Electricity procurement constitutes a significant share of operational costs for large electricity consumers, and thus exposure to extreme prices poses a substantial financial risk. This paper proposes a method to generate EUPHEMIA-compatible bids for flexible demand to enable their participation in the European day-ahead electricity market while minimizing risks. Two strategies are considered, resulting in two bid formats: hourly bids (HBs), representing flexibility via marginal price responsiveness through price-quantity pairs, and exclusive-group bids (EBs), representing flexibility via mutually exclusive operational schedules submitted at opportunity cost. Our method is evaluated on a hypothetical electrolyzer system and a real-world steel plant under different market conditions. Results show that the economic performance of each strategy depends on the operational characteristics of the load and market conditions. Under volatile market conditions, highly flexible systems achieve better economic outcomes with EBs, while less flexible systems with stronger intertemporal constraints perform better with HBs.
We consider the problem of co-optimized energy-reserve market clearing with state-of-charge (SoC) dependent bids from battery storage participants. While SoC-dependent bids capture storage's degradation and opportunity costs, such bids result in a non-convex optimization in the market clearing process. More challenging is the regulation reserve capacity clearing, where the SoC-dependent cost is uncertain as it depends on the unknown regulation trajectories ex-post of the market clearing. Addressing the nonconvexity and uncertainty in a multi-interval co-optimized real-time energy-reserve market, we introduce a simple restriction on the SoC-dependent bids along with a robust optimization formulation, transforming the non-convex market clearing under uncertainty into a standard convex piece-wise linear program and making it possible for large-scale storage integration. Under reasonable assumptions, we show that SoC-dependent bids yield higher profit for storage participants than that from SoC-independent bids. Numerical simulations demonstrate a 28%-150% profit increase of the proposed SoC-dependent bids compared with the SoC-independent counterpart.
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
Online Budgeted Matching (OBM) is a classic problem with important applications in online advertising, online service matching, revenue management, and beyond. Traditional online algorithms typically assume a small bid setting, where the maximum bid-to-budget ratio (κ) is infinitesimally small. While recent algorithms have tried to address scenarios with non-small or general bids, they often rely on the Fractional Last Matching (FLM) assumption, which allows for accepting partial bids when the remaining budget is insufficient. This assumption, however, does not hold for many applications with indivisible bids. In this paper, we remove the FLM assumption and tackle the open problem of OBM with general bids. We first establish an upper bound of 1-κon the competitive ratio for any deterministic online algorithm. We then propose a novel meta algorithm, called MetaAd, which reduces to different algorithms with first known provable competitive ratios parameterized by the maximum bid-to-budget ratio κ\in [0, 1]. As a by-product, we extend MetaAd to the FLM setting and get provable competitive algorithms. Finally, we apply our competitive analysis to the design learning-augmented algorithm
The rapid growth of battery energy storage in wholesale electricity markets calls for a deeper understanding of storage operators' bidding strategies and their market impacts. This study examines energy storage bidding data from the California Independent System Operator (CAISO) between July 1, 2023, and October 1, 2024, with a primary focus on economic withholding strategies. Our analysis reveals that storage bids are closely aligned with day-ahead and real-time market clearing prices, with notable bid inflation during price spikes. Statistical tests demonstrate a strong correlation between price spikes and capacity withholding, indicating that operators can anticipate price surges and use market volatility to increase profitability. Comparisons with optimal hindsight bids further reveal a clear daily periodic bidding pattern, highlighting extensive economic withholding. These results underscore potential market inefficiencies and highlight the need for refined regulatory measures to address economic withholding as storage capacity in the market continues to grow.
