Pith. sign in

REVIEW 3 major objections 5 minor 52 references

Package Bids in Combinatorial Electricity Auctions: Selection, Welfare Losses, and Alternatives

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read This paper claims that the welfare loss from limiting XOR package bids in day-ahead electricity auctions is bounded by a Wasserstein distance between forecast and true prices, and that optimal bid selection is a linear program.

desk verdict The LP reformulation is a solid, citable result, but the headline Wasserstein bound does not actually bound the loss from a binding bid cap—so the paper's central claim is overstated. read the letter →

arxiv 2502.09420 v4 pith:2MALMCQS submitted 2025-02-13 econ.GN q-fin.EC

Thomas Hübner , Gabriela Hug This is my paper · ORCID
classification econ.GNq-fin.EC MSC 91B2690C0590C1590C27
keywords XORpackagebidscombinatorialauctionselectricitymarketdesignblockstochasticbileveloptimizationtotalunimodularityWassersteindistancewelfareloss
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 claims that the welfare loss caused by limiting the number of XOR package bids in day-ahead electricity auctions is both computationally manageable and quantitatively bounded. The authors show that the stochastic bilevel program a bidder must solve to choose a limited set of package bids becomes a linear program when the bidder's candidate packages are finite, because the constraint matrix is totally unimodular. They then derive an upper bound on the expected profit loss: it is no more than a Wasserstein distance between the true price distribution and the scenario distribution used for bid selection, scaled by the size of feasible power profiles. This matters because European day-ahead auctions cap exclusive groups at 24 block bids, and the paper gives bidders a fast way to spend that budget and gives auction designers a way to price the cap's welfare cost.

What carries the argument

The central object is the XOR package bid—called an exclusive group of block bids in European auctions—a collection of priced power profiles of which the auctioneer accepts at most one, or none. Two mechanisms carry the argument. First, the stochastic bilevel bid-selection program is shown to collapse to a single-level binary program under truthful bidding, and its constraint matrix is totally unimodular, so binary variables can be relaxed and the LP optimum is integral. Second, the profit-loss function is Lipschitz-continuous with constant $L = 2 \max\{\|x\|_2 : v(x) \neq -\infty\}$, and the resulting Wasserstein distance $d_W(P,Q)$ between the true and scenario price distributions converts forecast error directly into an expected-profit-loss bound. The Wasserstein distance is doing the quantitative work: it is the minimal transport cost between $P$ and $Q$, and the theorem says that if scenarios approximate the true distribution well, the worst-case expected loss shrinks proportionally.

What would settle it

On historical German day-ahead data, run the paper's algorithm (9) with the scenario generator of Section 4.2 and compare realized profit with the perfect-information maximum for the generator, battery, and heating utility; if the average shortfall ever exceeds $L \cdot d_W(P,Q)$, the Lipschitz argument behind Theorem 1 is false. Separately, solve the LP relaxation of program (8) on instances with many candidate packages; any fractional optimum strictly better than the best integral solution would contradict the total-unimodularity claim.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the XOR bid selection problem is not inherently hard. Assuming a Walrasian equilibrium exists and no bidder has market power, truthful bidding is a dominant strategy even when the bidder may only submit a limited set of packages, so the bilevel program collapses to a single-level problem. For a finite set of candidate packages, the resulting binary program has a totally unimodular constraint matrix, its LP relaxation is exact, and optimal bid selection can be solved in polynomial time. The first welfare theorem then translates per-bidder profit loss into total welfare loss, and Theorem 1 bounds the expected loss by $L \cdot d_W(P,Q)$, where $d_W(P,Q)$ is the Wasserstein-1 distance between the true price distribution $P$ and the scenario distribution $Q$, and $L$ is twice the largest feasible package norm. Simulations of a thermal generator, a battery, and a district heating utility on 2023 German data show profits rising with the number of bids and with forecast accuracy, approaching the perfect-information benchmark as the Wasserstein distance goes to zero.

Load-bearing premise

The load-bearing premise is that the day-ahead auction is Walrasian: uniform prices clear the market, no bidder can influence prices, and the auctioneer accepts each bidder's most profitable package at those prices; if any of those fail, the LP still solves an optimization problem but it no longer measures profit or welfare.

