Search Results (25)

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. Full article

Is it possible to control NPS (non-point source) pollution whose sources, sizes, and origins are difficult to identify? This study provides a positive answer in a non-cooperative n-firm oligopoly model in which the firms determine levels of differentiated goods and abatement technologies. It first derives a Cournot–Nash equilibrium in which the firms maximize their profit and emit pollution under the ambient charge scheme, combining rewards from the total NPS concentration less than a given standard with the penalties above. The effect of the ambient charge is then analytically shown in homogeneous and heterogeneous duopoly and triopoly. Further, possible controllability is numerically examined in the case of $n\ge 4$. Full article

We have built and investigated analytically and numerically a differential game model of Cournot oligopoly with consideration of pollution, network structure, and continuous updating. Up to this time, games with network structure and continuous updating were considered separately. We analyzed time consistency for a cooperative solution of the game. For a specific example, we built a non-empty subgame perfect subcore. We considered stochastic versions of the proposed model and received results similar to the deterministic case. Full article

Nowadays, traffic management challenges in the era of digital transport are rising, as the interactions of various stakeholders providing such technologies play a pivotal role in shaping traffic dynamics. The objective of this paper was to present a game-theory-based framework for modeling and optimizing urban traffic in road networks, considering the co-existence and interactions of different players composed of drivers of conventional vehicles, central governing authorities with traffic management capabilities, and competitive or cooperative connected mobility private service providers. The scope of this work was to explore and present the outcomes of diverse mixed equilibrium conditions in the road network of the city of Thessaloniki (Greece), integrating the principles of user equilibrium, system optimum, and Cournot oligopoly. The impacts of varying network attributes were systematically analyzed to provide quantitative indicators representing the overall network performance. Analysis of the results provided insights into the sensitivity and the resilience of the road network under various prevalence schemes of drivers of conventional vehicles, representing the user equilibrium characteristics, or drivers relying on traffic guidance provided by a central governing authority, representing the system optimum principles as well as the cooperation and competition schemes of private connected mobility providers with certain market shares in the network. Full article

The integration of Connected Vehicles into conventional traffic systems presents significant challenges due to the diverse behaviors and objectives of different drivers. Conventional vehicle drivers typically follow User Equilibrium principles, aiming to minimize their individual travel times without considering the overall network impact. In contrast, Connected Vehicle drivers, guided by real-time information from central authorities or private service providers, can adopt System Optimum strategies or Cournot-Nash oligopoly behaviors, respectively. The coexistence of these distinct player classes in mixed-traffic environments complicates the task of achieving optimal traffic flow and network performance. This paper presents a comprehensive framework for optimizing mixed-traffic road networks through a multiclass traffic assignment model. The framework integrates three distinct types of players: conventional vehicle drivers adhering to User Equilibrium principles, Connected Vehicle drivers following System Optimum principles under a central governing authority, and Connected Vehicle drivers operating under Cournot-Nash oligopoly conditions with access to services from private companies. The methodology includes defining a model to achieve optimal mixed equilibria, designing an algorithm for multiclass traffic assignment, formulating strategic games to analyze player interactions, and establishing key performance indicators to evaluate network efficiency and effectiveness. The framework is applied to a real-world road network, validating its practicality and effectiveness through computational results. The extraction and analysis of computational results are used to propose optimal traffic management policies for mixed-traffic environments. The findings provide significant insights into the dynamics of mixed traffic networks and offer practical recommendations for improving traffic management in increasingly complex urban transportation systems. Full article

With the rise of the sharing economy, shared bicycles have become an important component of urban transportation. This paper explores the nonlinear dual oligopoly system for the Cournot model in the bike-sharing market; both operators have maximized profits as their competitive goals. The analysis of pivotal factors influencing passenger preferences, including pricing discounts and comfort levels, is meticulously depicted by a bifurcation diagram. A new chaotic attractor—the shared bicycle attractor—is discovered. The research results indicate that larger discounts and adjustment speeds can cause the system to be in a chaotic state, which is not conducive to the long-term development of operators, although discounts can indeed attract more passengers to a certain extent. On the other hand, the increase in the marginal cost of comfort loss can also make it difficult for enterprises to operate, which requires continuous technological innovation to improve the comfort of cycling. Full article

