Pith. sign in

REVIEW 2 major objections 5 minor 62 references

On the Theoretical Foundations of Data Exchange Economies

T0 review · 2 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read A reciprocal and core-stable exchange exists for all monotone continuous utility functions and any share function satisfying monotonicity, normalization, and efficiency.

desk verdict A promising data-exchange model with a genuinely stronger core-stability notion, but the main existence proof has a false inequality at its center and needs repair. read the letter →

arxiv 2412.01968 v1 pith:YDIYI723 submitted 2024-12-02 cs.GT

Hannaneh Akrami , Bhaskar Ray Chaudhury , Jugal Garg , Aniket Murhekar This is my paper · ORCID
classification cs.GT MSC 91B2691A1291B5068Q17
keywords dataexchangereciprocitycorestabilityShapleysharefixed-pointexistenceCLScomplexityArrow-Debreumarketssubmodularutilities
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

This paper asks whether a group of agents holding datasets can exchange data voluntarily, without money, in a way that is both fair and stable. It proves that yes: for every instance in which utilities are monotone and continuous, and contributions are measured by any share function satisfying monotonicity, normalization, and efficiency (the Shapley value is the leading example), there is an exchange in which each agent receives at least as much utility as they contribute, and no coalition can all improve by exchanging only among themselves. The existence argument works by mapping almost acyclic exchange graphs to a convex polytope and applying a fixed-point theorem. For approximate versions with Lipschitz utilities and diminishing returns, the paper gives a local-search algorithm and shows the search problem lies in CLS. This gives the general existence guarantee that a price-free, coalition-proof data exchange is possible, which is the setting relevant to non-profit data-sharing consortia.

What carries the argument

The load-bearing object is a pair: the exchange graph G(x,α) and the convex domain Z = {z∈[0,M]^{n×n}: every directed cycle has z-sum at least n log(1/α)}, related to an exchange x by x_{ij} = 1−exp(−z_{ij}). Points of Z correspond exactly to exchanges whose exchange graph is acyclic, hence ε-core-stable. On this domain the paper defines a continuous map g that changes each coordinate z_{ij} toward the balanced-surplus direction, scaled by the distance to the boundary of Z along that coordinate, so g always stays inside Z. The move is truncated by β^+_{ij}(z) and β^−_{ij}(z), the maximum distances one can travel from z along ±e_{ij} without leaving Z. A fixed point of g equalizes all surpluses, and because the sum of surpluses is identically zero, equal surpluses mean every agent is reciprocal.

What would settle it

Take a three-agent instance with continuous monotone piecewise-linear utilities and Shapley shares, and enumerate all points z∈Z satisfying the fixed-point equations. If any boundary point has β^+_{ij}(z)=β^−_{ij}(z)=0 for every surplus-imbalanced pair while some Δ_i(z)≠0, then the missing path lemma is false and the written proof of Theorem 3 collapses; a numerical search could find such an instance or demonstrate that none exists, which would either refute or corroborate the proof's key step.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is Theorem 1: a reciprocal and core-stable exchange exists for all monotone continuous utility functions and all credit-sharing functions that are monotone, normalized, and efficient. The proof works with the surplus Δ_i(x)=∑_j ψ_{ij}(x_j)-u_i(x_i); by efficiency the surpluses sum to zero, so an exchange is reciprocal exactly when all surpluses are equal (at zero). Stability is captured through the exchange graph G(x,α), which records an edge (i,j) when i's data to j is still below 1−α; if this graph is acyclic, no coalition can deviate and give every member a strict utility gain. The paper maps the set of such almost-acyclic exchanges homeomorphically to a convex compact polytope, constructs a continuous map that nudges data from higher-surplus to lower-surplus agents, and uses Brouwer's fixed-point theorem. A separate compactness argument turns ε-core-stability into exact core-stability.

Load-bearing premise

The proof that every fixed point equalizes all agents' surplus (contribution to others minus utility received) assumes that whenever surpluses differ, at least one pair has a coordinate that can be nudged inside the domain; the written proof does not show this for boundary points where the allowed nudge is zero.