Editorial extensions

If this is right

  • A bidder with a finite set of candidate packages can find its optimal limited XOR bid list in polynomial time; the paper shows the LP relaxation is exact, and the same formulation covers risk-averse objectives such as CVaR.
  • The welfare cost of a bid limit is governed by forecast quality rather than by the limit itself: with accurate scenarios, additional bids buy little, while poor forecasts make the cap expensive.
  • Auctioneers can loosen limits for convex package bids (minimum acceptance ratio 0) and keep tight limits only for nonconvex fill-or-kill bids, preserving tractability while reducing the missing-bids welfare loss.
  • The 24-bid cap on exclusive groups in European day-ahead auctions is an artifact of hourly flexi orders, not a computational necessity, so the paper's evidence supports raising it.

Reading between the lines

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

  • The paper leaves implicit an operational rule for setting the bid cap: auctioneers could keep increasing the limit until the marginal Wasserstein-based welfare gain falls below a threshold, using the same bound as a monitoring metric.
  • A natural extension is distributionally robust bid selection, replacing the true price distribution with an ambiguity set and deriving a robust analogue of Theorem 1; the total unimodularity result suggests such an extension would likely stay tractable.
  • The LP machinery is not electricity-specific and could transfer to any Walrasian-style market with uniform prices and XOR package bids, such as spectrum or transportation auctions, when participants have usable price forecasts.
  • The empirical evidence covers one bidding zone and one year; repeating the profit-loss curves on intraday auctions with 96 periods or on other zones would test whether the 'more scenarios help only if fresh' pattern generalizes.
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

3 major / 5 minor

Summary. The paper studies how a price-taking participant in a uniform-price combinatorial electricity auction should select XOR package bids when the auctioneer caps the number of bids per exclusive group. It proposes a stochastic bilevel model, argues that truthful bidding dominates, and claims that with a finite package set the selection problem can be solved as an LP because the constraint matrix is totally unimodular. For infinite package sets it proposes a heuristic (Algorithm 9) that generates scenario-optimal profiles and then selects B of them. The main theoretical result is a Wasserstein-distance bound on the expected profit loss of the simple strategy that submits one optimal profile per scenario. The paper also reports simulations for a thermal generator, a battery, and a flexible load in the German 2023 day-ahead market, and discusses OR bids, convex package bids, and portfolio bidding.

Significance. If the LP reformulation and the Wasserstein bound were fully established, the paper would offer a practically appealing polynomial-time method for package-bid selection and a quantitative link between price-forecast error and efficiency loss. The paper is explicit about its Walrasian-equilibrium assumptions, provides reproducible code, and makes a genuine attempt to connect auction design to real European market rules. However, the two main theoretical pillars are currently not established in the regime that motivates the paper: Theorem 1 covers only the non-binding case S ≤ B, while the simulations and the recommended algorithm operate in the binding case S > B, and the total-unimodularity proof in Proposition 2 is demonstrably incorrect. The contribution is therefore conditional on substantial revision.

major comments (3)
  1. [Section 3, Theorem 1] The theorem bounds the expected profit loss of the simple strategy (5), which is only feasible when B ≥ S, as stated in Section 2.3. In the paper's main motivating regime, where the bid cap binds, Section 4.4 uses B = 24 with S = 50, 100, 200, and 400, and the recommended algorithm (9) is used instead. Thus Theorem 1 does not bound the loss caused by a binding bid cap; it bounds only the loss from approximating the true price distribution P by the scenario distribution Q when the agent may submit all S scenario-optimal profiles. The abstract's and Section 1's claim of an upper bound on the profit loss caused by the limit on the number of bids is therefore not supported in the B < S regime. The authors should either restrict the claim explicitly to S ≤ B or prove a bound for the actual selection algorithm (8)/(9).
  2. [Section 2.4, Proposition 2] The proof of Proposition 2 asserts that the constraint matrix formed by (7c)-(7e) is totally unimodular. This assertion is false. For K = 1, S = 2, B = 1, the submatrix using rows (7c) for s = 1, (7d) for (k,s) = (1,1) and (1,2), and columns γ11, γ12, δ1 is [[1,1,0],[1,0,-1],[0,1,-1]], whose determinant is 2. Therefore the claimed equivalence between (8) and its LP relaxation is not established by the total-unimodularity argument, and the paper's central claim of a polynomial-time LP reformulation is unsupported. The authors need to provide a correct integrality proof for the selection polytope or revise the algorithmic and complexity claims. If the LP relaxation is not exact, Algorithm (9) as described may produce fractional package selections, and the simulation results in Section 4 would need to be re-examined.
  3. [Section 4] The simulation results in Figures 4-6 are obtained with Algorithm (9), which Section 2.5 explicitly states does not guarantee an optimal solution to the original infinite-package problem. There is no theorem connecting the empirical profit losses to the Wasserstein bound, and the experiments measure the heuristic's performance on a finite candidate set rather than the economic loss from a binding bid cap. The paper should state this limitation in Section 4 and avoid presenting the numbers as validation of Theorem 1.
minor comments (5)
  1. [Appendix D, equation (17l)] The variable 'usj' in equation (17l) appears to be a typo for 'u_j' or 'u_t'; please correct it.
  2. [Appendix F, equation (19d)] Equation (19d) contains the string 'eT s=' which seems to be a formatting error; it should read 'e_T = E_0'.
  3. [Section 3.3, equation (12)] The Wasserstein distance definition has a typo: '∥λ1, λ2∥2' should be '∥λ1 − λ2∥2'.
  4. [Section 3, welfare aggregation] The passage from the per-agent surplus loss to a total welfare bound is informal; please provide the explicit aggregation formula, such as ∑_i L_i · d_W(P, Q_i) when agents have different Lipschitz constants and scenario distributions.
  5. [Section 4.3] Please specify whether the profit percentages in Figures 4-6 are averages over the same 100 sampled days for all curves, and add error bars or a measure of dispersion, since the differences between curves are often small.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the Wasserstein bound is a genuine Lipschitz/Wasserstein inequality, and the only self-citation is non-load-bearing; the main gap is a scope mismatch (B≥S vs B<S), not circularity.

