism; no external falsifiable handle.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Strategic Incentivization for Locally Differentially Private Federated Learning." pith.science (2026). https://pith.science/paper/SZJV4U5Y

@misc{pith2026250807138,
  author       = {Pith},
  title        = {Pith review of: Strategic Incentivization for Locally Differentially Private Federated Learning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SZJV4U5Y}},
  note         = {Machine review of arXiv:2508.07138}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

In Federated Learning (FL), multiple clients jointly train a machine learning model by sharing gradient information, instead of raw data, with a server over multiple rounds. To address the possibility of information leakage in spite of sharing only the gradients, Local Differential Privacy (LDP) is often used. In LDP, clients add a selective amount of noise to the gradients before sending the same to the server. Although such noise addition protects the privacy of clients, it leads to a degradation in global model accuracy. In this paper, we model this privacy-accuracy trade-off as a game, where the sever incentivizes the clients to add a lower degree of noise for achieving higher accuracy, while the clients attempt to preserve their privacy at the cost of a potential loss in accuracy. A token based incentivization mechanism is introduced in which the quantum of tokens credited to a client in an FL round is a function of the degree of perturbation of its gradients. The client can later access a newly updated global model only after acquiring enough tokens, which are to be deducted from its balance. We identify the players, their actions and payoff, and perform a strategic analysis of the game. Extensive experiments were carried out to study the impact of different parameters.

Figures

Figures reproduced from arXiv: 2508.07138 by Arunesh Sinha, Shamik Sural, Yashwant Krishna Pagoti.

Figure 1
Figure 1. Figure 1: Federated Learning Accuracy with Non-Strategic (baseline) Incentive Mechanism SBTLF under Intermediary Data Distribution, tested on the Global [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Client participation count across rounds in FL with Non-Strategic (baseline) Incentive Mechanism SBTLF under intermediary data distribution, tested [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Utility vs. No. of rounds for various ϵ values. values and determine an appropriate threshold for participa￾tion [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FL Accuracy variation for the MNIST dataset tested on a Global Dataset with Disjoint Distribution for 3 clients illustrating where the training collapse occurs (a) earliest, (b) after most delay, and (c) does not collapse at all. For this, we set the initial ϵ value same for all clients and perform the training with varying number of clients: 3 ( [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FL Accuracy variation for the MNIST dataset tested on a Global Dataset with Disjoint Distribution for 10 clients illustrating where the training collapse occurs (a) earliest, (b) after most delay, and (c) does not collapse at all. (a) (b) [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Utility vs. No. of rounds for group-based mechanism. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: Client participation count tested on a Global Dataset using [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Accuracy with (a) Group participation mechanism and (b) Individual participation using [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FL Accuracy variation for the CIFAR10 dataset tested on a Global Dataset with Disjoint Distribution for 3 clients illustrating where the training collapse occurs (a) earliest, (b) after most delay, and (c) does not collapse at all. (a) ϵ = 25 (b) ϵ = 20 (c) ϵ = 15 [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FL Accuracy variation for the CIFAR10 dataset tested on a Global Dataset with Disjoint Distribution for 10 clients illustrating where the training collapse occurs (a) earliest, (b) after most delay, and (c) does not collapse at all. [32] K. Donahue and J. Kleinberg, “Optimality and stability in federated learning: A game-theoretic approach,” 2021. [Online]. Available: https://arxiv.org/abs/2106.09580 [33]… view at source ↗
Figure 11
Figure 11. Figure 11: Client participation count tested on a Global Dataset using the [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Accuracy with (a) Group participation mechanism and (b) Individual participation using [PITH_FULL_IMAGE:figures/full_fig_p013_12.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

44 extracted references · 40 canonical work pages · 5 internal anchors

  1. [1]

    Towards efficient and privacy-preserving federated deep learning,

    M. Hao et al., “Towards efficient and privacy-preserving federated deep learning,” in IEEE ICC , 2019, pp. 1–6

    work page 2019

  2. [2]

