It is a common practice in the current literature of electricity markets to use game-theoretic approaches for strategic price bidding. However, they generally rely on the assumption that the strategic bidders have prior knowledge of rival bids, either perfectly or with some uncertainty. This is not necessarily a realistic assumption. This paper takes a different approach by relaxing such an assumption and exploits a no-regret learning algorithm for repeated games. In particular, by using the \emph{a posteriori} information about rivals' bids, a learner can implement a no-regret algorithm to optimize her/his decision making. Given this information, we utilize a multiplicative weight-update algorithm, adapting bidding strategies over multiple rounds of an auction to minimize her/his regret. Our numerical results show that when the proposed learning approach is used the social cost and the market-clearing prices can be higher than those corresponding to the classical game-theoretic approaches. The takeaway for market regulators is that electricity markets might be exposed to greater market power of suppliers than what classical analysis shows.
Control reserves are power generation or consumption entities that ensure balance of supply and demand of electricity in real-time. In many countries, they are operated through a market mechanism in which entities provide bids. The system operator determines the accepted bids based on an optimization algorithm. We develop the Vickrey-Clarke-Groves (VCG) mechanism for these electricity markets. We show that all advantages of the VCG mechanism including incentive compatibility of the equilibria and efficiency of the outcome can be guaranteed in these markets. Furthermore, we derive conditions to…
The connection between games and no-regret algorithms has been widely studied in the literature. A fundamental result is that when all players play no-regret strategies, this produces a sequence of actions whose time-average is a coarse-correlated equilibrium of the game. However, much less is known about equilibrium selection in the case that multiple equilibria exist. In this work, we study the convergence of no-regret bidding algorithms in auctions. Besides being of theoretical interest, bidding dynamics in auctions is an important question from a practical viewpoint as well. We study repea…
We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on the differences between day-ahead and real-time market prices; both prices, however, are random and unknown to market participants. An online learning algorithm is proposed to maximize the cumulative payoff over a finite number of trading sessions by allocating the trader's budget among his bids for K options in each session. It is shown that the proposed algorithm converges, with an almost optimal convergence rate, to the global optimal corresponding to t…
Recently the online advertising market has exhibited a gradual shift from second-price auctions to first-price auctions. Although there has been a line of works concerning online bidding strategies in first-price auctions, it still remains open how to handle budget constraints in the problem. In the present paper, we initiate the study for a buyer with budgets to learn online bidding strategies in repeated first-price auctions. We propose an RL-based bidding algorithm against the optimal non-anticipating strategy under stationary competition. Our algorithm obtains $\widetilde O(\sqrt T)$-regre…
We study a general class of repeated auctions, such as the ones found in electricity markets, as multi-agent games between the bidders. In such a repeated setting, bidders can adapt their strategies online based on the data observed in the previous auction rounds. Moreover, if no-regret algorithms are employed by the bidders to update their strategies, the game is known to converge to a coarse-correlated equilibrium, which generalizes the notion of Nash equilibrium to a probabilistic view of the auction state. Well-studied no-regret algorithms depend on the feedback information available at ev…
PRO-Bid: Pareto-Prioritized Regret Optimization for Constraint-Aware Generative Auto-Bidding
Dalian University of Technology Dalian China；Dalian University of Technology \& City University of Hong Kong Dalian China；Alibaba International Digital Commerce Group Hangzhou China；Dalian University of Technology；Dalian University of Technology \& City University of Hong Kong；Alibaba International Digital Commerce Group
The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Microsoft Research（微软研究院）
We consider the problem of bid prediction in repeated auctions and evaluate the performance of econometric methods for learning agents using a dataset from a mainstream sponsored search auction marketplace. Sponsored search auctions is a billion dollar industry and the main source of revenue of several tech giants. A critical problem in optimizing such marketplaces is understanding how bidders will react to changes in the auction design. We propose the use of no-regret based econometrics for bid prediction, modeling players as no-regret learners with respect to a utility function, unknown to t…
Optimal No-regret Learning in Repeated First-price Auctions
Center for Data Science, New York University（纽约大学数据科学中心）；Stern School of Business, New York University（纽约大学斯特恩商学院）；Department of Electrical Engineering, Stanford University（斯坦福大学电气工程系）