full rationale

The derivation chain is self-contained: Section 2's tractability claim rests on a total-unimodularity argument invoked from Nemhauser and Wolsey (1988), an external textbook result, and the LP relaxation is not calibrated to any data that is later called a prediction. Theorem 1 is proved from the Lipschitz continuity of the indirect utility function and the ζ-structure of the Wasserstein distance, with no fitted parameter entering the bound; the bound is a genuine inequality rather than an identity forced by construction. The only overlapping self-citation is Hübner (2025), used to support the equilibrium-price assumption as a real-world approximation, but that assumption is stated as an idealization and the theorem does not depend on it; the same point is also supported by Graf and Wozabal (2013) and Karasavvidis et al. (2024). A non-circular scope limitation is worth noting: Theorem 1 applies to strategy (5), which is feasible only when B ≥ S, whereas the simulations with binding bid caps (B=24 < S) use Algorithm (9), for which no theorem bounds the loss; this affects applicability, not circularity. Therefore no circular steps are identified.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

The central claims rest on explicit market-design assumptions (equilibrium, price-taking, most-profitable acceptance) and, for the infinite-package case, an unproven heuristic. No free parameters are fitted to the theoretical result. The paper introduces no new physical or economic entities; it uses existing bid formats such as XOR, OR, and minimum acceptance ratios.

free parameters (1)
  • Case-study asset parameters (thermal costs, battery limits, heating utility values) = Listed in Table 1
    Hand-chosen inputs for the three illustrative agents. They determine the simulation numbers but are not fitted to the target result and do not enter the LP reformulation or the Wasserstein bound.
assumptions (6)
  • domain assumption Walrasian equilibria exist and no agent has market power in the day-ahead auction
    Stated in Section 1: 'we assume those two ideals are true: (i) Walrasian equilibria exist, and (ii) no agent has market power.' This underpins the acceptance rule (1), the truthful-bidding argument, and the welfare-loss interpretation.
  • domain assumption The auctioneer accepts the bid maximizing pb - <λ,xb> for each agent at the uniform price (most-profitable-bid rule)
    Equation (1) in Section 2.1. Deviations in EUPHEMIA (paradoxically rejected bids) are treated as negligible, with supporting statistics from NEMO Committee (2024a).
  • domain assumption The agent is risk-neutral and maximizes expected profit over a finite scenario set with known probabilities
    Section 2.1. A CVaR extension appears in Appendix C, but the main analysis and the Wasserstein bound assume risk neutrality.
  • domain assumption Truthful bidding pb=v(xb) is weakly dominant, so the single-level program (4) is equivalent to the bilevel program (2)
    Proposition 1 in Section 2.2. The proof relies on the most-profitable-bid rule and price-taking behavior; the equivalence is used to justify the LP reformulation.
  • domain assumption The feasible set of power profiles is bounded, so L in Theorem 1 is finite
    Theorem 1 defines L=2 max||x|| over feasible x. Boundedness is not stated explicitly in the theorem but is physically natural and required for a nontrivial bound.
  • ad hoc to paper For the infinite-package heuristic (9), the S scenario-optimal profiles contain a good enough approximation to the unrestricted optimum
    Section 2.5 states the hybrid approach 'does not guarantee an optimal solution to (2)'. The simulations rely on this heuristic without an optimality gap or a bound for the B<S cases.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Package Bids in Combinatorial Electricity Auctions: Selection, Welfare Losses, and Alternatives." pith.science (2026). https://pith.science/paper/2MALMCQS