Editorial extensions

If this is right

  • Non-profit data exchange consortia are guaranteed a concrete price-free exchange in which every participant receives utility at least matching its own contribution, even when datasets are complements or substitutes and utilities are only continuous and monotone.
  • The guarantee is robust to the choice of credit-sharing rule: any rule satisfying monotonicity, normalization, and efficiency works, so institutions can pick Shapley, proportional, or another attribution without losing existence.
  • For Lipschitz, diminishing-returns preferences, an ε-fair and ε-core-stable exchange can be found by polynomially many local-search steps when L/ε is polynomial, and the problem sits in PPAD ∩ PLS = CLS.
  • The fixed-point formulation can be projected onto a box with polynomially many constraints, putting the approximate problem in PPAD while preserving the acyclicity invariant.

Reading between the lines

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

  • The convex almost-acyclic domain construction is a general recipe: any stability notion that can be certified by an acyclic graph can be bolted onto a continuous surplus-balancing map, so similar existence theorems should hold for other replicable-resource sharing problems with a central server.
  • The local-search and CLS results are stated for monotone submodular utilities with Shapley shares, but the proof actually uses only L-Lipschitzness and cross-monotonicity; the same polynomial-time guarantee should extend to any cross-monotone share function under a Lipschitz bound.
  • Whether the problem is CLS-complete or easier remains open; a natural next step is to try to embed a CLS-complete problem into the surplus-balancing dynamics, or to find a polynomial-time algorithm through the projection structure.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper introduces a formal model of data exchange economies in which agents exchange fractional shares of datasets without monetary transfers. An exchange is reciprocal if each agent's utility is at least the sum of her contributions to other agents' utilities, and core-stable if no coalition can, by exchanging only among themselves, give every member strictly higher utility. The central theoretical claim is that a reciprocal and exactly core-stable exchange exists for all monotone continuous utility functions and all continuous monotone, normalized, efficient credit-sharing functions (Theorems 1, 3, and 4). The proof route is to identify a convex polytope Z of approximate core-stable exchanges via a logarithmic homeomorphism, define a continuous map g on Z that adjusts surplus differences, invoke Brouwer's fixed-point theorem, and pass to the limit through a compactness argument. The paper also claims computational results: under L-Lipschitz utilities and cross-monotone shares, a local-search algorithm finds an ε-reciprocal and ε-core-stable exchange, and for L/ε = poly(n) the problem lies in CLS (Theorems 2, 6, 7, and 8).

Significance. If the main existence theorem is correct, it is a substantial result: it would show that fair and stable no-money data exchange is possible under very weak assumptions on utilities and credit-sharing rules, and it would contrast with the PPAD-hardness results for classical exchange economies. The computational upper bound of CLS for the approximate problem under diminishing-returns assumptions is also a meaningful contribution, and the paper is careful to formulate the model, definitions, and oracle model. The paper does not ship code or machine-checked proofs, but the theoretical framework is coherent and the technical overview is informative. However, the formal proof of the existence theorem contains a false inequality in a central lemma and a missing boundary argument in the fixed-point step, so the main claims are not established as written.

