Cournot-Nash Model Research Articles

GAME EQUILIBRIUM BASED CONTROL ANALYSIS ON THE SUSTAINABLE MARKET STRUCTURE OF RARE METAL MINERAL RESOURCES – EVIDENCE FROM CHINA

In rare metal mineral market, as a complex system, multiple decision-making among the stakeholders increases the complexity in its market structure and dynamic process. The unreasonable compensation pricing mechanism for the development of the rare metal mineral resources in China requires to be studied. Drawing on the methods of game theory model and chaos control analysis, this paper builds theoretical model of rare metal mineral market structure, corporating related parameters of rare metal in the game theory model, to conduct the chaotic nature and path analysis, expecting to solve the bottleneck problems that restrict the rare metal pricing and resource security and enhance the waste valorization for the sustainability. Specificly, a Cournot-Nash Equilibrium model is built to analyze the Cournot-equilibrium point, the stability of the Cournot Equilibrium point, the chaotic status, as well as the pattern to chaos of the game system in the rare metal mineral resource market, numerical simulation is used to verify the model. The conclusions facilitate the formulation of industrial economic policies and further improvement of managerial strategies to solve market problems.

A splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions and application to cournot-nash model

In this paper we propose a splitting subgradient algorithm for solving equilibrium problems involving the sum of two bifunctions. At each iteration of the algorithm, two strongly convex subprograms are required to solve separately, one for each component bifunction. In contrast to the splitting algorithms previously proposed in Anh and Hai (Numer. Algorithms 76 (2017) 67–91) and Hai and Vinh (Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 111 (2017) 1051–1069), our algorithm is convergent for paramonotone and strongly pseudomonotone bifunctions without any Lipschitz type as well as Hölder continuity condition of the bifunctions involved. Furthermore, we show that the ergodic sequence defined by the algorithm iterates converges to a solution without paramonotonicity property. Some numerical experiments on differentiated Cournot-Nash models are presented to show the behavior of our proposed algorithm with and without ergodic.

Cournot-Nash Competition Model of Logistic Chains based on a Spatial Price Equilibrium

Cournot-Nash Competition Model of Logistic Chains based on a Spatial Price Equilibrium

Unemployment equilibrium and economic policy in mixed markets

This paper features a simple static Cournot–Nash model of an exchange economy with two productive sectors at flexible prices and wages. The traders in the atomless sector are price-takers, while the atoms behave strategically. We focus on the consequences of strategic interactions on the market outcome. Firstly, strategic interactions create underemployment on the labor market. Secondly, when the number of atoms increases without limit, the CWE coincides with the competitive equilibrium. Thirdly, we compare the welfare reached by traders at both equilibria. Fourthly, we consider the implementation of a tax levied on strategic supplies. Finally, we compare the approach retained with the monopolistic competition framework.

Game Analysis of the China Wind-farm Investment Market

The global electricity supply from non-hydro renewable energies, such as wind and solar, has being growing at a high rate, and it is expected that this trend persists. In China, Wind power is one of the most mature renewable energy technologies and it is possible to be utilized in large-scale. However, in the long run, the malicious competition will break the rule of the monopoly wind power market under control of electricity utilities in China and prevent the development of Chinese wind power. Reasonable competition of the investment market is a key to promote healthy development of the wind power industries in China. Based on game theory, this paper investigates competitive behavior of the wind-farm investment companies. The competition mechanism and malicious competition behavior of the investment market of the non-asymmetric enterprisers, and the wind-farm investment market are discussed by the Stacklberg model and the Cournot-Nash model, respectively, and moreover, the theoretic analysises are verified to be effective by an example. Furthermore, some policy advices are put forwards to the Chinese wind power investment market.

Modeling Mexican Electricity Market: Experimental Results

In this paper, we propose an oligopolistic model of electricity market of Mexico and analyze numerical experiments based upon this model. Presently, the Mexican electricity market is presented by the state-regulated monopoly, so a competition market is not yet established. Our work can be evaluated as an empirical study of possible liberalization effects for Mexico. An oligopolistic market structure emerges from the energy market analysis and is characterized not only by the mutual influence upon prices due to the market shares and power but also by the naturally limited number of operating firms-producers at the market. In this Cournot-Nash model, the electricity firms maximize their profit and enlarge their market shares. For a comparison, we also introduce the notion of perfect competition, where each agent reacts as a price-taker equalizing prices and marginal costs in order to maximize its profit. The computational game theoretic modeling tool, offered in this paper, composed as a mixed complementarity problem (MCP), solved by the GAMS (www.gams.com) algorithm PATH. It was applied to the Mexican electricity market data to obtain Nash equilibrium in the perfect competition and Cournot cases, as well as open market scenario with international trade with the USA.

Barriers to retail competition and prices: evidence from Spain

Why do prices in Spain's regions fail to converge? The prime suspects for this puzzling result are differences in regional barriers to entry in retail distribution. This paper develops a Cournot-Nash model of imperfect competition to illustrate the effect of barriers on prices. A unique data set--derived from an extensive analysis of competition policies in Spain--provides evidence that barriers to entry increase regional prices. The evidence also suggests that, consistent with the model's predictions, barriers to entry raise prices up to a point, and thus indicate that barriers have a threshold effect on prices. Copyright 2010 Oxford University Press 2009 All rights reserved, Oxford University Press.