Over the past decade, bidding in power markets has attracted widespread attention. Reinforcement Learning (RL) has been widely used for power market bidding as a powerful AI tool to make decisions under real-world uncertainties. However, current RL methods mostly employ low dimensional bids, which significantly diverge from the N price-power pairs commonly used in the current power markets. The N-pair bidding format is denoted as High Dimensional Bids (HDBs), which has not been fully integrated into the existing RL-based bidding methods. The loss of flexibility in current RL bidding methods could greatly limit the bidding profits and make it difficult to tackle the rising uncertainties brought by renewable energy generations. In this paper, we intend to propose a framework to fully utilize HDBs for RL-based bidding methods. First, we employ a special type of neural network called Neural Network Supply Functions (NNSFs) to generate HDBs in the form of N price-power pairs. Second, we embed the NNSF into a Markov Decision Process (MDP) to make it compatible with most existing RL methods. Finally, experiments on Energy Storage Systems (ESSs) in the PJM Real-Time (RT) power market show
Data sharing is a key factor for ensuring reproducibility and transparency of scientific experiments, and neuroimaging is no exception. The vast heterogeneity of data formats and imaging modalities utilised in the field makes it a very challenging problem. In this context, the Brain Imaging Data Structure (BIDS) appears as a solution for organising and describing neuroimaging datasets. Since its publication in 2015, BIDS has gained widespread attention in the field, as it provides a common way to arrange and share multimodal brain images. Although the evident benefits it presents, BIDS has not been widely adopted in the field of MRI yet and we believe that this is due to the lack of a go-to tool to create and managed BIDS datasets. Motivated by this, we present the BIDS Toolbox, a web service to manage brain imaging datasets in BIDS format. Different from other tools, the BIDS Toolbox allows the creation and modification of BIDS-compliant datasets based on MRI data. It provides both a web interface and REST endpoints for its use. In this paper we describe its design and early prototype, and provide a link to the public source code repository.
In the context of energy market clearing, non-merchant assets are assets that do not submit bids but whose operational constraints are included. Integrating energy storage systems as non-merchant assets can maximize social welfare. However, the disconnection between consecutive market clearings poses challenges for market properties, and this is not well studied yet. We contribute to the literature on market clearing with non-merchant storage by proposing a market-clearing procedure that preserves desirable market properties, even under uncertainty. This approach is based on a novel representation of storage systems in which the energy available is discretized to reflect the different prices at which the storage system was charged. These prices are then included as virtual bids, establishing a link between different market clearings. We show that market clearing with such virtual linking bids has the advantage of guaranteeing cost recovery for market participants and can outperform traditional approaches in terms of social welfare.
We consider the process of bidding by electricity suppliers in a day-ahead market context where each supplier bids a linear non-decreasing function of her generating capacity with the goal of maximizing her individual profit given other competing suppliers' bids. Based on the submitted bids, the market operator schedules suppliers to meet demand during each hour and determines hourly market clearing prices. Eventually, this game-theoretic process reaches a Nash equilibrium when no supplier is motivated to modify her bid. However, solving the individual profit maximization problem requires information of rivals' bids, which are typically not available. To address this issue, we develop an inverse optimization approach for estimating rivals' production cost functions given historical market clearing prices and production levels. We then use these functions to bid strategically and compute Nash equilibrium bids. We present numerical experiments illustrating our methodology, showing good agreement between bids based on the estimated production cost functions with the bids based on the true cost functions. We discuss an extension of our approach that takes into account network congestio
In this article we propose a multi-zonal integrated energy-reserve market model. We assume that bidders may submit their demand and supply bids on the one hand in the form of conventional hourly step bids and block bids, which are cleared and paid according to market clearing prices (MCPs). On the other hand, suppliers may submit so called flexible production bids, while both suppliers and consumers may submit fill-or-kill type package-priced combined bids -- these bids are accepted if their acceptance implies an improvement in the resulting total social welfare, which the market clearing algorithm aims to optimize. The model includes network constraints for the nominal case (if no reserves are activated) and also for perturbed cases when the allocated reserves are activated.
Wholesale market participation of storage with state-of-charge (SoC) dependent bids results in a non-convex cost in a multi-interval economic dispatch, which requires a mixed-integer linear program in the market clearing. We show that the economic dispatch can be convexified to the standard linear program when the SoC-dependent bid satisfies the equal decremental-cost ratio (EDCR) condition. Such EDCR bids are shown to support individual rationalities of all market participants in both the day-ahead multi-interval economic dispatch under locational marginal pricing and the rolling-window look-ahead dispatch under temporal-locational marginal pricing in the real-time market. A numerical example is presented to demonstrate a higher profit margin with an SoC-dependent bid over that from an SoC-independent bid.