major comments (2)
  1. [Section 3.2, Lemma 4 and Eq. (3)] The assertion δ·|Δ_j(f(z))−Δ_i(f(z))|≤1 is false under the paper's axioms. Efficiency only forces Σ_i ψ_ij = u_j ≤ 1 per column, so an agent can contribute close to 1 to each of the other n−1 agents while receiving zero utility, giving surpluses differing by up to n. For example, for n=3 set u_1≡0, u_2(x)=x_12, u_3(x)=x_13, ψ_12=u_2, ψ_13=u_3, and all other ψ=0; these functions are continuous, monotone, normalized, and efficient. At any z∈Z with x_12,x_13 close to 1 and the remaining entries set sufficiently large, Δ_1≈2 and Δ_2≈−1, and with δ=1/max_i u_i(1)=1 we get δ|Δ_2−Δ_1|≈3>1. Consequently g_12(z)=z−e_12·δ·β^-_12(z)·(Δ_1−Δ_2) can leave Z, so Lemma 4 and the Brouwer fixed-point step of Theorem 3 are not established. Theorem 4 and the PPAD construction in Section 4.3 inherit this gap. The defect appears repairable, for example by taking δ no larger than 1/((n+1)·max_i u_i(1)) and adjusting the constants in Claim 3, but the proof as written is incorrect.
  2. [Section 3.2, proof of Theorem 3] The passage from g(z*)=z* to h_ij(z*)=0 for all i,j is unjustified when β_ij(z*)=0. The fixed-point equation only gives β_ij(z*)·h_ij(z*)=0 for each pair, so a boundary point with β_ij(z*)=0 and h_ij(z*)≠0 is not excluded. The informal path argument in Section 1.3 is the only place where this boundary case is addressed, but it is not proved in Section 3.2, and it is not a direct consequence of the definition of Z. For instance, a tight Hamiltonian cycle with every edge exactly at the threshold z_e=log(1/α) can have G(f(z),α) contain no edges, so the asserted path from j to i need not exist. A formal argument showing that an imbalanced surplus pair cannot be blocked in all directions is required before the fixed point can be identified with a reciprocal exchange.
minor comments (5)
  1. [Section 3.2] The definition δ = 1/max_i u_i(1^{n×n}) is undefined when all utilities are identically zero; the degenerate case should be handled explicitly, even though the result is trivial there.
  2. [Section 4.1.1, Algorithm 2] The pseudocode and the while loop do not specify the target agent j from Lemma 10; the reader must infer that a single fixed j is used throughout the threshold-based reduction, and this should be stated in the algorithm.
  3. [Section 4.1, Theorem 5] The statement "Given an exchange x which is not ε-core stable and ε-reciprocal" should read "not ε-reciprocal," since the algorithm maintains ε-core stability by the acyclicity invariant.
  4. [Section 1.3, Figure 3 caption] The caption writes "∆ i(b) < ∆ i(c)" where it appears to mean the surpluses of agents b and c; using Δ_b and Δ_c would avoid confusion.
  5. [Section 3.3, proof of Theorem 4] The notation i_ℓ for "the smallest integer i such that σ_i ≥ ℓ" is confusing because σ_i is already indexed; renaming this index t_ℓ would improve readability.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the existence and complexity results are derived from stated axioms, standard fixed-point theorems, and external complexity reductions, with no fitted parameter or load-bearing self-citation.

full rationale

The paper's central claims are not circular. Theorem 1 (exact reciprocal and core-stable exchange) is proved by defining a convex polytope Z of approximately core-stable exchanges and a continuous map g whose fixed points are intended to force all surplus differences to zero; reciprocity is a conclusion, not an input, and the theorem quantifies over all share functions satisfying monotonicity, normalization, and efficiency, so the fairness condition is not built into the data of the instance. The approximate and CLS results derive from an explicit local-search potential P(x) and from external reductions to EY10 and FGHS23; no parameter is fitted to the target exchange, and no prediction is renamed from a fitted input. The related-work citation [BGI+24] is presented as independent work with a different model and is not load-bearing for any theorem. The acyclicity-to-core-stability lemma (Lemma 1) and the compactness arguments are standard and self-contained. The only concerns visible in the text are mathematical-correctness issues (e.g., the bound δ·|Δ_j−Δ_i|≤1 in Lemma 4 and the boundary/beta-ij step in the proof of Theorem 3), which are potential proof gaps rather than circular reasoning. Those concerns do not fit any of the enumerated circularity patterns, and the paper does not reduce any derived statement to its own assumptions by construction.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

The paper is a pure mathematical model, so no numbers are fitted to data and no new entities are postulated. The central results rest on standard fixed-point theorems, the modeling axioms for utilities and share functions, and the Lipschitz and cross-monotone assumptions for the computational results. An unstated extra premise is continuity of share functions for the existence theorem.

