Equilibrium Bidding Research Articles

Market power detection and mitigation measures for the spot electricity market based on bidding equilibrium

The spot electricity market (SEM) faces the challenge of inefficiency problems from market power (MP) abuse. However, previous studies have not adequately addressed such issues as the feasibility of MP mitigation measurements and authenticity of MP detection indicators. In this study, mitigation methods are developed, and MP detection indicators are designed to detect and mitigate the exercise of MP in an SEM in which multiple generators compete unilaterally through a uniform marginal clearing price mechanism. First, the incentives and general rules for rational generators to exercise their MP are analysed, providing theoretical support for the developed approaches. Then, two mechanisms that can mitigate the exercise of MP are devised by limiting the bid increase rate and maximising the consumer surplus. Furthermore, a behavioural detection indicator is designed to measure the MP of an individual generator, while an overall indicator is defined to assess the MP of an entire market. Finally, a joint clearing model is established to help implement the mechanism while promoting a high proportion of renewable energy consumption in the SEM. Case studies demonstrate the effectiveness and feasibility of the proposed approaches.

Risk aversion in first-price security-bid auctions

We study how risk aversion affects equilibrium bidding strategies in a first-price security-bid auction. We show that if the bidder's expected utility is concave and their marginal expected utility decreases as the degree of risk aversion increases – conditions that are shown to be satisfied under some conditions for four prominent securities (cash, equity, debt, and call option) –, the increase in the degree of risk aversion leads to lower bids in equilibrium.

Optimization Decomposition of Monthly Contracts for Integrated Energy Service Provider Considering Spot Market Bidding Equilibria

Under the current power trading model, especially in the context of the large-scale penetration of renewable energy and the rapid integration of renewable energy into the power system, reasonable medium- and long-term decomposition can reduce the fluctuation in the energy price when the integrated energy service provider (IESP) participates in the spot market. It helps to avoid the price risk of the spot market. Additionally, it promotes the optimization of the operation of the regional energy day-ahead scheduling. At the present stage, most of the medium- and long-term contract decomposition methods focus on the decomposition of a single power and take less consideration of the bidding space in the spot market. This limitation makes it challenging to achieve efficient interaction and interconnection among multi-energy resources and smooth integration between the medium- and long-term market and the spot market. To address these issues, this paper proposes an optimal monthly contract decomposition method for IESPs that takes into account the equilibrium of spot bidding. First, the linking process and rolling framework of multi-energy transactions between the medium- and long-term market and the spot market are designed. Second, an optimal decomposition model for monthly contracts is constructed, and a daily decomposition method for monthly medium- and long-term contracts that accounts for the spot bidding equilibrium is proposed. Then, the daily preliminary decomposition result of medium- and long-term multi-energy contracts is used as the boundary condition of the day-ahead scheduling model, and the coupling characteristics of the multi-energy networks of electricity, gas, and heat are taken into account, as well as the operational characteristics. Then, considering the coupling characteristics and operating characteristics of electricity, gas, and heat networks, the optimal scheduling model of a multi-energy network is constructed to minimize the sum of cumulative daily operating costs, and the monthly final contract decomposition value and daily spot bidding space are derived. Finally, examples are calculated to verify the validity of the decomposition model, and the examples show that the proposed method can reduce the variance in spot energy purchase by about 4.64%, and, at the same time, reduce the cost of contract decomposition by about USD 0.33 million.

Micro-grid tri-level EPEC based model for finding equilibria in the day-ahead and balancing markets

This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.

Toeholds and information quality in common‐value takeover auctions

AbstractIn this article I analyze the effect of the sensitivity of firm value on the information available to potential acquirers in common‐value takeover auctions with toeholds. I show that the quality of information does not affect equilibrium when bidders have equal toeholds but has a significant effect when toeholds are different. My article demonstrates that increasing the relative information quality of the bidder with a smaller toehold makes both bidders bid more aggressively and leads to a higher price. I also analyze the combined effect of toeholds and information quality on equilibrium bidding strategies and discuss ways target shareholders can increase the expected final price.

