ABSTRACT This article shows that dynamic efficiency gains should be better considered in merger control policy, especially in innovative sectors where they are very high and play an essential role. Neglecting those effects leads to serious mistakes in merger assessment (type-1 [Type-1 error relates to erroneously considering anti-competitive a merger which is in reality pro-competitive.]) to the detriment of industry and consumers alike. Starting with the Cournot model with homogeneous products and adding investment in marginal cost reduction, we show that mergers increase firms’ investment and reduce marginal costs. These dynamic efficiency gains add to any static efficiency gains, like synergy and economies of scale. If the total efficiency gains are large enough, they can lower prices and benefit consumers. Technical progress increases the dynamic effects and makes mergers much more likely to be pro-competitive.

This paper develops a practical computational framework for the Bayesian Cournot model with bilateral incomplete cost information, where each player is uncertain about the opponent’s marginal cost, drawn from a continuous compact interval [c*, c*] with 0<c*<c*<∞. The infinite dimensionality of the functional strategy spaces (mappings from types to production quantities) renders analytical closed-form solutions infeasible in this continuous-type setting. To overcome this challenge, we restrict the strategy spaces to finite-dimensional differentiable sub-manifolds—specifically, one-parameter families of oscillatory functions (cosine, sine, and mixed forms). After suitable affine Q-rescaling to map the oscillatory range into the production interval [0, Q], and with parameter ranges satisfying α, β>(π/2)/c*, these curves ensure near-exhaustivity: the joint production map (α, β)↦(xα(s), yβ(t)) covers [0, Q]2 densely for every fixed cost pair (s, t), thereby recovering (up to density and closure) the full ex-post payoff space. We introduce the ex-post payoff mapping Φ(s, t, x, y)=(es(x, y)(t), ft(x, y)(s)), which collects every realizable payoff pair once nature draws the types and players select their strategies. The image of Φ defines the general payoff space of the game, and its non-dominated points constitute the general ex-post Pareto frontier—all efficient realized outcomes across type-strategy realizations, without dependence on private probability measures over types. Using multi-objective genetic algorithms, we numerically approximate this frontier (and selected collusive compromises) within the restricted but representative sub-manifolds. The resulting frontiers are computationally accessible, robust to parameter variations, and validated through hypervolume convergence, sensitivity analysis, and comparisons with NSGA-II, PSO and scalarization methods. The findings are significant because they provide decision-makers in oligopolistic markets (e.g., electric vehicles) with viable, implementable production policies that explore efficient trade-offs under genuine cost uncertainty, without requiring explicit forecasts of the opponent’s type distribution—a limitation of traditional expected-utility approaches. By focusing on ex-post efficiency, the method reveals belief-independent compromise solutions that may guide tacit coordination or collusive outcomes in real-world strategic settings.

Abstract This paper analyzes the economic impact of plant-parasitic nematodes in the U.S. potato industry, focusing on how both unanticipated and anticipated yield losses affect producer decisions, market outcomes, and welfare. We use a modified Cournot model and estimate a system of supply and demand equations using Three-Stage Least Squares (3SLS). We simulate scenarios to measure how varying levels of nematode infestation influence producer profits and consumer surplus in the short-run and the long-run. Simulations suggest that reducing nematode damage could yield substantial gains in output and consumer welfare particularly in concentrated markets where strategic producer behavior amplifies these effects. Our findings underscore the need to account for both biological uncertainty and market structure when evaluating pest impacts and designing policy responses.

