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Risk Sensitivity and Firm Power: Price Competition with Mean2-Variance Profit Objective Under Multinomial Logit Demand Firms with varying degrees of risk sensitivity perceive the same stochastic profit prospect differently. It is important to understand the equilibrium pricing behaviors under risk aversion and their implications on firms' survival and market health. The authors identify a power index, which is the ratio of product attractiveness to risk sensitivity, and show that the set of profitable firms is power index ordered. Firms with a favorable power index value earn a positive profit in a price competition, and others are driven to zero profit. Interestingly, although high risk aversion handicaps a firm, this paper shows that moderate risk aversion may give a firm an advantage over an otherwise equivalent competitor that is less risk sensitive. The authors also establish that in an equilibrium with market entry and exit, the power index is generalized to the ratio of product attractiveness and an entry cost-adjusted risk sensitivity measure. This paper is the first in the literature to address a risk-sensitive price competition under the multinomial logit choice model, with each participating firm maximizing a risk-adjusted profit objective. We find that, at equilibrium, a subset of firms earns a positive profit, whereas others are driven to zero profit, contrasting with the risk-neutral equilibrium in which all firms earn a positive profit regardless of quality and cost. We identify a power index—the ratio of effective product attractiveness to risk sensitivity—and show that the set of profitable firms is power index ordered. Risk aversion drives firms toward a more aggressive equilibrium pricing strategy and intensifies competition. However, the relative profit impact across firms is not monotone; although high risk aversion handicaps a firm, moderate risk aversion may place a firm at an advantage over an otherwise equivalent competitor that is less risk sensitive, contrary to intuition. In an equilibrium with market entry cost, we show that the set of active firms at equilibrium follows a generalized power index order that depends on entry cost. Furthermore, although the power index is decreasing in risk aversion, the generalized power index may initially be increasing in risk aversion. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2466. [ABSTRACT FROM AUTHOR]

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. • Parking demanders' endogenous withdrawal behaviors are modeled in the auction-based parking mechanism (ABPM). • Three ABPMs regarding the usage of withdrawal right are designed and compared under the market equilibrium framework. • The withdrawal right stimulates parking demanders to raise bids for winning. • The ABPM with non-free withdrawal right generates the highest revenue under certain conditions. • Managerial implications regarding boosting the parking platform's revenue are proposed. [ABSTRACT FROM AUTHOR]

Two-stage distributionally robust stochastic noncooperative games with continuous decision variables are studied. In such games, each player solves a two-stage distributionally robust optimization problem depending on the decisions of the other players. Existing studies in this area have been limited with strict assumptions, such as linear decision rules, and supposed that each player solves a two-stage linear distributionally robust optimization with a specifically structured ambiguity set. This limitation motivated us to generalize and analyze the game in a nonlinear case. The contributions of this study are (ⅰ) demonstrating the conditions for the existence of two-stage Nash equilibria under convexity and compactness assumptions, and (ⅱ) consideration of a two-stage distributionally robust Cournot–Nash competition as an application, as well as an investigation into the conditions for the existence of market equilibria in an economic sense. We also report some results of numerical experiments to illustrate how distributional robustness affects the decision of each player in the Cournot–Nash competition. [ABSTRACT FROM AUTHOR]

The business activity is inseparable from the support of documental information flow. In the past, the commercial documents needed a lot of time to get to the point-to-point, which could lead to problems, such as insecurity or the relatively long time. With the emergence of new technologies, it is possible to change this information transmission method to enable fast and accurate dissemination. For considering the possibility of technology adoption, this study investigates the role of blockchain service in term of market size and file circulation time. Specifically, we construct a game-theoretic model to find the equilibrium strategy from a manufacturer and two competing retailers. From the perspective of equilibrium, we investigate the results for market effects, economic effects, service effects, and service efficiency, respectively. Moreover, we also analyze the service strategy of retailers providing service by manufacturer, time sensitivity, and competitive intensity, respectively. Based on the above analysis, this study has obtained an equilibrium to support the commercial practice. In summary, this study has two contributions. On the one hand, we analyze the impact of the technological investment in blockchain service on asymmetric market scale competition. This result extends the application scope of blockchain service in the market. On the other hand, this study discusses the impact of time value on technology investment in blockchain service. Therefore, through the discussion of our study, the results show the value of blockchain service in information exchanges. [ABSTRACT FROM AUTHOR]