assumptions (6)
  • standard math Brouwer's fixed point theorem applies to the compact convex polytope Z and the continuous map g: Z to Z.
    Invoked in the proof of Theorem 3 in Section 3.2 to obtain a fixed point z* that is then claimed to correspond to a reciprocal exchange.
  • domain assumption Utility functions are monotone, continuous, normalized to zero at no data, and valued in [0,1].
    Defined in Section 2 as the base model; the existence and complexity theorems are stated relative to these assumptions.
  • domain assumption Share functions satisfy monotonicity, normalization, efficiency, and are continuous for the existence proofs.
    Definition 2 states the first three axioms; continuity is added in Theorems 3 and 4 but omitted from Theorem 1, which is flagged as an overclaim.
  • domain assumption For computational results, utilities are L-Lipschitz and shares are cross-monotone, with exact oracle access to ui and psi_ij.
    Section 4 states these assumptions to obtain the local search algorithm and the PPAD and CLS membership results.
  • standard math The EY10 sufficient conditions for PPAD membership and the FGHS23 identity CLS = PPAD intersect PLS are accepted.
    Used in Section 4.3 and Theorem 8 to establish the final complexity classification.
  • domain assumption In core-stability, a deviating coalition may use any exchange among its members, including full sharing and unfair allocations.
    This modeling choice, described in Section 1.1, makes the notion of core stability stronger than in the related work [BGI+24].

how reviews work

0 comments
Cite this review

Pith. "Pith review of On the Theoretical Foundations of Data Exchange Economies." pith.science (2026). https://pith.science/paper/YDIYI723

@misc{pith2026241201968,
  author       = {Pith},
  title        = {Pith review of: On the Theoretical Foundations of Data Exchange Economies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YDIYI723}},
  note         = {Machine review of arXiv:2412.01968}
}
read the original abstract

The immense success of ML systems relies heavily on large-scale, high-quality data. The high demand for data has led to many paradigms that involve selling, exchanging, and sharing data, motivating the study of economic processes with data as an asset. However, data differs from classical economic assets in terms of free duplication: there is no concept of limited supply since it can be replicated at zero marginal cost. This distinction introduces fundamental differences between economic processes involving data and those concerning other assets. We study a parallel to exchange (Arrow-Debreu) markets where data is the asset. Here, agents with datasets exchange data fairly and voluntarily, aiming for mutual benefit without monetary compensation. This framework is particularly relevant for non-profit organizations that seek to improve their ML models through data exchange, yet are restricted from selling their data for profit. We propose a general framework for data exchange, built on two core principles: (i) fairness, ensuring that each agent receives utility proportional to their contribution to others; contributions are quantifiable using standard credit-sharing functions like the Shapley value, and (ii) stability, ensuring that no coalition of agents can identify an exchange among themselves which they unanimously prefer to the current exchange. We show that fair and stable exchanges exist for all monotone continuous utility functions. Next, we investigate the computational complexity of finding approximate fair and stable exchanges. We present a local search algorithm for instances with monotone submodular utility functions, where each agent contributions are measured using the Shapley value. We prove that this problem lies in CLS under mild assumptions. Our framework opens up several intriguing theoretical directions for research in data economics.

Figures

Figures reproduced from arXiv: 2412.01968 by the authors.

Figure 1
Figure 1. Illustration of the issue of non-separability. Th → [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Illustration of how an acyclic exchange graph will [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Illustration of our fixed point proof. Since [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: Illustration of the main bottleneck when we decrea [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Definition of the functions β + ij (z) and β − ij (z). The values β + ij (z) and β − ij (z) are the distances from z to the boundary of the convex set Z along the directions eij and −eij respectively. 3.2 Defining the function g : Z → Z to capture reciprocity Having de…
Figure 6
Figure 6. Figure 6: Illustrating the function g(z). The point z ∈ [0, M] 2 is such that ∆1(f(z)) < ∆2(f(z)). Hence g increases z12 to g 12(z) and decreases z21 to g 21(z), and returns g(z) as a convex combination of z, g 12(z), and g 21(z). As a corollary, we obtain the continuity of the …

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

62 extracted references · 52 canonical work pages

  1. [1]

    Existence of an equilibrium for a competitive economy

    Kenneth J Arrow and Gerard Debreu. Existence of an equilibrium for a competitive economy. Econometrica: Journal of the Econometric Society , pages 265--290, 1954

    work page 1954

  2. [2]

    Towards Data Auctions with Externalities

    Anish Agarwal, Munther A. Dahleh, Thibaut Horel, and Maryann Rui. Towards data auctions with externalities. CoRR , abs/2003.08345, 2020

    work page Pith review arXiv 2003

  3. [3]