Information asymmetry between informed and uninformed sellers poses a critical challenge for retail platforms, necessitating differentiated information-sharing strategies. This paper examines how a platform should design its information-sharing policy when serving two heterogeneous seller types (informed with private demand signals vs. uninformed) under Cournot competition. Our study bridges classic Cournot models with platform-centric information economics by introducing seller heterogeneity. By characterising equilibrium production decisions and Pareto-improving strategies, we provide actionable insights for platforms to optimise information services while enhancing market efficiency. We develop a game-theoretic model where sellers with asymmetric initial information engage in Cournot competition. The platform strategically shares demand signals through a noise-injection mechanism to maximise commission revenue, considering four sharing formats. Our analysis shows that the platform has incentives to share information exclusively with uninformed sellers, as this approach is most beneficial for the overall market. Furthermore, there exists a Pareto region in which informed sellers do not suffer from information leakage. Finally, we identify a pricing mechanism to maximise market efficiency. These findings provide valuable guidance for platform managers aiming to design effective information-sharing services that enhance both market efficiency and platform profitability. Specifically, the results suggest that platform managers should prioritise an exclusive information-sharing strategy targeted at uninformed sellers. Moreover, platforms can adopt differentiated pricing mechanisms to encourage participation from these sellers and thereby achieve optimal market performance.

As an emerging e-commerce model, live-streaming commerce has attracted widespread attention from merchants. Since many merchants do not have their own anchors, they need to hire professional anchors, who are called commissioned live-streaming commerce. Merchants can choose either agent anchors or celebrity anchors, that is, a choice between two different live-streaming channels. Choosing celebrity anchors with large fan bases can crank up higher sales for merchants, but comes with higher commission expenses and potential competition from the anchors’ own brand products. Conversely, choosing agent anchors whose popularity is far less than that of celebrity anchors may still bring high profits, as these agents charge lower commissions. Inspired by this interesting phenomenon, the present study examines the challenges faced by merchants in live-streaming channel selection using commissioned live-streaming commerce. The study employs a Cournot model to investigate the issues at hand and analyze the impact of different factors on merchants' channel selection based on simulation. The results show that when the effort cost of a merchant choosing anchors is high and the merchant's brand image advantage is significant, the merchant is more inclined to choose agent anchors; otherwise, the inclination is to choose celebrity anchors. The findings provide support for the decision-making process of different parties involved in live-streaming commerce and thus, promote the sustainable development of the live-streaming commerce industry.

ABSTRACT This research tackles the issue of the rational (endogenous) choice of constant-return-to-scale (CRS) or decreasing-return-to-scale (DRS) technologies in a strategic setting. In this regard, the paper considers a simultaneous-move (Cournot) duopoly showing that the emerging sub-game perfect Nash equilibrium (SPNE) ranges from the prisoner’s dilemma to the deadlock, passing through the anti-coordination game. The article also identifies the SPNE’s social welfare outcomes, highlighting win-win solutions and policy implications. It finally introduces horizontal product differentiation and considers the technology decision game (TDG) in a Bertrand-rivalry setting, comparing it with the Cournot model. The TDG à la Cournot with iso-elastic demand and the sequential TDG à la Stackelberg are also considered.

Technology Licensing and the Direction of Innovation

Dynamics of quantum Cournot model under strategic delegation

The article is devoted to the analysis of the application of mathematical models of game theory in business for modelingthe interaction of economic agents, with an emphasis on competitive strategies, the behavior of companies and consumers in adynamic market environment. The obtained scientific results demonstrate that game theory effectively models the competitivebehavior of firms, in particular through dominant strategies and Nash equilibria, allowing the prediction of the consequencesof price wars and the breakdown of agreements, as in the classical prisoner’s dilemma. In modeling consumer behavior, thephenomenon of conspicuous consumption is highlighted, where payoff matrices of costs and benefits show how social effectsinfluence choice, shaping zero-sum games and mixed strategies to minimize losses. In marketing decisions, illustrated by theexample of the air conditioning systems market, payoff matrices with correction coefficients make it possible to determineoptimal combinations of strategies, such as network expansion or advertising campaigns, taking into account the absence ofsaddle points and the transition to probabilistic profiles. The Cournot model illustrates the dynamics of a duopoly, wherecooperative strategies provide higher profits, but competitive incentives lead to defection, emphasizing the need for coordinationgames for sustainable development. The practical value of the study lies in providing tools for business management, particularlyfor optimizing strategies in marketing, logistics, and pricing, which helps companies minimize risks under competition andincrease profitability. The application of the proposed models allows forecasting the reactions of competitors and consumers,contributing to effective decision-making in real market situations such as retail trade or supply chains.