This paper extends the Cournot duopoly model by allowing the government to impose firm-dependent specific taxes or subsidies while keeping the budget balanced. It considers two possible government goals: maximizing the social surplus and maximizing the consumer surplus. It shows that, with identical firms, the best government policy is not to intervene. In the case of cost asymmetry, social surplus and consumer surplus maximization goals require opposite strategies: to maximize the social surplus, the government should tax the high-cost firm driving the economy toward monopoly and increasing productive efficiency at the expense of lower production. In the case of consumer surplus maximization, the tax should be imposed on the low-cost firm reducing the gap between the firms’ outputs. Such a strategy, however, increases productive inefficiency and reduces the social surplus. Full article

In the study we explore an oligopoly market for equilibrium and stability based on statistical data with the help of response functions rather than payoff maximization. To achieve this, we extend the concept of coupled fixed points to triple fixed points. We propose a new model that leads to generalized triple fixed points. We present a possible application of the generalized tripled fixed point model to the study of market equilibrium in an oligopolistic market dominated by three major competitors. The task of maximizing the payout functions of the three players is modified by the concept of generalized tripled fixed points of response functions. The presented model for generalized tripled fixed points of response functions is equivalent to Cournot payoff maximization, provided that the market price function and the three players’ cost functions are differentiable. Furthermore, we demonstrate that the contractive condition corresponds to the second-order constraints in payoff maximization. Moreover, the model under consideration is stable in the sense that it ensures the stability of the consecutive production process, as opposed to the payoff maximization model with which the market equilibrium may not be stable. A possible gap in the applications of the classical technique for maximization of the payoff functions is that the price function in the market may not be known, and any approximation of it may lead to the solution of a task different from the one generated by the market. We use empirical data from Bulgaria’s beer market to illustrate the created model. The statistical data gives fair information on how the players react without knowing the price function, their cost function, or their aims towards a specific market. We present two models based on the real data and their approximations, respectively. The two models, although different, show similar behavior in terms of time and the stability of the market equilibrium. Thus, the notion of response functions and tripled fixed points seems to present a justified way of modeling market processes in oligopoly markets when searching whether the market has reached equilibrium and if this equilibrium is unique and stable in time Full article

Coopetition means that in economic interactions, both competition and cooperation are presented in the same time. We built and investigated analytically and numerically game theoretic models of coopetition in normal form and in the form of characteristic function. The basic model in normal form reflects competition between firms in Cournot oligopoly and their cooperation in mutually profitable activities such as marketing, R&D, and environmental protection. Each firm divides its resource between competition and cooperation. In the model in normal form we study Nash and Stackelberg settings and compare the results. In cooperative setting we consider Neumann–Morgenstern, Petrosyan–Zaccour, and Gromova–Petrosyan versions of characteristic functions and calculate the respective Shapley values. The payoffs in all cases are compared, and the respective conclusions about the relative efficiency of different ways of organization for separate agents and the whole society are made. Full article

We built and investigated analytically and numerically a differential game model of Cournot oligopoly with consideration of pollution for the general case and the case of symmetrical agents. We conducted a comparative analysis of selfish agents’ behavior (a differential game in normal form), their hierarchical organization (differential Stackelberg games), and cooperation (optimal control problem) using individual and collective indices of relative efficiency. The same analysis wasperformed for the models with the green effect when players chose both output volumes and environmental protection efforts. We used the Pontryagin maximum principle for analytical investigation and the method of qualitatively representative scenarios in simulation modeling for numerical calculations. This method allows for reducing the number of computer simulations, providing sufficient precision. As a result of the comparative analysis, systems of collective and individual preferences were obtained. Full article

The subject of this study is an oligopolistic market in which three firms operate in an environment of quantitative competition known as the Cournot oligopoly model. Firms and their production are differentiated, which brings the theoretical model closer to real market conditions. The main objective was to expand the Cournot duopoly and add another firm, resulting in an oligopolistic market structure assuming a partially differentiated production and coalition strategy between two firms. This article contains an oligopolistic model specifically designed for three different types of expectations, and has been applied to find and verify the stability of the net equilibrium of oligopolists. The market of telecommunication operators in Slovakia was selected as a real market case with accessible data on an oligopoly with three companies and partial differentiation. There are studies in which the authors limit their considerations to a certain number of repetitions of oligopolistic games. An infinite time interval is considered here. Three types of future expectations were considered: a simple dynamic model (or naïve expectations) in which the oligopolist assumes that its competitors will behave in the future based on their response functions, an adaptive expectations model in which the oligopolist considers a weighted average of the quantities offered by its competitors, and real expectations in which firms behave as rational players and do not have complete information about demand and offer output based on expected marginal profit. While the presented model proved to be stable under naïve and adaptive expectations, no stable equilibrium was found under real expectations and further results indicate a chaotic behavior. Full article