Auctions are now central to blockchain markets, settling NFT sales, token launches, DeFi liquidations, and arbitrage opportunities. Each on-chain bid is a public transaction whose inclusion is decided by a single consensus proposer per block. The proposer can observe pending bids, exclude competitors, and submit bids of their own, breaking the fairness guarantees of classical sealed-bid auctions. To enable latency-sensitive sealed-bid auctions in blockchain settings, we formalize four properties -- each necessary to prevent a concrete attack -- and design a protocol achieving all four: hiding bid contents, existence, and bidder identity until reveal (Hiding); counting all timely honest bids and rejecting late adversarial bids (Simultaneous Release); preventing silent withdrawal of committed bids (No Free Bid Withdrawal); and charging on-chain fees only to winners (Auction Participation Efficiency). Our protocol uses a timestamping oracle (instantiated with a committee of 2f_ts+1 timestampers) and a censorship-resistant inclusion predicate (instantiated using a FOCIL-based inclusion list), with only the winning bid settled on-chain. Our construction relies on two zero-knowledge proo
Generative Recommender Systems using semantic ids, such as TIGER (Rajput et al., 2023), have emerged as a widely adopted competitive paradigm in sequential recommendation. However, existing architectures are designed solely for semantic retrieval and do not address concerns such as monetization via ad revenue and incorporation of bids for commercial retrieval. We propose GEM-Rec, a unified framework that integrates commercial relevance and monetization objectives directly into the generative sequence. We introduce control tokens to decouple the decision of whether to show an ad from which item to show. This allows the model to learn valid placement patterns directly from interaction logs, which inherently reflect past successful ad placements. Complementing this, we devise a Bid-Aware Decoding mechanism that handles real-time pricing, injecting bids directly into the inference process to steer the generation toward high-value items. We prove that this approach guarantees allocation monotonicity, ensuring that higher bids weakly increase an ad's likelihood of being shown without requiring model retraining. Experiments demonstrate that GEM-Rec allows platforms to dynamically optimize
Auto-bidding is central to computational advertising, achieving notable commercial success by optimizing advertisers' bids within economic constraints. Recently, large generative models show potential to revolutionize auto-bidding by generating bids that could flexibly adapt to complex, competitive environments. Among them, diffusers stand out for their ability to address sparse-reward challenges by focusing on trajectory-level accumulated rewards, as well as their explainable capability, i.e., planning a future trajectory of states and executing bids accordingly. However, diffusers struggle with generation uncertainty, particularly regarding dynamic legitimacy between adjacent states, which can lead to poor bids and further cause significant loss of ad impression opportunities when competing with other advertisers in a highly competitive auction environment. To address it, we propose a Causal auto-Bidding method based on a Diffusion completer-aligner framework, termed CBD. Firstly, we augment the diffusion training process with an extra random variable t, where the model observes t-length historical sequences with the goal of completing the remaining sequence, thereby enhancing th
A \emph{bidding} game is played on a graph as follows. A token is placed on an initial vertex and both players are allocated budgets. In each turn, the players simultaneously submit bids that do not exceed their available budgets, the higher bidder moves the token, and pays the bid to the lower bidder. We focus on \emph{discrete}-bidding, which are motivated by practical applications and restrict the granularity of the players' bids, e.g, bids must be given in cents. We study, for the first time, discrete-bidding games with {\em mean-payoff} and {\em energy} objectives. In contrast, mean-payoff {\em continuous}-bidding games (i.e., no granularity restrictions) are understood and exhibit a rich mathematical structure. The {\em threshold} budget is a necessary and sufficient initial budget for winning an energy game or guaranteeing a target payoff in a mean-payoff game. We first establish existence of threshold budgets; a non-trivial property due to the concurrent moves of the players. Moreover, we identify the structure of the thresholds, which is key in obtaining compact strategies, and in turn, showing that finding threshold is in \NP~and \coNP even in succinctly-represented games
Online bidding is a classical problem in online decision-making, with applications in resource allocation, hierarchical clustering, and the analysis of approximation algorithms. We study its randomized learning-augmented variant, where an online algorithm generates a sequence of random bids while leveraging predictions from an oracle. We provide analytical upper and lower bounds on the optimal consistency $C$ as a function of the robustness $R$, which match when $R \geq 2.885$, effectively closing the gap left by previous work. The key technical ingredient is the notion of a bidding function, a novel abstraction that provides a unified framework for the design and analysis of randomized bidding strategies. We complement our theoretical results with an experimental application of randomized bidding to the incremental median problem, demonstrating the applicability of our algorithm in practical clustering settings.