Horizontal mergers in a Cournot market are generally unprofitable for the merged entities and create a free-riding problem unless they involve more than 80% of market participants. This phenomenon is known as the merger paradox. This paper aims to explain the concept of the paradox and reasons for its emergence by modifying one assumption in the Cournot model while keeping the other assumptions constant in order to identify the primary contributor. The results suggest that the merger paradox can be partially addressed by modifying key assumptions of the Salant, Switzer and Reynolds (1983) model; however, the practical sustainability of these modifications remains uncertain.

The global electric vehicle (EV) market has experienced sustained growth over the last decade; however, adoption within the commercial EV segment remains comparatively sluggish. This disparity is driven by three primary factors: the intrinsic limitations of lithium-ion battery chemistry, which imposes constraints on charge–discharge cycling, excessive charging durations for large battery packs used in long-haul semi-trucks, and diminished charging effectiveness under cold weather conditions, which further extends downtime and increases grid demand. To address these operational and infrastructural challenges, this article proposes a novel battery swapping station layout with ‘design-integrated safety’ features, enabling rapid battery replacement while ensuring compliance with safety codes and standards. Two complementary pricing strategies are developed for deployment under differing market structures. The first is a Cournot competition, applicable to deregulated environments, where firms strategically allocate battery inventory between EV swapping services and participation in a secondary energy market. As an extension of the Cournot competition model, the profit functions are analytically derived for a duopoly in which one firm engages in dual markets, enabling assessment of equilibrium outcomes under competitive conditions. The second strategy is a degradation-sensitive pricing framework, intended for regulated markets, which dynamically adjusts swap prices based on state-of-charge depletion, duty cycle intensity, environmental exposure, and nonlinear battery degradation effects. This formulation is evaluated for six representative operational cases, demonstrating its ability to incentivize shallow cycling, penalize deep discharges, and incorporate fair usage-based pricing. The proposed architectures and pricing models offer a viable pathway to accelerate commercial EV adoption while optimizing asset utilization and profitability for station operators.

A Cournot triopoly is a type of oligopoly market involving three firms that produce and sell homogeneous or similar products without cooperating with one another. In Cournot models, firms’ decisions about production levels play a crucial role in determining overall market output. Compared to duopoly models, oligopolies with more than two firms have received relatively less attention in the literature. Nevertheless, triopoly models are more reflective of real-world market conditions, even though analyzing their dynamics remains a complex challenge. A reaction–diffusion system of PDEs generalizing a nonlinear triopoly model describing a master–slave Cournot game is introduced. The effect of diffusion on the stability of Nash equilibrium is investigated. Self-diffusion alone cannot induce Turing pattern formation. In fact, linear stability analysis shows that cross-diffusion is the key mechanism for the formation of spatial patterns. The conditions for the onset of cross-diffusion-driven instability are obtained via linear stability analysis, and the formation of several Turing patterns is investigated through numerical simulations.