The paper presents a study of equilibrium in a two-sided market for network platforms with cross externalities between buyers and sellers. The proposed model is a generalization of Armstrong's (2006) monopoly model for the case of a duopoly in a two-sided market for network platforms located on a plane. The paper solves the problem of optimal pricing and investigates the question of the optimal location of platforms in the market, provided that the heterogeneous utility of agents of both groups (buyers and sellers) is formed taking into account the Hotelling specification with the Manhattan metric. [ABSTRACT FROM AUTHOR]

This paper proposes a semi-analytical method to obtain the equilibrium bidding strategies for generation and demand units in a combined oligopoly and oligopsony wholesale electricity market. Such market structure is the outcome of the increasing deployment of demand response programs that facilitate active participation of demand-side players 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 imperfect competition 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 insightful observations 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. [ABSTRACT FROM AUTHOR]

We study deferred acceptance algorithm (DA) with retrade by formulating a two-stage model where DA is played in the first stage, and a decentralized market opens in the second. Both non-monetary and monetary retrades are considered. Perfect market equilibrium (PME) is defined: market equilibrium prevails in the second stage both on and off the path, and Nash equilibrium is played in the first stage game induced by the second-stage markets. In the economies with no money, the stable and Pareto optimal allocation is the truthful PME allocation if and only if the priority structure is acyclical. A pure PME object allocation is unique if and only if the priority structure is unreversed. In the economies with money, an efficient PME allocation exists if and only if the minimum demand across tangible objects exceeds a certain threshold. A pure PME object allocation is always unique. • We study deferred acceptance algorithm (DA) with decentralized retrade. • Perfect market equilibrium (PME) is defined for economies with and without money. • With no money, a truthful PME exists iff the priority structure is acyclical. • A pure PME allocation is unique iff the priority structure is unreversed. • With money, any pure PME allocation is efficient iff demand is sufficient. [ABSTRACT FROM AUTHOR]

Autonomous ride-hailing platforms, such as Waymo and Cruise, are quickly expanding their services, but their interactions with the existing ride-hailing companies, such as Uber and Lyft, are rarely discussed. To fill this gap, this paper focuses on the competition between an emerging autonomous ride-hailing platform and a traditional ride-hailing platform by characterizing the equilibrium of their competition and the impact of technology transfer. In particular, we consider an autonomous ride-hailing platform that owns the AV technology and offers ride-hailing services to passengers through a fleet of AVs. In the meanwhile, it competes with a traditional ride-hailing platform that primarily relies on a fleet of human-driver vehicles (HDVs) but may rent a sub-fleet of AVs from the autonomous ride-hailing platform to complement the human-driver fleet (referred to as AV technology transfer). A game-theoretic model is formulated to characterize the competition between the autonomous ride-hailing platform and the traditional ride-hailing platform over a transportation network, encapsulating the passengers' mode choices, the drivers' job options, the network traffic flows and the strategic decisions of the platforms. An algorithm is proposed to compute the approximate Nash equilibrium of the game and conduct an ex-post evaluation on the performance of the obtained solutions. The proposed framework and solution algorithm are validated through a realistic case study for Manhattan. Based on numerical simulations, we find that technology transfer of AVs between the two platforms can lead to a win-win situation where both two platforms get a higher profit, but this comes at the cost of reduced surpluses for human drivers and passengers. In the simulation, a critical trade-off is revealed for the autonomous ride-hailing platform: it strategically forfeits some of its market share in ride-hailing services to encourage the traditional ride-hailing platform to rent more AVs, thereby increasing its rental revenue and consequently, the overall profit. Furthermore, we also find it intriguing that as AV technology improves and operational costs decrease, the traditional ride-hailing platform cannot enjoy any benefit in its profit although it has the option of leasing AVs from the autonomous ride-hailing platform at lower operational costs. Instead, it is compelled to rent a larger fleet of AVs from the autonomous ride-hailing platform at a higher rental price, consequently suffering a reduced profit. Conversely, the autonomous ride-hailing platform significantly benefits from the reduced AV operational cost by capturing a larger market share in the ride-hailing market and earning higher revenue from the AV technology transfer. • Investigated the competition between autonomous and traditional ride-hailing platforms. • A game-theoretic model to capture the incentives of players over transportation networks. • An algorithm is proposed to obtain an approximate Nash equilibrium. • Examined the impacts of AVs on traditional ride-hailing market under platform competition. [ABSTRACT FROM AUTHOR]