Equilibrium bidding and expected revenue ranking when bidders have outside options

Equilibrium bidding and expected revenue ranking when bidders have outside options

Auction-based parking mechanisms considering withdrawal behaviors

Auction-based parking mechanisms (ABPM) have been recognized as promising solutions to the parking problem. As the operator of the ABPM, the parking platform should not only be well-operated to provide parking services for demanders in need but also maintain commercial viability for sustainable operations. Motivated by this, we propose three ABPMs, namely, the ABPM without withdrawal right, the ABPM with costless withdrawal right, and the ABPM with non-free withdrawal right. Particularly, we characterize the parking demanders' withdrawal behaviors in the ABPMs. This behavior is motivated by the demanders' negative utilities derived from the auction sequence, where the demanders will first submit bid prices and are then allowed to withdraw from the parking market after the announcement of auction results when they are aware of their true valuations. We derive the equilibrium bidding strategies and the platform's expected revenues under the above three mechanisms and compare them in terms of the analytical results. It has been found that the introduction of withdrawal right will stimulate demanders to raise their bids for winning and the ABPM with non-free withdrawal right generates the highest revenue under certain conditions. A case study of parking in Beijing Financial Street has been conducted to illustrate the findings and explore managerial implications, including adapting the ABPM with non-free withdrawal right, narrowing the parking supply-demand gap, and enhancing travel experiences on the way to parking.

Boundedly rational bidding decision for land auctions during the transformation of real estate markets

Real estate developers in China exhibit different boundedly rational behaviors when bidding in different land auction formats, resulting in deviation from fully rational bidding, and the transformation of China’s real estate industry has intensified this deviation. To address this problem, this study establishes a reference utility model and a subjective decision probability model under the framework of incomplete information game to characterize developers’ utility distortion and winning probability distortion in open-bid auctions and sealed-bid auctions for land, respectively. The results show that the deviation between bounded rational bidding and fully rational bidding increases as developer competition intensifies. The equilibrium bidding of cost-disadvantaged developers in the boundedly rational model deviates less from the standard model. Moreover, in sealed-bid auctions, the "hiding degree" of cost-advantaged developers is greater, showing size effects, while the bids in open-bid auctions are more complex and affected by market conditions and developers’ risk preferences. Thus, this study characterizes boundedly rational bidding in land auctions and interprets the deviation from fully rational bidding, which can provide a more real basis for land auction mechanism design.

Comparisons of standard royalty auctions with seller post-auction effort

This study considers standard royalty auctions, in which each bidder’s valuation is determined endogenously by his type and the seller’s post-auction effort. We first characterize the unique symmetric separating D1 PBE of both sealed bid and ascending bid royalty auctions and compare them in terms of allocative efficiency, production efficiency, and seller revenue. We then show that no symmetric (semi-) pooling PBE survives the D1 criterion in these auctions (under mild conditions). Furthermore, we explore each bidder’s equilibrium bidding strategy, the associated efficiency and revenue, under a second-price royalty auction without disclosing the winning bid. We also consider a scenario where the seller adopts an entry fee instead of a reserve price to maximize their expected payoff. Finally, we examine the robustness of revenue ranking with respect to general forms of value creation.

Nontruthful Position Auctions Are More Robust to Misspecification

We consider the classical model of sponsored search due to Edelman et al. and Varian and examine how robust standard position auctions are to a misspecification of the position-dependent quality factors used by this model. We show that under both complete and incomplete information a nontruthful position auction admits an efficient equilibrium for a strictly broader range of parameter values than the Vickrey-Clarke-Groves (VCG) mechanism, which would be truthful if the parameters were specified correctly. Our result for complete information concerns the generalized second-price (GSP) mechanism and is driven by a detailed understanding of the Nash equilibrium polytopes of the VCG mechanism and the GSP mechanism. Our result for incomplete information concerns the generalized first-price (GFP) mechanism and uses a surprising connection between the unique candidate equilibrium bidding functions of the VCG mechanism and the GFP mechanism. Funding: F. Fischer was supported by the Engineering and Physical Sciences Research Council [Grant EP/T015187/1] and Einstein Stiftung Berlin.