    Dahleh, and Tuhin Sarkar

    Anish Agarwal, Munther A. Dahleh, and Tuhin Sarkar. A marketplace for data: An algorithmic solution. In EC , pages 701--726. ACM , 2019

    work page 2019

  4. [4]

    Integrating business intelligence and predictive analytics in banking: A framework for optimizing financial decision-making

    Ibrahim Adedeji Adeniran, Christianah Pelumi Efunniyi, Olajide Soji Osundare, Angela Omozele Abhulimen, and UK OneAdvanced. Integrating business intelligence and predictive analytics in banking: A framework for optimizing financial decision-making. Finance & Accounting Research Journal , 6(8), 2024

    work page 2024

  5. [5]

    A monopolistic market for information

    Anat R Admati and Paul Pfleiderer. A monopolistic market for information. Journal of Economic Theory , 39(2):400--438, 1986

    work page 1986

  6. [6]

    Direct and indirect sale of information

    Anat R Admati and Paul Pfleiderer. Direct and indirect sale of information. Econometrica: Journal of the Econometric Society , pages 901--928, 1990

    work page 1990

  7. [7]

    The economics of social data

    Dirk Bergemann, Alessandro Bonatti, and Tan Gan. The economics of social data. The RAND Journal of Economics , 53(2):263--296, 2022

    work page 2022

  8. [8]

    The design and price of information

    Dirk Bergemann, Alessandro Bonatti, and Alex Smolin. The design and price of information. American economic review , 108(1):1--48, 2018

    2018

Show all 62 references
  1. [9]

    Business intelligence in the healthcare industry: The utilization of a data-driven approach to support clinical decision making

    Luigi Jesus Basile, Nunzia Carbonara, Roberta Pellegrino, and Umberto Panniello. Business intelligence in the healthcare industry: The utilization of a data-driven approach to support clinical decision making. Technovation , 120:102482, 2023

    2023

  2. [10]

    Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, Kamesh Munagala, and Govind S. Sankar. Data exchange markets via utility balancing. In WWW , pages 57--65. ACM , 2024

    2024

  3. [11]

    One for one, or all for all: Equilibria and optimality of collaboration in federated learning

    Avrim Blum, Nika Haghtalab, Richard Lanas Phillips, and Han Shao. One for one, or all for all: Equilibria and optimality of collaboration in federated learning. In ICML , volume 139 of Proceedings of Machine Learning Research , pages 1005--1014. PMLR , 2021

    2021

  4. [12]

    Optimal mechanisms for selling information

    Moshe Babaioff, Robert Kleinberg, and Renato Paes Leme. Optimal mechanisms for selling information. CoRR , abs/1204.5519, 2012

    2012 arXiv

  5. [13]

    Bertsekas, A

    D. Bertsekas, A. Nedic, and A. Ozdaglar. Convex Analysis and Optimization . Athena Scientific optimization and computation series. Athena Scientific, 2003

    2003

  6. [14]

    Settling the complexity of arrow-debreu equilibria in markets with additively separable utilities

    Xi Chen, Decheng Dai, Ye Du, and Shang-Hua Teng. Settling the complexity of arrow-debreu equilibria in markets with additively separable utilities. In 2009 50th Annual IEEE Symposium on Foundations of Computer Science , pages 273--282. IEEE, 2009

    2009

  7. [15]

    Data-sharing markets: model, protocol, and algorithms to incentivize the formation of data-sharing consortia

    Raul Castro Fernandez. Data-sharing markets: model, protocol, and algorithms to incentivize the formation of data-sharing consortia. Proceedings of the ACM on Management of Data , 1(2):1--25, 2023

    2023

  8. [16]

    Selling data to a machine learner: Pricing via costly signaling

    Junjie Chen, Minming Li, and Haifeng Xu. Selling data to a machine learner: Pricing via costly signaling. In ICML , volume 162 of Proceedings of Machine Learning Research , pages 3336--3359. PMLR , 2022

    2022

  9. [17]

    Combinatorial algorithms for general linear arrow-debreu markets

    Bhaskar Ray Chaudhury and Kurt Mehlhorn. Combinatorial algorithms for general linear arrow-debreu markets. In FSTTCS , volume 122 of LIPIcs , pages 26:1--26:16. Schloss Dagstuhl - Leibniz-Zentrum f \" u r Informatik, 2018

    2018

  10. [18]

    Market equilibrium for ces exchange economies: Existence, multiplicity, and computation

    Bruno Codenotti, Benton McCune, Sriram Penumatcha, and Kasturi Varadarajan. Market equilibrium for ces exchange economies: Existence, multiplicity, and computation. In FSTTCS 2005: Foundations of Software Technology and Theoretical Computer Science: 25th International Conferen...