Our paper aims at introducing a moving-horizon interaction in a strategic context. We assume that, in each instant of time, players can predict the effects of their actions and those of their opponents on a finite moving horizon. We define an equilibrium concept, which is consistent in this setting, and develop an appropriate algorithm to compute it by using nonlinear model predictive control techniques. Focusing on the length of forecasting horizon, we propose two economic interpretations for our equilibrium, based on the limited rationality and political economy literature: a simple 2 players' nonlinear policy game, and what happens to debt stabilization when policymakers have different values of the forecasting horizon. To provide some practical insights of our approach, we consider a debt stabilization game in a monetary union. We consider three players; two nonlinear differential constraints; and assume that one player controls one instrument which is not additive but has some multiplicative effects on the state variables. [ABSTRACT FROM AUTHOR]

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Market makers choose and design market rules to serve certain objectives, such as to maximize revenue from the sales in the case of a single seller and multiple buyers. Given such rules, market participants play against each other to maximize their utility function values on goods acquired, possibly by hiding or misrepresenting their information needed in the implementation of market rules. Today's Internet economy has changed the information collection process and may make some of the assumptions of market rule implementation obsolete. Here we make a fresh review of works on this challenge on the Internet where new economic systems operate. [ABSTRACT FROM AUTHOR]

Platforms: How Much and What Should They Control? Platforms exert control in many ways: from determining which buyers are shown to which sellers to directly controlling allocation of aggregate supply across different consumer markets. How should platforms exercise control to increase social welfare? In "Transparency and Control in Platforms for Networked Markets," authors J. Pang, W. Lin, H. Fu, J. Kleeman, E. Bitar, and A. Wierman examine the trade-offs that emerge between efficiency loss, transparency, and control across different platform designs. They show that open access platforms incentivize increased production toward perfectly competitive levels and limit efficiency loss, whereas controlled allocation designs can lead to supply-side withholding, resulting in unbounded efficiency loss. Balancing transparency and control, discriminatory access designs strictly improve upon the worst-case efficiency loss of both open access and controlled allocation platforms. Besides providing insights into the design and operation of two-sided platforms, this paper contributes to the growing theory of Cournot competition in networked markets. In this paper, we analyze the worst-case efficiency loss of online platform designs under a networked Cournot competition model. Inspired by some of the largest platforms in operation today, we study a variety of platform designs to examine the impacts of market transparency and control on the worst-case efficiency loss of Nash equilibria in networked Cournot games. Our results show that open access designs incentivize increased production toward perfectly competitive levels and limit efficiency loss, while controlled allocation designs lead to producer-platform incentive misalignment, resulting in low participation rates and unbounded efficiency loss. We also show that discriminatory access designs balance transparency and control, achieving the best of both worlds by maintaining high participation rates while limiting efficiency loss. [ABSTRACT FROM AUTHOR]

• The utilization of game theory in an EPEC format to obtain the strategic bidding equilibrium of the MG. This novel application of game theory enhances the understanding of the competitive dynamics within the MG context. • The adoption of a tri-level MPEC approach, where each strategic producer, including the MG and other strategic and non-strategic rivals, aims to maximize their profits. This comprehensive approach captures the complex interactions and decision-making processes of the market participants. • The development of tri-level model formulations tailored specifically for MGs, considering the inherent fluctuations in wind unit power within the third level, which corresponds to the balancing market. This inclusion allows for a more realistic representation of the MG's behavior and dynamics in the context of power system operations. 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. [ABSTRACT FROM AUTHOR]

We consider the problem of determining information equilibria in a triopoly market in the presence of a Stackelberg leader (leaders) taking into account the reflexive behavior of all market agents in the case of the same reflexion ranks for linear functions of demand and costs of agents. Models of reflexive games are formed, formulas for calculating information equilibria are derived, and conjectural variations are investigated. The description of the complete group of reflexive reasonings of three agents has made it possible to single out reflexive coalitions, i.e., groups of mentally similar agents, and show that such coalitions are profitable, since the highest payoffs are received by agents who put forward the same ideas about the strategies of the environing. The properties of conjectural variations (negativity and boundedness of the sum) are proved, which are inherent in any aggregative game in which the utility function is a combination of linear price and cost functions. [ABSTRACT FROM AUTHOR]