Purpose The purpose of this paper is to investigate the impact of carbon price and competition intensity and the optimal decisions in a two-echelon low-carbon supply chain, consisting of a manufacturer, a retailer and a third party, under carbon cap and trade (CCT) and in two different competitive behaviors in the sales and recycling markets. First, two models are built and the optimal solutions are obtained. Second, a comparative analysis of these optimal solutions and the effects of some key parameters on optimal decisions are examined. Design/methodology/approach The authors adopt the manufacturer-led Stackelberg game theoretic framework, where the manufacturer decides the wholesale price, followed by the retailer and third party to determine the retail and recycling quantities. Moreover, the retailer and third party engage in Stackelberg or Cournot game. Findings Firstly, the CCT benefits the third party more. A rise in carbon price negatively affects manufacturer production and retailer recycling but boosts the third party’s recycling. Secondly, the Stackelberg model allows the third party to get more recycling volume and profit, while the Cournot model is better for the manufacturer and retailer. Thirdly, when faced with the increasing competition intensity in the recycling and sales market, the third party and retailer adopt various strategies in response to different competition intensities. Finally, social welfare in the Cournot model is higher in most of the cases, but when the third party and retailer’s recycling competition intensity decreases below a certain threshold, the social welfare in the Stackelberg model exceeds that in the Cournot model. Research limitations/implications Firstly, in both models, as the carbon price increases, the amounts of new products, the retailer’s recycling volume and profit decrease. The manufacturer’s profit rebounds when the carbon price surpasses a threshold. Secondly, when the third party faces a rise in the retailer’s recycling market competition, its strategy differs from that of the retailer in the sales market. Finally, the retailer and third party tend to set a higher recycling price than in the Cournot model. The retailer and manufacturer can obtain higher profits in the Cournot model, while the third party is more profitable in the Stackelberg model. Practical implications This paper can also further relax the assumptions, so our paper can expand the research from several aspects. First, this paper only considers the single-period model; thus, the multi-periods can be considered in the supply chain model. Second, only the consequences of the CCT mechanism are the subject of this paper. However, in real life, there are still carbon emissions reduction (CER) regulatory mechanisms such as carbon tax, so comparing and analyzing the effects of various CER mechanisms is an interesting task. Social implications The government should provide more support and opportunities for the third party in the early stage of development under the CCT mechanism. Meanwhile, the government ought to establish acceptable carbon quotas and strengthen the supervision of the carbon market. The manufacturer should monitor carbon price changes and adjust production and CER strategies and increase CER technology investment. The retailer should gather information and aim to make concurrent decisions with the third party. The third party should grasp decision-making initiative and be a competitive leader. The retailer and third party should closely watch competition intensity and flexibly adjust recycling and pricing strategies in both markets. Originality/value This paper concentrates on the scenario where retailer and third party compete in both the sales and recycling markets under CCT and focuses on the differences in competition intensity between retailer and third party. Furthermore, this paper considers different competitive behaviors and analyzes the optimal decisions of all parties when competing simultaneously in the sales and recycling markets, which provide more targeted guidance for practical operation.

Abstract The costs associated with electricity generation include costs that are independent of their marginal output, such as the cost of starting their units, and constraints such as minimum generation levels. Modelling these costs and constraints requires integer formulation of the units, and so they have typically been ignored in electricity market modelling and simulation to date. We present a stochastic equilibrium model to include these costs and constraints in a Cournot game. We solve it using the Gauss-Seidel diagonalization algorithm and apply it to a model of the power system of the island of Ireland for varying levels of variable renewable power generation. We find that the impacts of integer modelling are non-trivial, and are heterogeneous across firms and wind levels. Furthermore, excluding integer modelling exaggerates the impact of price-making behaviour. We conclude that neglecting integer constraints in power system market models leads to inaccurate results, particularly at high penetrations of renewable energy sources.

Electricity systems in many parts of the world are becoming more dependent upon natural gas as an electricity-generation fuel. As such, electricity and natural-gas markets are becoming more interconnected. Contemporaneously, some electricity and natural-gas markets are integrating vertically, through the merger of electricity and natural-gas suppliers. The market-efficiency impacts of such vertical integration are unclear. On one hand, vertical integration could exacerbate market power, whereas on another it could mitigate double marginalization. To study this question, this paper develops a Nash–Cournot model of the two interconnected markets. The model is converted into a linear complementarity problem, which allows deriving Nash equilibria readily. Some theoretical results are derived for the case of a merger involving symmetric firms. In addition, the model is applied to a stylized example with a range of parameter values. We find that integration is social-welfare enhancing—which implies that mitigating double marginalization outweighs the exercise of market power. In most cases, the effects of merger can give rise to a prisoner’s-dilemma-type outcome. Merger is beneficial to the merging firms. However, profits of non-merging firms and total supplier profits decrease following a merger. Overall, our results suggest that vertical integration in energy markets may be socially beneficial. JEL Classification: C61, C72, D43, L1, L94, L95, Q4