    2005

  11. [19]

    The complexity of non-monotone markets

    Xi Chen, Dimitris Paparas, and Mihalis Yannakakis. The complexity of non-monotone markets. Journal of the ACM (JACM) , 64(3):1--56, 2017

    2017

  12. [20]

    Leontief economies encode nonzero sum two-player games

    Bruno Codenotti, Amin Saberi, Kasturi Varadarajan, and Yinyu Ye. Leontief economies encode nonzero sum two-player games. In SODA , volume 6, pages 659--667, 2006

    2006

  13. [21]

    Spending is not easier than trading: O n the computational equivalence of F isher and A rrow- D ebreu equilibria

    Xi Chen and Shang - Hua Teng. Spending is not easier than trading: O n the computational equivalence of F isher and A rrow- D ebreu equilibria. In Proc.\ 20th Intl.\ Symp.\ Algorithms and Computation (ISAAC) , pages 647--656, 2009

    2009

  14. [22]

    How to sell information optimally: An algorithmic study

    Yang Cai and Grigoris Velegkas. How to sell information optimally: An algorithmic study. arXiv preprint arXiv:2011.14570 , 2020

    2011 arXiv

  15. [23]

    Dynamic games for social model training service market via federated learning approach

    Wenqing Cheng, Yuze Zou, Jing Xu, and Wei Liu. Dynamic games for social model training service market via federated learning approach. IEEE Transactions on Computational Social Systems , 9(1):64--75, 2021

    2021

  16. [24]

    Constant inapproximability for F isher markets

    Argyrios Deligkas, John Fearnley, Alexandros Hollender, and Themistoklis Melissourgos. Constant inapproximability for F isher markets. In Proc.\ 25th Conf.\ Economics and Computation (EC) , 2024

    2024

  17. [25]

    An improved combinatorial polynomial algorithm for the linear arrow-debreu market

    Ran Duan, Jugal Garg, and Kurt Mehlhorn. An improved combinatorial polynomial algorithm for the linear arrow-debreu market. In SODA , pages 90--106. SIAM , 2016

    2016

  18. [26]

    A rational convex program for linear arrow-debreu markets

    Nikhil R Devanur, Jugal Garg, and L \'a szl \'o A V \'e gh. A rational convex program for linear arrow-debreu markets. ACM Transactions on Economics and Computation (TEAC) , 5(1):1--13, 2016

    2016

  19. [27]

    Optimality and stability in federated learning: A game-theoretic approach

    Kate Donahue and Jon Kleinberg. Optimality and stability in federated learning: A game-theoretic approach. Advances in Neural Information Processing Systems , 34:1287--1298, 2021

    2021

  20. [28]

    A combinatorial polynomial algorithm for the linear arrow-debreu market

    Ran Duan and Kurt Mehlhorn. A combinatorial polynomial algorithm for the linear arrow-debreu market. Inf. Comput. , 243:112--132, 2015

    2015

  21. [29]

    Federated learning for predicting clinical outcomes in patients with covid-19

    Ittai Dayan, Holger R Roth, Aoxiao Zhong, Ahmed Harouni, Amilcare Gentili, Anas Z Abidin, Andrew Liu, Anthony Beardsworth Costa, Bradford J Wood, Chien-Sung Tsai, et al. Federated learning for predicting clinical outcomes in patients with covid-19. Nature medicine , 27(10):173...