Budgets play a significant role in ad markets that implement sequential auctions such as those hosted by internet companies. In "Multiplicative Pacing Equilibria in Auction Markets," the authors look at pacing in an ad marketplace using the lens of game theory. The goal is understanding how bids must be shaded to maximize advertiser welfare, at equilibrium. Motivated by the real-world auction mechanism, they construct a game where advertisers in the auctions choose a multiplicative factor not larger than 1 to possibly reduce their bids and best respond to the other advertisers. The article studies the theoretical properties of the game such as existence and uniqueness of equilibria, offers an exact algorithm to compute them, connects the game to well-known abstractions such as Fisher markets, and performs a computational study with real-world-inspired instances. The main insights are that the solutions to the studied game can be used to improve the outcomes achieved by a closer-to-reality dynamic pacing algorithm and that buyers do not have an incentive to misreport bids or budgets when there are enough participants in the auction. Budgets play a significant role in real-world sequential auction markets such as those implemented by internet companies. To maximize the value provided to auction participants, spending is smoothed across auctions so budgets are used for the best opportunities. Motivated by a mechanism used in practice by several companies, this paper considers a smoothing procedure that relies on pacing multipliers: on behalf of each buyer, the auction market applies a factor between 0 and 1 that uniformly scales the bids across all auctions. Reinterpreting this process as a game between buyers, we introduce the notion of pacing equilibrium, and prove that they are always guaranteed to exist. We demonstrate through examples that a market can have multiple pacing equilibria with large variations in several natural objectives. We show that pacing equilibria refine another popular solution concept, competitive equilibria, and show further connections between the two solution concepts. Although we show that computing either a social-welfare-maximizing or a revenue-maximizing pacing equilibrium is NP-hard, we present a mixed-integer program (MIP) that can be used to find equilibria optimizing several relevant objectives. We use the MIP to provide evidence that: (1) equilibrium multiplicity occurs very rarely across several families of random instances, (2) static MIP solutions can be used to improve the outcomes achieved by a dynamic pacing algorithm with instances based on a real-world auction market, and (3) for the instances we study, buyers do not have an incentive to misreport bids or budgets provided there are enough participants in the market. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the introduction of a nonbinding minimum wage in a search–matching model with wage bargaining. Applying the Kalai–Smorodinsky bargaining solution instead of the commonly applied Nash solution, we provide a theoretical explanation for spillover effects of minimum wages on other wages higher up in the wage distribution. The labor market equilibrium in the Kalai–Smorodinsky solution with a minimum wage is characterized by lower market tightness, a higher unemployment rate, and lower vacancy rate than the equilibrium in the Nash solution. Moreover, we show that a nonbinding minimum wage can increase social welfare. [ABSTRACT FROM AUTHOR]

Network effects typically generate multiple equilibria in two‐sided markets. To overcome the methodological challenge of selecting an appropriate equilibrium, this article shows that many two‐sided market models are weighted potential games, and therefore, a refinement of Nash equilibrium justified by many theoretical and experimental studies, potential maximization, pins down an equilibrium. Under potential maximization, platforms often subsidize one side and charge the other, that is, divide and conquer. The primary determinant of which side to subsidize/monetize is cross‐side network effects. This divide‐and‐conquer strategy implies that platforms are often designed to favor the money side much more than the subsidy side. [ABSTRACT FROM AUTHOR]

• Introducing a Nash equilibrium model for futures and day-ahead electricity markets. • Proposing a model for optimal gaming of speculators in futures electricity market. • The model can follow real-world rules, hence, is suitable for power system analysis. • Confirming the role of speculators in increasing market liquidity and reducing prices. • Highlighting the role of futures market in dealing with power grid uncertainties. Uncertainties in different parameters such as the output power of renewable energy sources, available capacity of generators, or the condition of grid lines in the future, face market players with financial risks in the power system. Futures contracts are used in parallel with the day-ahead electricity markets to protect market players against financial risks of undesirable price fluctuations. Supplying a demand by both futures and day-ahead markets leads to mutual impacts between these two markets. In this paper, a Nash equilibrium approach is introduced to model the interactions between the futures and day-ahead markets. The proposed model includes producers, retailers, and speculators as market players, the uncertainty in the output power of wind farms (WFs), the possibility of the financial settlement of contracts, market players' risk preferences, and transmission system limitations. Using this approach, the optimal strategy of market players in futures and day-ahead markets, the effects of transmission system congestion on the Nash equilibrium of the system, and the role of the financial settlement of contracts in dealing with the uncertainty of WFs' output power and transmission lines capacity are discussed. Eventually, the behavior of speculators and their impacts on the gaming of other market players are evaluated. Simulation results highlight the role of the financial delivery feature in the effective utilization of futures contracts and the behavior of market players. [ABSTRACT FROM AUTHOR]