@misc{pith2026250209420,
  author       = {Pith},
  title        = {Pith review of: Package Bids in Combinatorial Electricity Auctions: Selection, Welfare Losses, and Alternatives},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2MALMCQS}},
  note         = {Machine review of arXiv:2502.09420}
}
read the original abstract

A key challenge in combinatorial auctions is designing bid formats that accurately capture agents' preferences while remaining computationally feasible. This is especially true for electricity auctions, where complex preferences complicate straightforward solutions. In this context, we examine the XOR package bid, the default choice in combinatorial auctions and adopted in European day-ahead and intraday auctions under the name "exclusive group of block bids". Unlike parametric bid formats often employed in US power auctions, XOR package bids are technology-agnostic, making them particularly suitable for emerging demand-side participants. However, the challenge with package bids is that auctioneers must limit their number to maintain computational feasibility. As a result, agents are constrained in expressing their preferences, potentially lowering their surplus and reducing overall welfare. To address this issue, we propose decision support algorithms that optimize package bid selection, evaluate welfare losses resulting from bid limits, and explore alternative bid formats. In our analysis, we leverage the fact that electricity prices are often fairly predictable and, at least in European auctions, tend to approximate equilibrium prices reasonably well. Our findings offer actionable insights for both auctioneers and bidders.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

52 extracted references · 51 canonical work pages

  1. [1]

    E. K. Aasg rd, S.-E. Fleten, M. Kaut, K. Midthun, and G. A. Perez-Valdes. Hydropower bidding in a multi-market setting. Energy Systems, 10: 0 543--565, 2019

    work page 2019

  2. [2]

    Adelowo and M

    J. Adelowo and M. Bohland. Redesigning automated market power mitigation in electricity markets. International Journal of Industrial Organization, 97: 0 103108, 2024

    work page 2024

  3. [3]

    Adomavicius, A

    G. Adomavicius, A. Gupta, and M. Yang. Bidder support in multi-item multi-unit continuous combinatorial auctions: A unifying theoretical framework. Information Systems Research, 33 0 (4): 0 1174--1195, 2022

    work page 2022

  4. [4]

    Ahlqvist, P

    V. Ahlqvist, P. Holmberg, and T. Tanger s. A survey comparing centralized and decentralized electricity markets. Energy Strategy Reviews, 40: 0 100812, 2022

    work page 2022

  5. [5]

    M. S . Ahunbay, M. Bichler, and J. Kn \"o rr. Pricing optimal outcomes in coupled and non-convex markets: Theory and applications to electricity markets. Operations Research, Ahead of Print, 2024

    work page 2024

  6. [6]

    E. M. Azevedo and E. Budish. Strategy-proofness in the large. The Review of Economic Studies, 86 0 (1): 0 81--116, 2019

    work page 2019

  7. [7]

    Bichler, V

    M. Bichler, V. Fux, and J. Goeree. A matter of equality: Linear pricing in combinatorial exchanges. Information Systems Research, 29 0 (4): 0 1024--1043, 2018

    work page 2018

  8. [8]

    Bichler, P

    M. Bichler, P. Milgrom, and G. Schwarz. Taming the communication and computation complexity of combinatorial auctions: the fuel bid language. Management Science, 69 0 (4): 0 2217--2238, 2023

    work page 2023

Show all 52 references
  1. [9]

    L. Bobo, L. Mitridati, J. A. Taylor, P. Pinson, and J. Kazempour. Price-region bids in electricity markets. European Journal of Operational Research, 295 0 (3): 0 1056--1073, 2021

    2021

  2. [10]

    Burger, J

    S. Burger, J. P. Chaves- \'A vila, C. Batlle, and I. J. P \'e rez-Arriaga. A review of the value of aggregators in electricity systems. Renewable and Sustainable Energy Reviews, 77: 0 395--405, 2017

    2017

  3. [11]

    Byers and B

    C. Byers and B. Eldridge. Auction designs to increase incentive compatibility and reduce self-scheduling in electricity markets. arXiv preprint, 2023

    2023

  4. [12]