    Collecting telemetry data privately,

    B. Ding et al., “Collecting telemetry data privately,” NEURIPS, vol. 30, 2017

    work page 2017

  3. [3]

    Motivating workers in federated learning: A stackelberg game perspective,

    Y . Sarikaya and O. Ercetin, “Motivating workers in federated learning: A stackelberg game perspective,” 2019. [Online]. Available: https://arxiv.org/abs/1908.03092

    Pith/arXiv arXiv 2019

  4. [4]

    A learning-based incentive mechanism for federated learning,

    Y . Zhan et al. , “A learning-based incentive mechanism for federated learning,” IEEE Internet of Things Journal , vol. 7, no. 7, pp. 6360– 6368, 2020

    work page 2020

  5. [5]

    Joint Service Pricing and Cooperative Relay Communication for Federated Learning

    S. Feng et al. , “Joint service pricing and cooperative relay communication for federated learning,” 2018. [Online]. Available: https://arxiv.org/abs/1811.12082

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  6. [6]

    Fmore: An incentive scheme of multi-dimensional auction for federated learning in mec,

    R. Zeng et al. , “Fmore: An incentive scheme of multi-dimensional auction for federated learning in mec,” in IEEE ICDCS, 2020, pp. 278– 288

    work page 2020

  7. [7]

    Toward an Automated Auction Framework for Wireless Federated Learning Services Market

    Y . Jiao et al. , “Toward an automated auction framework for wireless federated learning services market,” 2020. [Online]. Available: https://arxiv.org/abs/1912.06370

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  8. [8]

    Auction based incentive design for efficient federated learning in cellular wireless networks,

    T. H. T. Le et al., “Auction based incentive design for efficient federated learning in cellular wireless networks,” in IEEE WCNC , 2020, pp. 1–6

    work page 2020

  9. [9]

    Incentivized federated learning with local differential privacy using permissioned blockchains,

    S. De Chaudhury et al. , “Incentivized federated learning with local differential privacy using permissioned blockchains,” in IFIP DBSEC , 2024, pp. 301–319

    work page 2024

  10. [10]

    Blockchain based secure federated learning with local differential privacy and incentivization,

    ——, “Blockchain based secure federated learning with local differential privacy and incentivization,” IEEE Transactions on Privacy , vol. 1, pp. 31–44, 2024

    work page 2024

  11. [11]

    Incentive mechanism for differentially private federated learning in industrial internet of things,

    Y . Xu et al. , “Incentive mechanism for differentially private federated learning in industrial internet of things,” IEEE Transactions on Industrial Informatics, vol. 18, no. 10, pp. 6927–6939, 2022

    work page 2022

  12. [12]

    The mnist database of handwritten digit images for machine learning research,

    L. Deng, “The mnist database of handwritten digit images for machine learning research,” IEEE Signal Processing Magazine , vol. 29, no. 6, pp. 141–142, 2012

    2012

  13. [13]

    Learning multiple layers of features from tiny images,

    A. Krizhevsky, “Learning multiple layers of features from tiny images,” University of Toronto , 05 2012

    work page 2012

  14. [14]

    Communication-efficient learning of deep networks from decentralized data,

    H. B. McMahan et al. , “Communication-efficient learning of deep networks from decentralized data,” 2023. [Online]. Available: https://arxiv.org/abs/1602.05629

    Pith/arXiv arXiv 2023

  15. [15]

    What is federated learning?

    IBM, “What is federated learning?” 2022, https://research.ibm.com/blog/ what-is-federated-learning

    work page 2022

  16. [16]

    Advances and open problems in federated learning,

    P. Kairouz et al. , “Advances and open problems in federated learning,” F ound. Trends Mach. Learn., vol. 14, no. 1–2, p. 1–210, Jun. 2021

    work page 2021

  17. [17]

    Calibrating noise to sensitivity in private data analysis,

    C. Dwork et al., “Calibrating noise to sensitivity in private data analysis,” in Theory of Cryptography , 2006, pp. 265–284

    work page 2006

  18. [18]

    Local Differential Privacy and Its Applications: A Comprehensive Survey

    M. Yang et al. , “Local differential privacy and its applications: A comprehensive survey,” arXiv preprint arXiv:2008.03686 , 2020

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  19. [19]

    What can we learn privately?