We study consumer strategy, vendor strategy and their equilibrium in a duopoly market where vendors bear the costs in the production process. If consumers have an identical preference that is unknown, we obtain the equations satisfied by the total social surplus and the profit of each vendor. Moreover, we prove that the second derivatives of the total social surplus function and the profit function are continuous at the cutoff by the well-known conditions of value matching and smooth pasting. In a duopoly market, vendors can increase the total social surplus by adjusting their output, which causes fewer profits for vendors. However, rational vendors usually do not make such concessions, which implies that it is almost impossible to maximize total social surplus in a duopoly market. Thus, the planner needs to control vendors' output to maximize the total social surplus. We obtain the planner's optimal strategy and the socially efficient allocation. When vendors and consumers maximize their value, we find that the price of goods may be less than their costs due to price competition. By Bayesian learning and price competition model, we discuss a Markov perfect equilibrium and the relationship between the socially efficient allocation and the Markov perfect equilibrium. [ABSTRACT FROM AUTHOR]

• Nash equilibrium of ride-sourcing duopoly encapsulating waiting time uncertainty. • Derivation of order cancellation probability under different waiting time perceptions. • Comparison of leveraging cancellation penalty under heterogenous road conditions. • The punishing effect and blocking effect of cancellation penalty. This paper investigates the optimal fare and penalty strategy of ride-sourcing platforms in a competing market. When ordering ride-sourcing services, passengers encounter waiting time variability due to the uncertainty in the matching and pickup processes. In some scenarios, some passengers order ride-sourcing services from multiple platforms to save waiting time, which results in subsequent order cancellations. To capture the behavior of order cancellation, this paper derives the cancellation probability based on the perceived inhomogeneous Poisson process. In view of the punishing effect and blocking effect of order cancellation penalty, this paper investigates the impact of order cancellation penalties on market equilibrium and platform revenue. We formulate a game-theoretic framework and obtain the duopoly market equilibrium to explore the optimal pricing (including penalties and fares) of different platforms. By incorporating passenger perceptions into the order cancellation behavior, this study produces insightful pricing schemes for the ride-sourcing platforms. [ABSTRACT FROM AUTHOR]

Energy storage can provide a range of revenue streams for investors in electricity markets. However, as their deployments continue to rise, storage will no longer be a player on the sidelines and remain a price-taker, rather, these assets will start to impact prices. In this study, accounting for energy storage as a price-maker and using data from CAISO, we investigate strategic market behavior among competing investors using a non-cooperative game. We establish a centralized optimization problem to compute the market equilibrium. In the game, each investor initially decides on how much to invest and then how to operate their asset over a time horizon. Investors are allowed to deploy different energy storage technologies. Analytically, we show that an increasing number of investors will increase the market competition thereby reducing profits while increasing the total capacity of storage deployed. Numerically, our key findings include: (a) the difference in optimal investments under price-taker and price-maker assumptions, (b) as wind and solar assets expand under different resource-mix scenarios, there is a corresponding non-monotonic variation in arbitrage potential for energy storage, (c) when competition is intense and investors are allowed to invest in different technologies, a slight increase in storage technology performance can significantly improve an investor's profit share, (d) when the arbitrage opportunity increases with renewables, longer duration storage technologies may gain an advantage, (e) Li-ion batteries dominate the market under low-moderate renewable energy penetration or with steep energy-capacity cost reductions in the future. • We develop a game-theoretical framework for strategic investments in energy storage. • The framework derives a centralized optimization problem to compute the Nash equilibrium. • The impact of energy storage on market price is characterized using CAISO data. • We present insights on arbitrage potential and market competition for energy storage investors. • We quantify the effects of the number of investors, renewable energy levels, and technology heterogeneity. [ABSTRACT FROM AUTHOR]