    Caprara, M

    A. Caprara, M. Carvalho, A. Lodi, and G. J. Woeginger. A study on the computational complexity of the bilevel knapsack problem. SIAM Journal on Optimization, 24 0 (2): 0 823--838, 2014

    2014

  5. [13]

    Carri \'o n and J

    M. Carri \'o n and J. M. Arroyo. A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem. IEEE Transactions on power systems, 21 0 (3): 0 1371--1378, 2006

    2006

  6. [14]

    De Vivero-Serrano, K

    G. De Vivero-Serrano, K. Bruninx, and E. Delarue. Implications of bid structures on the offering strategies of merchant energy storage systems. Applied Energy, 251: 0 113375, 2019

    2019

  7. [15]

    Transparency Platform , 2024

    ENTSO-E . Transparency Platform , 2024. A vailable online: https://transparency.entsoe.eu/

    2024

  8. [16]

    Market Rules , 2024

    EpexSpot . Market Rules , 2024. A vailable online: https://www.epexspot.com/en/downloads

    2024

  9. [17]

    Fleten and T

    S.-E. Fleten and T. K. Kristoffersen. Stochastic programming for optimizing bidding strategies of a nordic hydropower producer. European Journal of Operational Research, 181 0 (2): 0 916--928, 2007

    2007

  10. [18]

    Goetzendorff, M

    A. Goetzendorff, M. Bichler, P. Shabalin, and R. W. Day. Compact bid languages and core pricing in large multi-item auctions. Management Science, 61 0 (7): 0 1684--1703, 2015

    2015

  11. [19]

    Graf and D

    C. Graf and D. Wozabal. Measuring competitiveness of the epex spot market for electricity. Energy Policy, 62: 0 948--958, 2013

    2013

  12. [20]

    C. Graf, F. Quaglia, and F. A. Wolak. Simplified market mechanisms for non-convex markets: Evidence from italian electricity market. Working Paper Stanford University, 2023

    2023

  13. [21]

    C. Graf, T. Kuppelwieser, and D. Wozabal. Frequent auctions for intraday electricity markets. The Energy Journal, 45 0 (1): 0 231--256, 2024

    2024

  14. [22]

    a chele, and F. Kr \

    O. Grothe, F. K \"a chele, and F. Kr \"u ger. From point forecasts to multivariate probabilistic forecasts: The schaake shuffle for day-ahead electricity price forecasting. Energy Economics, 120: 0 106602, 2023

    2023

  15. [23]

    Hammami, M

    F. Hammami, M. Rekik, and L. C. Coelho. Exact and hybrid heuristic methods to solve the combinatorial bid construction problem with stochastic prices in truckload transportation services procurement auctions. Transportation Research Part B: Methodological, 149: 0 204--229, 2021

    2021

  16. [24]

    Herrero, P

    I. Herrero, P. Rodilla, and C. Batlle. Evolving bidding formats and pricing schemes in usa and europe day-ahead electricity markets. Energies, 13 0 (19): 0 5020, 2020

    2020

  17. [25]

    H \"u bner

    T. H \"u bner. Approximate equilibria in nonconvex markets: Theory and evidence from european electricity auctions. arXiv preprint arXiv:2503.02464, 2025

    2025 arXiv

  18. [26]

    Jha and F

    A. Jha and F. A. Wolak. Can forward commodity markets improve spot market performance? evidence from wholesale electricity. American Economic Journal: Economic Policy, 15 0 (2): 0 292--330, 2023

    2023

  19. [27]

    Karasavvidis, D

    M. Karasavvidis, D. Papadaskalopoulos, and G. Strbac. Optimal offering of a power producer in electricity markets with profile and linked block orders. IEEE Transactions on Power Systems, 37 0 (4): 0 2704--2719, 2021

    2021

  20. [28]

    Karasavvidis, D

    M. Karasavvidis, D. Papadaskalopoulos, and G. Strbac. Optimal offering of energy storage in electricity markets with loop blocks. IEEE Transactions on Power Systems, 39 0 (1): 0 299--315, 2023

    2023

  21. [29]

    Karasavvidis, D

    M. Karasavvidis, D. Papadaskalopoulos, and G. Strbac. Optimal bidding of flexible demand in electricity markets with block orders. IEEE Transactions on Energy Markets, Policy and Regulation, Early Access, 2024

    2024

  22. [30]

    Kleinert, M

    T. Kleinert, M. Labb \'e , I. Ljubi \'c , and M. Schmidt. A survey on mixed-integer programming techniques in bilevel optimization. EURO Journal on Computational Optimization, 9: 0 100007, 2021