    Kasiviswanathan et al. , “What can we learn privately?” SIAM Journal on Computing , vol. 40, no. 3, pp. 793–826, 2011

    work page 2011

  20. [20]

    Differentially private asynchronous federated learning for mobile edge computing in urban informatics,

    Y . Lu et al. , “Differentially private asynchronous federated learning for mobile edge computing in urban informatics,” IEEE Transactions on Industrial Informatics , vol. 16, no. 3, pp. 2134–2143, 2020

    work page 2020

  21. [21]

    Ldp-fed: Federated learning with local differential privacy,

    S. Truex et al. , “Ldp-fed: Federated learning with local differential privacy,” in Third ACM International Workshop on Edge Systems, Analytics and Networking , 2020, pp. 61–66

    work page 2020

  22. [22]

    Local differential privacy-based federated learning for internet of things,

    Y . Zhao et al. , “Local differential privacy-based federated learning for internet of things,” IEEE Internet of Things Journal , vol. 8, no. 11, pp. 8836–8853, 2020

    work page 2020

  23. [23]

    LDP-FL: Practical private aggregation in federated learning with local differential privacy,

    L. Sun et al. , “LDP-FL: Practical private aggregation in federated learning with local differential privacy,” in IJCAI, 2021, pp. 1571–1578

    work page 2021

  24. [24]

    Nisan et al., Algorithmic Game Theory

    N. Nisan et al., Algorithmic Game Theory. Cambridge University Press, 2007

    work page 2007

  25. [25]

    Ldp-fl: Practical private aggregation in federated learning with local differential privacy,

    L. Sun et al., “Ldp-fl: Practical private aggregation in federated learning with local differential privacy,” 08 2021, pp. 1571–1578

    work page 2021

  26. [26]

    Local differential privacy for federated learning,

    P. C. Mahawaga Arachchige et al. , “Local differential privacy for federated learning,” in ESORICS, 2022, pp. 195–216

    work page 2022

  27. [27]

    Incentivizing federated learning,

    S. Kong, Y . Li, and H. Zhou, “Incentivizing federated learning,” 2022. [Online]. Available: https://arxiv.org/abs/2205.10951

    Pith/arXiv arXiv 2022

  28. [28]

    Towards Fair and Privacy-Preserving Federated Deep Models

    L. Lyu et al. , “Towards fair and privacy-preserving federated deep models,” 2020. [Online]. Available: https://arxiv.org/abs/1906.01167

    work page internal anchor Pith review Pith/arXiv arXiv 2020

  29. [29]

    Incentive-aware federated learning with training- time model rewards,

    Z. Wu et al. , “Incentive-aware federated learning with training- time model rewards,” in The Twelfth International Conference on Learning Representations , 2024. [Online]. Available: https: //openreview.net/forum?id=FlY7WQ2hWS

    work page 2024

  30. [30]

    A sustainable incentive scheme for federated learning,

    H. Yu et al. , “A sustainable incentive scheme for federated learning,” IEEE Intelligent Systems , vol. 35, no. 4, pp. 58–69, 2020

    work page 2020

  31. [31]

    A note on stackelberg games,

    P. yan Nie and P. ai Zhang, “A note on stackelberg games,” in 2008 Chinese Control and Decision Conference , 2008, pp. 1201–1203. (a) ϵ = 25 (b) ϵ = 20 (c) ϵ = 15 Fig. 9. FL Accuracy variation for the CIFAR10 dataset tested on a Global Dataset with Disjoint Distribution for 3 clients illustrating where the training collapse occurs (a) earliest, (b) after ...

    work page 2008

  32. [32]