Contextual Standard Auctions with Budgets: Revenue Equivalence and Efficiency Guarantees

The internet advertising market is a multibillion dollar industry in which advertisers buy thousands of ad placements every day by repeatedly participating in auctions. An important and ubiquitous feature of these auctions is the presence of campaign budgets, which specify the maximum amount the advertisers are willing to pay over a specified time period. In this paper, we present a new model to study the equilibrium bidding strategies in standard auctions, a large class of auctions that includes first and second price auctions, for advertisers who satisfy budget constraints on average. Our model dispenses with the common yet unrealistic assumption that advertisers’ values are independent and instead assumes a contextual model in which advertisers determine their values using a common feature vector. We show the existence of a natural value pacing–based Bayes–Nash equilibrium under very mild assumptions. Furthermore, we prove a revenue equivalence showing that all standard auctions yield the same revenue even in the presence of budget constraints. Leveraging this equivalence, we prove price of anarchy bounds for liquid welfare and structural properties of pacing-based equilibria that hold for all standard auctions. In recent years, the internet advertising market has adopted first price auctions as the preferred paradigm for selling advertising slots. Our work, thus, takes an important step toward understanding the implications of the shift to first price auctions in internet advertising markets by studying how the choice of the selling mechanism impacts revenues, welfare, and advertisers’ bidding strategies. This paper was accepted by Itai Ashlagi, revenue management and market analytics. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2023.4719 .

A method for identifying parameterizations of the Compensation election and Quadratic voting that admit pure-strategy equilibria

The recent birth and proliferation of online digital community platforms have led to an increased interest in more efficient voting mechanisms than simple yes–no majority voting. Quadratic voting and the Compensation election have shown some promise in the laboratory, however some gaps still remain in our understanding of the strategic features of these mechanisms. Using proof by example and the properties of infinitely divisible distributions, we develop a procedure for generating parameterizations of these voting mechanisms that admit Pure Strategy Bayes–Nash equilibria (PSBNE). We illustrate the equilibrium bid (or voting) functions graphically and derive their linear approximations.

Loss aversion in sequential auctions

I analyze sequential auctions with expectations‐based loss‐averse bidders who have independent private values and unit demand. Equilibrium bids are history dependent and subject to a “discouragement effect”: the higher is the winning bid in the current round, the less aggressive are the bids of the remaining bidders in the next round. Moreover, because they experience a loss in each round in which they fail to obtain an object, bidders are willing to pay a premium to win sooner rather than later. This desire to win earlier leads prices to decline in equilibrium. I also show how various disclosure policies regarding the outcome of earlier auctions affect equilibrium bids, and that sequential and simultaneous auctions are neither bidder‐payoff equivalent nor revenue equivalent.

Decentralized payment clearing using blockchain and optimal bidding

In this paper, we construct a decentralized clearing mechanism which endogenously and automatically provides a claims resolution procedure. This mechanism can be used to clear a network of obligations through blockchain. In particular, we investigate default contagion in a network of smart contracts cleared through blockchain. In so doing, we provide an algorithm which constructs the blockchain so as to guarantee the payments can be verified and the miners earn a fee. We, additionally, consider the special case in which the blocks have unbounded capacity to provide a simple equilibrium clearing condition for the terminal net worths; existence and uniqueness are proven for this system. Finally, we consider the optimal bidding strategies for each firm in the network so that all firms are utility maximizers with respect to their terminal wealths. We show that a pure strategy Nash equilibrium need not exist, and then look for mixed Nash equilibrium bidding strategies. The implications of these strategies, and more broadly blockchain, on systemic risk are considered.

Entry in first-price auctions with signaling

We study the optimal entry fee in a symmetric private value first-price auction with signaling, in which the participation decisions and the auction outcome are used by an outside observer to infer the bidders’ types. We show that this auction has a unique fully separating equilibrium bidding function. When the bidders’ sensibility for the signaling concern is sufficiently strong, the expected revenue maximizing entry fee is the maximal fee that guarantees full participation. The larger is the bidder’s sensibility, the higher is the optimal participation.

A Conceptual Analysis of Equilibrium Bidding Strategy in a Combined Oligopoly and Oligopsony Wholesale Electricity Market

This paper proposes a semi-analytical method to obtain the equilibrium bidding strategies for generation and demand units in a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">combined</i> oligopoly and oligopsony wholesale electricity market. Such market structure is the outcome of the increasing deployment of demand response programs that facilitate <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">active participation of demand-side players</i> in the price-setting process. In this analysis, the concept of supply function equilibrium (SFE) is used to investigate the oligopolistic competition among generation units. The SFE model is extended and the demand function equilibrium (DFE) is obtained to study the oligopsonistic competition among demand units. The economic behavior of a market participant is formulated as a bi-level programming (BLP) problem. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">imperfect competition</i> among generation units, as well as among demand units, are modeled as a non-cooperative game. Next, a direct method is developed to calculate all candidate equilibriums of the market, and the locational marginal prices (LMPs) in terms of the bidding strategies of the market participants. The BLP problem is solved by obtaining the coordinated Pareto-dominant Nash equilibrium of the market participants’ non-cooperative games. Finally, the proposed analysis is examined in case studies. Accordingly, we report <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">insightful observations</i> with respect to the impact of the changes in the new market structure, at firm-level and market-level, such as in terms of mitigating market power of generation units, the market clearing prices and quantities, surplus for generation units and demand units, and potential impact on market efficiency.