    2021

  23. [31]

    J. Lago, G. Marcjasz, B. De Schutter, and R. Weron. Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark. Applied Energy, 293: 0 116983, 2021

    2021

  24. [32]

    Y. Liu, J. T. Holzer, and M. C. Ferris. Extending the bidding format to promote demand response. Energy Policy, 86: 0 82--92, 2015

    2015

  25. [33]

    L \"o hndorf and D

    N. L \"o hndorf and D. Wozabal. The value of coordination in multimarket bidding of grid energy storage. Operations Research, 71 0 (1): 0 1--22, 2023

    2023

  26. [34]

    L \"o hndorf, D

    N. L \"o hndorf, D. Wozabal, and S. Minner. Optimizing trading decisions for hydro storage systems using approximate dual dynamic programming. Operations Research, 61 0 (4): 0 810--823, 2013

    2013

  27. [35]

    Mas-Colell, M

    A. Mas-Colell, M. D. Whinston, J. R. Green, et al. Microeconomic theory. Oxford University Press, New York, 1995

    1995

  28. [36]

    P. Milgrom. Discovering prices: auction design in markets with complex constraints. Columbia University Press, 2017

    2017

  29. [37]

    Milgrom and M

    P. Milgrom and M. Watt. Walrasian mechanisms for non-convex economies and the bound-form first welfare theorem. Working Paper Stanford University, 2024

    2024

  30. [38]

    G. L. Nemhauser and L. A. Wolsey. Integer and combinatorial optimization. John Wiley & Sons, 1988

    1988

  31. [39]

    CACM Annual Report 2023 , 2024 a

    NEMO Committee . CACM Annual Report 2023 , 2024 a . A vailable online: https://www.nemo-committee.eu/assets/files/cacm-annual-report-2023.pdf

    2023

  32. [40]

    EUPHEMIA Public Description , 2024 b

    NEMO Committee . EUPHEMIA Public Description , 2024 b . A vailable online: https://www.nemo-committee.eu/assets/files/euphemia-public-description.pdf

    2024

  33. [41]

    N. Nisan. Bidding languages. Combinatorial auctions, pages 400--420, 2006

    2006

  34. [42]

    Peke c and M

    A. Peke c and M. H. Rothkopf. Combinatorial auction design. Management science, 49 0 (11): 0 1485--1503, 2003

    2003

  35. [43]

    S. T. Rachev. The Methods of Distances in the Theory of Probability and Statistics. Springer New York, 1st edition, 2013

    2013

  36. [44]

    S. J. Rassenti, V. L. Smith, and R. L. Bulfin. A combinatorial auction mechanism for airport time slot allocation. The Bell Journal of Economics, pages 402--417, 1982

    1982

  37. [45]

    M. Reguant. Complementary bidding mechanisms and startup costs in electricity markets. The Review of Economic Studies, 81 0 (4): 0 1708--1742, 2014

    2014

  38. [46]

    R. T. Rockafellar and S. Uryasev. Optimization of conditional value-at-risk. Journal of Risk, 2: 0 21--42, 2000

    2000

  39. [47]

    Ruhnau, L

    O. Ruhnau, L. Hirth, and A. Praktiknjo. Time series of heat demand and heat pump efficiency for energy system modeling. Scientific data, 6 0 (1): 0 1--10, 2019

    2019

  40. [48]

    Rujeerapaiboon, K

    N. Rujeerapaiboon, K. Schindler, D. Kuhn, and W. Wiesemann. Scenario reduction revisited: Fundamental limits and guarantees. Mathematical Programming, 191 0 (1): 0 207--242, 2022

    2022

  41. [49]

    Scheffel, G

    T. Scheffel, G. Ziegler, and M. Bichler. On the impact of package selection in combinatorial auctions: an experimental study in the context of spectrum auction design. Experimental Economics, 15: 0 667--692, 2012

    2012

  42. [50]

    R. M. Starr. Quasi-equilibria in markets with non-convex preferences. Econometrica: journal of the Econometric Society, pages 25--38, 1969

    1969

  43. [51]

    Stevens, A

    N. Stevens, A. Papavasiliou, and Y. Smeers. On some advantages of convex hull pricing for the european electricity auction. Energy Economics, 134: 0 107542, 2024

    2024

  44. [52]

    C. Villani. Optimal transport: old and new. Springer, 1st edition, 2009

    2009

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.