A novel Cournot model design for trading price functions, incorporating line-losses in the electricity market (EM), is proposed in this paper. The proposed transactive EM framework has a major EM and a local market (LM) inside a microgrid. The protagonist in major EM is the transmission network operator, which buys electric units from a generating company and sells them to different buses connected to various loads. The LM is constructed in one of these buses. LM operator is the price-deciding entity in this market, where electricity is traded between prosumers, which facilitate solar photovoltaic (SPV) installations, and the LM operator. In order to articulate the effectiveness of SPV utilization in EM, the present work considers that the LM operator owns an SPV plant in LM. A cost-benefit analysis determines the period to recoup the initial investment for establishing the SPV plant in LM. The electricity status of a prosumer determines its role at a particular time in LM: either as seller or buyer of electric units. The design of a penalty mechanism for prosumers in LM using Gaussian process regression is proposed to minimize the reduction in the operator's profit during trading hours.

This paper introduces and scrutinizes three groundbreaking models aimed at probing the intricacies of duopoly dynamics within perfect complement factors: (1) the spontaneous assembly model, (2) the non-spontaneous assembly model, and (3) the sequential spontaneous assembly model. This study delves into oligopoly with perfect complementarity and makes the following discoveries. First, the renowned and significant quantity competition model, the Cournot model, is equivalent to the price competition models studied in this research, the spontaneous assembly model and the non-spontaneous assembly model using ECPR. Second, the renowned and significant quantity competition model, known as the chain monopoly model, aligns with the price competition model explored in this study, termed the sequential spontaneous assembly model. Third, the three price competition models examined in this study are found to be as follows. Initially, a comprehensive investigation of the spontaneous assembly model lays the basis for a compelling argument, demonstrating that the equilibrium price of the ‘system goods’ in duopoly surpasses that of the monopoly scenario. Subsequently, we meticulously establish the mathematical equivalence between the non-spontaneous assembly model, using the ‘efficient component pricing rule’, and the spontaneous assembly model. Our focus then shifts to the sequential spontaneous assembly model, where a meticulous comparison with the simultaneous model unveils elevated equilibrium prices for the ‘system goods’. In particular, we elucidate that those industrial profits are based on the price elasticity of demand, with this sequential model yielding higher profits under conditions of inelastic demand.

Enhancing the Cournot Model by Integrating Risk Events and Attitudes Towards Risk

This paper incorporates an operational risk event in the Cournot model. The risk event has impacts on the operational costs, but it is possible to control these costs after the event by implementing actions to mitigate those impacts. Naturally, these actions demand higher operational costs before the event. This study considers a common situation where risk-neutral company owners hire managers to establish both the production levels and the actions to mitigate the impacts of the risk event. While studying different combinations of risk attitude for managers, it is found that the highest expected profit in the equilibrium is reached when the managers present some degree of risk-seeking behaviour.

In recent years, government incentives and subsidies have driven significant growth in wind power plant (WPP) capacity, establishing WPPs as key players in the evolving electricity market. However, the inherent variability of wind generation introduces challenges, including potential penalties for deviations in energy output. Energy Storage Systems (ESS) serve as a versatile solution to mitigate the uncertainties associated with wind power variability. This paper proposes a comprehensive model for the joint bidding of WPPs and ESS in competitive electricity markets. The interactions between WPPs and ESS are modeled using a stochastic Cournot framework, accounting for wind power uncertainties through inter-hour ramp constraints. A Location-Based Dual Imbalance Price (DIP) mechanism is adopted for wind-storage systems operating within a network-constrained oligopolistic electricity market. The Nash equilibrium strategy is used to optimize the WPP-ESS bids, considering the competitive behavior of other market participants. A Mixed Integer Linear Programming (MILP) model is developed to determine the Nash equilibrium by evaluating a payoff matrix. Various practical scenarios are analyzed to demonstrate the efficacy of the proposed approach. Furthermore, the study investigates the influence of different imbalance price mechanisms on WPP-ESS profits, market clearing operations, and Nash equilibrium outcomes.