    Optimality and Stability in Federated Learning: A Game-theoretic Approach

    K. Donahue and J. Kleinberg, “Optimality and stability in federated learning: A game-theoretic approach,” 2021. [Online]. Available: https://arxiv.org/abs/2106.09580

    work page internal anchor Pith review Pith/arXiv arXiv 2021

  33. [33]

    Stackelberg game approach for resource alloca- tion in device-to-device communication with heterogeneous networks,

    R. Rathi et al. , “Stackelberg game approach for resource alloca- tion in device-to-device communication with heterogeneous networks,” Robotics and Autonomous Systems , vol. 156, p. 104222, 08 2022

    work page 2022

  34. [34]

    A game theory-based incentive mechanism for collabora- tive security of federated learning in energy blockchain environment,

    Y . He et al. , “A game theory-based incentive mechanism for collabora- tive security of federated learning in energy blockchain environment,” IEEE Internet of Things Journal , vol. 10, no. 24, pp. 21 294–21 308, 2023

    work page 2023

  35. [35]

    Decentral and incentivized federated learning frame- works: A systematic literature review,

    L. Witt et al. , “Decentral and incentivized federated learning frame- works: A systematic literature review,” IEEE Internet of Things Journal , vol. 10, no. 4, pp. 3642–3663, 2023

    work page 2023

  36. [36]

    When federated learning meets game theory: A cooperative framework to secure iiot applications on edge computing,

    Z. A. E. Houda et al. , “When federated learning meets game theory: A cooperative framework to secure iiot applications on edge computing,” IEEE Transactions on Industrial Informatics , vol. 18, no. 11, pp. 7988– 7997, 2022

    work page 2022

  37. [37]

    A game-theoretic approach for federated learning: A trade- off among privacy, accuracy and energy,

    L. Yin et al., “A game-theoretic approach for federated learning: A trade- off among privacy, accuracy and energy,” Digital Communications and Networks, vol. 10, no. 2, pp. 389–403, 2024

    work page 2024

  38. [38]

    A game-theoretic approach for robust federated learning,

    E. Tahanian et al. , “A game-theoretic approach for robust federated learning,” International Journal of Engineering , vol. 34, no. 4, pp. 832– 842, 2021. [Online]. Available: https://www.ije.ir/article 127844.html

    work page 2021

  39. [39]

    Collaboration in participant-centric federated learning: A game-theoretical perspective,

    G. Huang et al., “Collaboration in participant-centric federated learning: A game-theoretical perspective,” IEEE Transactions on Mobile Comput- ing, vol. 22, no. 11, pp. 6311–6326, 2023. APPENDIX For the sake of brevity, the following figures on experimen- tal results using the CIFAR10 dataset were not included in the main text and hence, those are being ...

    work page 2023

  40. [40]

    A 2D convolutional layer with 32 filters (3 ×3), ReLU activation, followed by a 2D max pooling layer (2 ×2)

    work page

  41. [41]

    Next, a convolutional layer with 64 filters (3 ×3), ReLU activation, followed by 2D max pooling layer (2 ×2)

    work page

  42. [42]

    A third convolutional layer with 128 filters (3 ×3) and ReLU activation

    work page

  43. [43]

    For the baseline scheme, we considered only use the MNIST dataset, while for the proposed schemes in the paper, we use both the MNIST and CIFAR10 datasets

    A flatten layer followed by a dense layer with 128 neurons and ReLU activation followed by an output dense layer with 10 units (no activation). For the baseline scheme, we considered only use the MNIST dataset, while for the proposed schemes in the paper, we use both the MNIST and CIFAR10 datasets. In subsection V-D, we detailed the observations for exper...

    work page

  44. [44]

    Figure 12 shows the accuracy of clients participating in the experiment same as in Figure 8a but with CIFAR10 dataset

    Recall that the utility remains positive until the end of 30 rounds. Figure 12 shows the accuracy of clients participating in the experiment same as in Figure 8a but with CIFAR10 dataset. The accuracy of the clients is shown for the group- based mechanism in Figure 12a. It can be observed that the accuracy of the clients is much lower than that of the MNI...

    work page

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.