In this paper, we deal with the renowned problem of plastic pollution caused by food consumption and its conservation. Specifically, we consider the producer/reseller decision problem of industrial organizations in conditions of perfect competition within small oligopoly clusters. Indeed, very often, one major sustainability problem is that the presence of direct competitors in the same market determines entrepreneurship choices which lower production costs and packaging costs at the expense of the environment and public health. For this purpose, in order to show economic scenarios in which the respect and preservation of the environment and natural resources are quantitatively compatible with profits and economic growth, we present a provisional coopetitive model of the strategic interaction of two food enterprises, in direct duopoly competition, through investments in sustainable-packaging technologies. The macroeconomic goal is to propose possible actions to reduce carbon footprints and the inflow of plastics to the marine environment, following the environmental targets established by the United Nations, also in the presence of direct perfect oligopolistic competition in the same market. From a microeconomic point of view, we assume the existence of two competitors selling a very similar type of food in the same market; therefore, within a competitive interaction, we adopt a classic “Cournot duopoly” core upon which we define a parametric game, namely, a coopetitive game, together with its possible dynamical scenarios and solutions. We should notice that beyond the parameter arising from the cooperation construct, we introduce a matrix of stochastic variables, which we can also consider as the state of the world. Moreover, we numerically examine one possible state of the world to exemplify our model proposal. We determine, analytically and graphically, the optimal investment in the cooperative strategy, the purely coopetitive solution and some super-cooperative solutions. The cooperative strategy represents the common investment chosen to acquire advanced green technologies for innovative packaging, while the fourth component of any solution in the strategy space represents the state of the world at the end of the coopetitive process in which, finally, we can see the profits and costs deriving from the adoption of the green technologies. Full article

This paper analyzes the environmental tax’s effect on manufacturers’ choice of low-carbon technology in competitive supply chains. The existing studies only consider a single oligopoly enterprise and ignore the competition between supply chains. Few papers study the manufacturer’s technology choice under the carbon tax policy in the competitive supply chains, especially investigating the factors influencing the technology choice, including the market volume, and technology carbon emission reduction efficiency because different industry sectors have their distinctive carbon emissions reduction efficiencies and facing the different market volume. The study adopts a game theoretical approach, including the three-level supply chain consisting of the regulator, the manufacturers, and the retailers. A high carbon tax does not always help firms choose low-carbon technology. However, the monotonous effect of the carbon tax on manufacturer technology selection is no longer valid if the market volume and the carbon-reducing efficiency are considered. When the market volume is large, the regulator can set a high carbon tax to induce the manufacturers to choose low-carbon technology. We identify cases where the manufacturers are caught in a prisoner’s dilemma. When the market volume is small, and the carbon-reducing efficiency is high, the competitive manufacturers adopt the common technology. However, if the regulator increases the carbon tax, the manufacturers acquire the differential technology strategic choice, which is the Pareto optimal. We also extend the base model to the imperfect substitutable Cournot model and the Bertrand model to check the robustness and find our main results still hold in these extensions. Full article

The technological improvements modeled for Cournot competition have primarily focused on production cost reductions and scope effects. We consider a case where the technology improves the ability to affect the production capacity constraints instead. We find that although such technological progress entails public benefits in the form of greater consumer surplus and social welfare, it is likely to have limited and even sometimes harmful private effects (e.g., to firm profits). We formally model this technological improvement possibility through the relevant variants of oligopolies and rival technological asymmetries. We describe and discuss the strategic implications for managers and policy-makers considering investing and exploiting such capacity-adjusting technologies. We also flesh out the many core areas for future work to follow up on in our initial unique results. Full article

The present paper provides theoretical insights regarding the determinants of firms’ incentives to invest in a Circular Economy. The analysis relies on a Cournot model disaggregating the disposal cost in the production function. In a non-simultaneous sequential game, two risk-neutral firms are endowed with a green innovation project that, if successful, would reduce the overall production costs and implement a Circular Economy. Firms are plagued by asymmetric information about the exact value of the other firm’s innovation. In this setting, the R&D investment in a Circular Economy, by affecting the distribution of production and disposal costs, influences the production decisions of both the innovating and the rival firms. The sign of the impact depends on the firms’ strategy in the product market. Furthermore, the analysis points out that cooperation in R&D of firms competing in the product market reinforces incentives to invest in green innovation. This suggests that governments aimed to advance a Circular Economy should encourage firms’ cooperation. Full article