We consider the problem of bidding in online advertising, where an advertiser aims to maximize value while adhering to budget and Return-on-Spend (RoS) constraints. Unlike prior work that assumes knowledge of the value generated by winning each impression ({e.g.,} conversions), we address the more realistic setting where the advertiser must simultaneously learn the optimal bidding strategy and the value of each impression opportunity. This introduces a challenging exploration-exploitation dilemma: the advertiser must balance exploring different bids to estimate impression values with exploiting current knowledge to bid effectively. To address this, we propose a novel Upper Confidence Bound (UCB)-style algorithm that carefully manages this trade-off. Via a rigorous theoretical analysis, we prove that our algorithm achieves $\widetilde{O}(\sqrt{T\log(|\mathcal{B}|T)})$ regret and constraint violation, where $T$ is the number of bidding rounds and $\mathcal{B}$ is the domain of possible bids. This establishes the first optimal regret and constraint violation bounds for bidding in the online setting with unknown impression values. Moreover, our algorithm is computationally efficient an
This paper proposes a novel method to generate bid bounds that can serve as offer caps for energy storage in electricity markets to help reduce system costs and regulate potential market power exercises. We derive the bid bounds based on a tractable multi-period economic dispatch chance-constrained formulation that systematically incorporates the uncertainty and risk preference of the system operator. The key analytical results verify that the bounds effectively cap storage bids across all uncertainty scenarios with a guaranteed confidence level. We show that bid bounds decrease as the state of charge increases but rise with greater netload uncertainty and risk preference. We test the effectiveness of the proposed pricing mechanism based on the 8-bus ISO-NE test system, including agent-based storage bidding models. Simulation results demonstrate that the proposed bid bounds effectively align storage bids with the social welfare objective and outperform existing deterministic bid bounds. Under 30% renewable capacity and 20% storage capacity, the bid bounds contribute to an average reduction of 0.17% in system cost, while increasing storage profit by an average of 10.16% across vario
Traditional auction theory posits that bid value exhibits a positive correlation with the probability of securing the auctioned object in ascending auctions. However, under uncertainty and incomplete information, as is characteristic in real-time advertising markets, truthful bidding may not always represent a dominant strategy or yield a Pure Strategy Nash Equilibrium. Real-Time Bidding (RTB) platforms operationalize impression-level auctions via programmatic interfaces, where advertisers compete in first-price auction settings and often resort to bid shading, i.e., strategically submitting bids below their private valuations to optimize payoff. This paper empirically investigates bid shading behaviors and strategic adaptation using large-scale RTB auction data from the Yahoo Webscope dataset. Integrating Minority Game Theory with clustering algorithms and variance-scaling diagnostics, we analyze equilibrium bidding behavior across temporally segmented impression markets. Our results reveal the emergence of minority-based bidding strategies, wherein agents partition hourly ad slots into submarkets and place bids strategically where they anticipate being in the numerical minority.
Auto-bidding has become a cornerstone of modern online advertising platforms, enabling many advertisers to automate bidding at scale and optimize campaign performance. However, prevailing industrial systems rely on single-agent auto-bidding methods that are scalable but overlook the strategic interdependence among advertisers' bids, leading to unstable or suboptimal outcomes. While recent works recognize the game-theoretic nature of auto-bidding, existing approaches remain either computationally intractable at scale or lack a principled equilibrium-selection that aligns with platform-wide objectives. In this paper, we bridge this gap by introducing Nash Equilibrium-Constrained Bidding (NCB), a principled and scalable auto-bidding framework that recasts auto-bidding as a platform-wide optimization problem subject to Nash equilibrium constraints. This approach accounts for fine-grained strategic interdependencies among advertisers, ensuring both agent-level stability and ecosystem-level optimality. Notably, we develop a theoretically sound penalty-based primal-dual gradient method with rigorous convergence guarantees, supported by an efficient algorithm suitable for industrial deploy