• Describe equilibrium of ride-sourcing market with a number of competitive platforms. • Quantify the price (efficiency gain or loss) of competition and fragmentation. • Examine trends of platform profits and social welfare towards fragmentation level. • Discuss market scenarios with increasing, constant, and decreasing returns to scale. • Our model covers monopoly, duopoly, oligopoly, and perfect competition. This paper proposes a general model for describing the equilibrium state of a ride-sourcing market with an arbitrary number of platforms competing with each other. As the number of platforms increases, the market changes from monopoly to duopoly, oligopoly, and finally perfect competition, bringing about two different effects on system efficiency. On the one hand, as in other service markets, competition in the ride-sourcing markets prevents a monopolist platform from extracting excessive profit by distorting its operating strategies from socially efficient levels. On the other hand, competition between platforms leads to market fragmentation, thereby increasing matching frictions and passengers' waiting time. To well characterize these two opposite driven forces, we develop a game-theoretical model to find out the Nash equilibrium solutions of a competitive ride-sourcing market, at which no platform can increase its profits by unilaterally changing its own strategy. Then we try to quantify the price (efficiency gain or loss) of competition and fragmentation by establishing an upper bound of the inefficiency ratio, i.e., the ratio of social welfare under a social optimum to social welfare under a competitive Nash equilibrium. We show that the results of market equilibrium, including the inefficiency ratio, are jointly governed by the degree of market fragmentation and competition among platforms. In particular, we find that some key market measures, such as consumer surplus, platform profits, social welfare, display diverse trends of changes with respect to the number of platforms, as the on-demand matching between passengers and drivers exhibits increasing, constant, and decreasing returns to scale. [ABSTRACT FROM AUTHOR]

• Nash and Stackelberg models to capture the interactions of DNO and SEV operator. • A best response-based algorithm is proposed to solve the bilevel problem. • Supply-demand equilibrium existence is proved and uniqueness is numerically tested. • Cruising traffic is increased with medium travel demand while reduced in other cases. This paper considers a group of shared electric vehicles (SEV) that provide transport and energy services through a ride-sourcing platform. Under the novel business model, the transport and power networks are coupled and the resulting market equilibrium depends on the pricing strategies of the distribution network operator (DNO) and the SEV platform operator. To capture the interaction between the DNO and the SEV platform operator, we develop two market competition models, including (a) a Stackelberg competition model where the DNO makes the decision first and the SEV operator reacts accordingly, and (b) a Nash competition model where the DNO and the SEV operator make decisions simultaneously. The strategic interactions of the DNO and the SEV platform operator are analyzed over a coupled transport and power network, which captures the routing and discharging behaviors of EV drivers, the matching process between passengers and drivers, and the corresponding traveler and power flows. We analytically prove that the supply and demand equilibrium between travelers and EV drivers over the transport network always exists. We also numerically validate that the equilibrium solution between the SEV operator and the DNO is stable and unique. By varying the transport demands, we show that the SEV platform operator, the DNO and EV drivers always benefit from the discharge business even though passengers may be slightly worse off. Surprisingly, we find that integrating the discharging service will have diverse impacts on the cruising traffic depending on the demand levels of the transport service: under low demand level, it will reduce the cruising traffic; under medium demand level, it will increase the cruising traffic; under high demand level, it has no impact on the cruising traffic. [ABSTRACT FROM AUTHOR]

• A peer-to-peer energy trading market mechanism with shared energy storage units is proposed. • A non-cooperative game among peer-to-peer market participants is presented. • The generalized Nash equilibrium problem among shared energy storage users is depicted. • A game equilibrium solution based on KKT condition is proposed. • Proposed mechanism improves the efficiency and ensures fairness. The high penetration of distributed energy resources with local renewable energy consumption facilitates the emergence of peer-to-peer (P2P) energy trading, where a peer can share excessive energy with local peers. P2P energy trading is expected to be a promising business model in the future transactive energy market. Influenced by the sharing economy principle, shared energy storage(SES) is investigated to reduce the costly initial investment and improve the utilization rate of storage devices. Given the context, this paper proposes an equilibrium model of a P2P energy trading market, considering the deployment of shared energy storage in the residential consumer-side. The market equilibrium problem consists of two interwoven games. Considering the benefit conflicts between energy sellers and buyers in P2P energy trading, the P2P transaction between peers can be described as a non-cooperative game. Considering the limited SES capacity resources, the competition among SES users can be viewed as a generalized Nash equilibrium problem. These two games in the P2P market interact with each other and can be summarized as a holistic equilibrium problem, in which the P2P transaction price is endogenously determined and storage capacity is allocated. The market equilibrium problem can be solved based on Karush-Kuhn-Tucker (KKT) optimality conditions and linearization techniques, finally cast as a mixed-integer linear program. Numerical simulation demonstrates that P2P energy trading benefits all participants and the introduction of shared energy storage can further reduce energy costs. [ABSTRACT FROM AUTHOR]