    2021

  22. [30]

    Federated learning in vehicular networks

    Ahmet M Elbir, Burak Soner, and Sinem Coleri. Federated learning in vehicular networks. arXiv preprint arXiv:2006.01412 , 2020

    2006 arXiv

  23. [31]

    On the complexity of nash equilibria and other fixed points

    Kousha Etessami and Mihalis Yannakakis. On the complexity of nash equilibria and other fixed points. SIAM Journal on Computing , 39(6):2531--2597, 2010

    2010

  24. [32]

    The complexity of gradient descent: CLS = PPAD \( \) PLS

    John Fearnley, Paul Goldberg, Alexandros Hollender, and Rahul Savani. The complexity of gradient descent: CLS = PPAD \( \) PLS . J. ACM , 70(1):7:1--7:74, 2023

    2023

  25. [33]

    Auction algorithms for market equilibrium with weak gross substitute demands

    Jugal Garg, Edin Husi \'c , and L \'a szl \'o A V \'e gh. Auction algorithms for market equilibrium with weak gross substitute demands. arXiv preprint arXiv:1908.07948 , 2019

    1908 arXiv

  26. [34]

    Settling the complexity of leontief and plc exchange markets under exact and approximate equilibria

    Jugal Garg, Ruta Mehta, Vijay V Vazirani, and Sadra Yazdanbod. Settling the complexity of leontief and plc exchange markets under exact and approximate equilibria. In Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing , pages 890--901, 2017

    2017

  27. [35]

    College admissions and the stability of marriage

    David Gale and Lloyd S Shapley. College admissions and the stability of marriage. The American Mathematical Monthly , 69(1):9--15, 1962

    1962

  28. [36]

    V \' e gh

    Jugal Garg and L \' a szl \' o A. V \' e gh. A strongly polynomial algorithm for linear exchange markets. Oper. Res. , 71(2):487--505, 2023

    2023

  29. [37]

    Equilibrium of data markets with externality

    Safwan Hossain and Yiling Chen. Equilibrium of data markets with externality. In ICML . OpenReview.net, 2024

    2024

  30. [38]

    Higher education data sharing consortium (https://www.hedsconsortium.org/)

    HEDS. Higher education data sharing consortium (https://www.hedsconsortium.org/)

  31. [39]

    Damir Ivankovic, Pascal Garel, Niek Klazinga, and Dionne Kringos. Data-driven collaboration between hospitals and other healthcare organisations in europe during the covid-19 pandemic: An explanatory sequential mixed-methods study among mid-level hospital managers. Internation...

    2023

  32. [40]

    Equilibrium pricing of semantically substitutable digital goods

    Kamal Jain and Vijay Vazirani. Equilibrium pricing of semantically substitutable digital goods. arXiv preprint arXiv:1007.4586 , 2010

    2010 arXiv

  33. [41]

    Sai Praneeth Karimireddy, Wenshuo Guo, and Michael I. Jordan. Mechanisms that incentivize data sharing in federated learning. CoRR , abs/2207.04557, 2022

    2022 arXiv

  34. [42]

    Federated learning for edge networks: Resource optimization and incentive mechanism

    Latif U Khan, Shashi Raj Pandey, Nguyen H Tran, Walid Saad, Zhu Han, Minh NH Nguyen, and Choong Seon Hong. Federated learning for edge networks: Resource optimization and incentive mechanism. IEEE Communications Magazine , 58(10):88--93, 2020

    2020

  35. [43]

    Vertical federated learning: Concepts, advances, and challenges

    Yang Liu, Yan Kang, Tianyuan Zou, Yanhong Pu, Yuanqin He, Xiaozhou Ye, Ye Ouyang, Ya-Qin Zhang, and Qiang Yang. Vertical federated learning: Concepts, advances, and challenges. IEEE Transactions on Knowledge and Data Engineering , 2024

    2024

  36. [44]

    How to sell a data set? pricing policies for data monetization

    Sameer Mehta, Milind Dawande, Ganesh Janakiraman, and Vijay Mookerjee. How to sell a data set? pricing policies for data monetization. Information Systems Research , 32(4):1281--1297, 2021

    2021

  37. [45]

    Communication-efficient learning of deep networks from decentralized data

    Brendan McMahan, Eider Moore, Daniel Ramage, Seth Hampson, and Blaise Aguera y Arcas. Communication-efficient learning of deep networks from decentralized data. In Artificial intelligence and statistics , pages 1273--1282. PMLR, 2017

    2017

  38. [46]

    Incentives in federated learning: Equilibria, dynamics, and mechanisms for welfare maximization