Convergence bidding, a.k.a., virtual bidding, has been widely adopted in wholesale electricity markets in recent years. It provides opportunities for market participants to arbitrage on the difference between the day-ahead market locational marginal prices and the real-time market locational marginal prices. Given the fact that convergence bids (CBs) have a significant impact on the operation of electricity markets, it is important to understand how market participants strategically select their CBs in real-world. We address this open problem with focus on the electricity market that is operat…
Tie-line scheduling in multi-area power systems in the US largely proceeds through a market-based mechanism called Coordinated Transaction Scheduling (CTS). We analyze this market mechanism through a game-theoretic lens. Our analysis characterizes the effect of market liquidity, market participants' forecasts about inter-area price spreads, transactions fees and coupling of CTS markets with up-to-congestion virtual transactions. Using real data, we empirically verify that CTS bidders can employ simple learning algorithms to discover Nash equilibria that support the conclusions drawn from equil…
We consider the problem of a single seller repeatedly selling a single item to a single buyer (specifically, the buyer has a value drawn fresh from known distribution $D$ in every round). Prior work assumes that the buyer is fully rational and will perfectly reason about how their bids today affect the seller's decisions tomorrow. In this work we initiate a different direction: the buyer simply runs a no-regret learning algorithm over possible bids. We provide a fairly complete characterization of optimal auctions for the seller in this domain. Specifically: - If the buyer bids according to EX…
This paper proposes a doubled-sided auction mechanism with price discrimination for social welfare (SW) maximization in the electricity and heating market. In this mechanism, energy service providers (ESPs) submit offers and load aggregators (LAs) submit bids to an energy trading center (ETC) to maximize their utility; in turn, the selfless ETC as an auctioneer leverages dis-criminatory price weights to regulate the behaviors of ESPs and LAs, which combines the individual benefits of each stakeholder with the overall social welfare to achieve the global optimum. Nash games are employed to desc…
A line of recent work provides welfare guarantees of simple combinatorial auction formats, such as selling m items via simultaneous second price auctions (SiSPAs) (Christodoulou et al. 2008, Bhawalkar and Roughgarden 2011, Feldman et al. 2013). These guarantees hold even when the auctions are repeatedly executed and players use no-regret learning algorithms. Unfortunately, off-the-shelf no-regret algorithms for these auctions are computationally inefficient as the number of actions is exponential. We show that this obstacle is insurmountable: there are no polynomial-time no-regret algorithms f…
In this paper, we study behavior of bidders in an experimental launch of a new advertising auction platform by Zillow, as Zillow switched from negotiated contracts to using auctions in several geographically isolated markets. A unique feature of this experiment is that the bidders in this market are real estate agents that bid on their own behalf, not using third-party intermediaries. To help bidders, Zillow also provided a recommendation tool that suggested a bid for each bidder. Our main focus in this paper is on the decisions of bidders whether or not to adopt the platform-provided bid reco…
We address online learning in complex auction settings, such as sponsored search auctions, where the value of the bidder is unknown to her, evolving in an arbitrary manner and observed only if the bidder wins an allocation. We leverage the structure of the utility of the bidder and the partial feedback that bidders typically receive in auctions, in order to provide algorithms with regret rates against the best fixed bid in hindsight, that are exponentially faster in convergence in terms of dependence on the action space, than what would have been derived by applying a generic bandit algorithm …
We study revenue optimization learning algorithms for repeated second-price auctions with reserve where a seller interacts with multiple strategic bidders each of which holds a fixed private valuation for a good and seeks to maximize his expected future cumulative discounted surplus. We propose a novel algorithm that has strategic regret upper bound of $O(\log\log T)$ for worst-case valuations. This pricing is based on our novel transformation that upgrades an algorithm designed for the setup with a single buyer to the multi-buyer case. We provide theoretical guarantees on the ability of a tra…
Spot electricity markets are considered under a Game-Theoretic framework, where risk averse players submit orders to the market clearing mechanism to maximise their own utility. Consistent with the current practice in Europe, the market clearing mechanism is modelled as a Social Welfare Maximisation problem, with zonal pricing, and we consider inflexible demand, physical constraints of the electricity grid, and capacity-constrained producers. A novel type of non-parametric risk aversion based on a defined worst case scenario is introduced, and this reduces the dimensionality of the strategy va…
Learning to Bid Optimally and Efficiently in Adversarial First-price Auctions
Courant Institute of Mathematical Sciences and the Center for Data Science, New York University（Courant数学科学研究所和数据科学中心，纽约大学）；Stern School of Business, New York University（商学院，纽约大学）；Department of Electrical Engineering, Stanford University（电气工程系，斯坦福大学）；Yahoo! Research at Verizon Media（Verizon Media的Yahoo!研究）