Signalling in auctions for risk-averse bidders.

We study risk-averse equilibrium bidding in first-price and second-price sealed-bid auctions where bidders have signalling concerns, i.e., they care about how the auction outcome is interpreted by an outside observer. We find that when the winner’s identity and her payment are revealed to the outside observer, risk aversion yields less aggressive bidding behaviour in the second-price sealed-bid auction than in the risk-neutral case. Our analysis explains various revenue ranking reversals relative to the risk-neutral equilibrium observed in a recent experiment by Bos (2021).

The Strange Role of Information Asymmetry in Auctions—Does More Accurate Value Estimation Benefit a Bidder?

We study the second-price auction in which bidders have asymmetric information regarding the item’s value. Each bidder’s value for the item depends on a private component and a public component. While each bidder observes their own private component, they hold different and asymmetric information about the public component. We characterize the equilibrium of this auction game and study how the asymmetric bidder information affects their equilibrium bidding strategies. We also discover multiple surprisingly counter-intuitive equilibrium phenomena. For instance, a bidder may be better off if she is less informed regarding the public component. Conversely, a bidder may sometimes be worse off if she obtains more accurate estimation about the auctioned item. Our results suggest that efforts devoted by bidders to improve their value estimations, as widely seen in today’s online advertising auctions, may not always be to their benefit.

2PnS-EG: A general two-population n-strategy evolutionary game for strategic long-term bidding in a deregulated market under different market clearing mechanisms

Based on assumptions of bounded rationality and limited information, the evolutionary game theory (EGT) can well describe evolution rule of population behaviors and predict individuals’ decision behaviors. Therefore, this paper focuses on a general two-population n-strategy evolutionary game (2PnS-EG), especially for the general two-population three-strategy evolutionary game (2P3S-EG), and applies it to investigate the evolutionary equilibrium properties of long-term strategic bidding issues in deregulated homogeneous and heterogeneous power generation-side markets (PGMs) under different market clearing mechanisms. First, relative net payoff (RNP) parameters are defined for two types of PGMs. Then, based on RNP parameters, the long-term equilibrium characteristics of 2P3S-EG-based homogeneous PGM bidding are investigated in 4 cases based on theoretical analysis and dynamic simulation. Moreover, long-term evolutionarily stable equilibrium characteristics of 2P3S-EG based heterogeneous PGM bidding are investigated via qualitative analysis and dynamic simulation in the conditions of with and without government supervision, which are then further studied via quantitative analysis and dynamic simulation in two clearing mechanisms of MCP and PAB. Results reveal that MCP is more effective than PAB in guiding PGMs to evolve toward an expected and reasonable long-term evolutionarily stable bidding equilibrium state via adjusting the markets’ RNP parameters appropriately. Finally, the future development of EGT-based strategic bidding issues in PGM is discussed. Overall, the models, methods and conclusions of this paper are practicable and scalable to some extent, aiming to enrich research work on long-term bid equilibrium of PGM, and provide some ideas and theoretical reference for relevant departments and PGMs in competitive on-grid bidding with bounded rationality and limited information.

Bid signaling in first-price royalty auction

It is common that seller’s post-auction input affects winner’s valuation in the widely used royalty auctions. This study considers bidders’ signaling incentives and seller’s choice of reserve price in the first-price royalty auction. We first characterize the unique symmetric D1 PBE in which the quasi-separating bidding strategy can be decomposed into the equilibrium bid without signaling incentive and the signaling premium. The signaling premium increases in bidder’s type, indicating that a higher type has more incentive to raise bid to induce more effort from the seller. The optimal reserve price is lower than that under the post-auction complete information scenario, which leads to a more efficient allocation and a higher payoff for the seller. The optimal reserve price is non-monotonic in royalty rate while the seller’s equilibrium payoff increases in it, and full surplus extraction is obtained when the royalty rate approaches 100%.