    Aniket Murhekar, Zhuowen Yuan, Bhaskar Ray Chaudhury, Bo Li, and Ruta Mehta. Incentives in federated learning: Equilibria, dynamics, and mechanisms for welfare maximization. In NeurIPS , 2023

    2023

  39. [47]

    A survey on data pricing: from economics to data science

    Jian Pei. A survey on data pricing: from economics to data science. IEEE Transactions on knowledge and Data Engineering , 34(10):4586--4608, 2020

    2020

  40. [48]

    Incentivize to build: A crowdsourcing framework for federated learning

    Shashi Raj Pandey, Nguyen H Tran, Mehdi Bennis, Yan Kyaw Tun, Zhu Han, and Choong Seon Hong. Incentivize to build: A crowdsourcing framework for federated learning. In Proceedings-IEEE Global Communications Conference, GLOBECOM , page 9014329, 2019

    2019

  41. [49]

    Data-driven research in retail operations—a review

    Meng Qi, Ho-Yin Mak, and Zuo-Jun Max Shen. Data-driven research in retail operations—a review. Naval Research Logistics (NRL) , 67(8):595--616, 2020

    2020

  42. [50]

    Big data market size: Global industry, share, analysis, trends and forecast 2022 - 2030

    Acumen Research. Big data market size: Global industry, share, analysis, trends and forecast 2022 - 2030

    2022

  43. [51]

    Distributed task allocation in mobile device cloud exploiting federated learning and subjective logic

    Palash Roy, Sujan Sarker, Md Abdur Razzaque, Md Mamun-or Rashid, Mohmmad Mehedi Hassan, and Giancarlo Fortino. Distributed task allocation in mobile device cloud exploiting federated learning and subjective logic. Journal of Systems Architecture , 113:101972, 2021

    2021

  44. [52]

    Inapproximability of nash equilibrium

    Aviad Rubinstein. Inapproximability of nash equilibrium. SIAM Journal on Computing , 47(3):917--959, 2018

    2018

  45. [53]

    Big data driven supply chain management: A framework for implementing analytics and turning information into intelligence

    Nada R Sanders. Big data driven supply chain management: A framework for implementing analytics and turning information into intelligence . Pearson Education, 2014

    2014

  46. [54]

    The core of an n person game

    Herbert E Scarf. The core of an n person game. Econometrica: Journal of the Econometric Society , pages 50--69, 1967

    1967

  47. [55]

    Notes on the n-person game—ii: The value of an n-person game

    Lloyd S Shapley. Notes on the n-person game—ii: The value of an n-person game. 1951

    1951

  48. [56]

    A value for n-person games

    Lloyd S Shapley. A value for n-person games. Contribution to the Theory of Games , 2, 1953

    1953

  49. [57]

    On cores and indivisibility

    Lloyd Shapley and Herbert Scarf. On cores and indivisibility. Journal of mathematical economics , 1(1):23--37, 1974

    1974

  50. [58]

    Big data and sentiment analysis to highlight decision behaviours: a case study for student population

    Orlando Troisi, Mara Grimaldi, Francesca Loia, and Gennaro Maione. Big data and sentiment analysis to highlight decision behaviours: a case study for student population. Behaviour & Information Technology , 37(10-11):1111--1128, 2018

    2018

  51. [59]

    Market equilibrium under separable, piecewise-linear, concave utilities

    Vijay Vazirani and Mihalis Yannakakis. Market equilibrium under separable, piecewise-linear, concave utilities. J. ACM , 58(3):10, 2011

    2011

  52. [60]

    Elements of pure economics

    Leon Walras. Elements of pure economics . Routledge, 2013

    2013

  53. [61]

    Federated learning for healthcare informatics

    Jie Xu, Benjamin S Glicksberg, Chang Su, Peter Walker, Jiang Bian, and Fei Wang. Federated learning for healthcare informatics. Journal of Healthcare Informatics Research , 5(1):1--19, 2021

    2021

  54. [62]

    Dynamic games in federated learning training service market

    Yuze Zou, Shaohan Feng, Jing Xu, Shimin Gong, Dusit Niyato, and Wenqing Cheng. Dynamic games in federated learning training service market. In 2019 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (PACRIM) , pages 1--6. IEEE, 2019

    2019

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.