Dynamic oligopolistic competition on an electric power network with ramping costs and joint sales constraints

Most previous Cournot-Nash models of competition among electricity generators have assumed a static perspective, resulting in finite dimensional variational and quasi-variational inequality formulations. However, these models' system costs and constraints fail to capture the dynamic nature of power networks. In this paper we propose a more general and complete model of Cournot-Nash competition on power networks that accounts for these features by including ($i$) explicit intra-day dynamics that describe the market's evolution from one Generalized Cournot-Nash Equilibrium to another for a 24 hour planning horizon, ($ii$) ramping constraints and costs for changing the power output of generators, and ($ iii $) joint constraints that include variables from other generating companies within the profit maximization problems for individual generators. These joint constraints yield a generalized Nash equilibrium problem which can be represented as a differential quasi-variational inequality (DQVI); such generalized Nash equlibrium problems can have multiple solutions. The resulting formulation poses computational challenges that can cause traditional algorithms for DVIs to fail. A restricted formulation is proposed that can be solved by an implicit fixed point algorithm. A numerical example is provided.

Barriers to Retail Competition and Prices: Evidence from Spain

Why do prices in Spain's regions fail to converge? The prime suspects for this puzzling result are differences in regional barriers to entry in retail distribution. This paper develops a Cournot-Nash model of imperfect competition to illustrate the effect of barriers on prices. A unique data set-derived from an extensive analysis of competition policies in Spain- provides evidence that barriers to entry increase regional prices. The evidence also suggests that, consistent with the model's predictions, barriers to entry raise prices up to a point, and thus indicate that barriers have a threshold effect on prices.

Barriers to Retail Competition and Prices: Evidence From Spain

Why do prices in Spain's regions fail to converge? The prime suspects for this puzzling result are differences in regional barriers to entry in retail distribution. This paper develops a Cournot-Nash model of imperfect competition to illustrate the effect of barriers on prices. A unique data set-derived from an extensive analysis of competition policies in Spain- provides evidence that barriers to entry increase regional prices. The evidence also suggests that, consistent with the model's predictions, barriers to entry raise prices up to a point, and thus indicate that barriers have a threshold effect on prices.

Differential information economies: Introduction

Since the Cournot-Nash and Arrow-Debreu-McKenzie contributions to equilibrium theory with complete information, two main advances in equilibrium theory with differential information appeared. The first one is by Harsanyi (1967), who introduces differential information into the Cournot-Nash model, and the second one is by Radner (1968), who introduces differential information into the Arrow-Debreu-McKenzie model. Those two papers generated a literature on Bayesian Cournot-Nash equilibrium and on Walrasian expectations equilibrium respectively. In the seventies and eighties there was a growing literature on Rational Expectations Equilibrium (REE), which is a natural extension of the Arrow-DebreuMcKenzie deterministic model of Walrasian equilibrium to a differential information framework. This literature on REE (a non-cooperative equilibrium concept) didn’t provide an adequate explanation as to how prices reveal the same information to agents who are differentially informed, or to put it differently, how agents who have different information obtain the same information from the equilibrium prices. In other words, prices don’t reflect the informational asymmetries of agents and this can be a major criticism of the REE concept under full revelation. A new literature emerges from two early seminal works on cooperative equilibrium concepts with differential information. The first one was by Wilson (1979), who considers the core of an economy with differential information,

Market Structure and the Demand for Free Trade

We explore the interplay of market structure and government trade policy in the context of a heterogenous goods duopoly model (allowing for goods to be substitutes or complements) wherein governments simultaneously and noncooperatively choose whether or not to provide subsidies for their firms and then firms noncooperatively choose output levels, either sequentially (i.e., in a Stackelberg leader-follower model) or simultaneously (i.e., in a Cournot-Nash model). We focus on competition in quantities but also provide results when firms compete in prices. In both the quantity and price models we further allow for endogenous market structure by considering two game forms wherein one of the firms, a potential leader, can choose to lead or not lead (play Cournot). We find that government trade policy and market structure can interact. First, the trade regime can alter traditional firm preferences over sequential versus simultaneous play. Second, different market structures can influence governments' preferences about free trade versus subsidies. Further, if one of the firms is a potential leader, allowing for endogenous market structure generates equilibrium outcomes that sometime reinforce, and sometimes counter, received results in the extant strategic trade literature. For example, when firms compete in quantities, endogenous market structure results in Cournot-Nash competition, but competition in prices results in a leader-follower structure.

Market structure of multi-product firms under free entry

Three sources of advantages to multi-product firm are considered: economies of scope, risk reduction and demand complementarity. Each source if of sufficient magnitude leads to a market equilibrium dominated by multi-product firms. As the market becomes sufficiently large the multi-product Cournot-Nash model is shown to converge to an efficient outcome.

A Graphical Analysis of the Cournot-Nash and Stackelberg Models

(1997). A Graphical Analysis of the Cournot-Nash and Stackelberg Models. The Journal of Economic Education: Vol. 28, No. 1, pp. 48-57.

Duopoly, Delivered Pricing and Horizontal Mergers

Federal merger guidelines recognize that when sellers are spatially dispersed, the closeness of competitors can be crucial in evaluating the welfare consequences of a merger.1 This recognition makes it surprising that more research has not focused on the issue of horizontal mergers in spatial models. The spatial setting is particularly interesting since the fact that a merger might occur in the future can alter the location decision made by firms. We analyze a spatial duopoly with price discrimination. In the first stage, firms choose locations noncooperatively, along a linear market, with the foresight that a merger may occur in a later stage. In the second stage, firms decide whether to merge. Delivered price schedules are announced in stage three. Within this structure, we study the effects of simultaneous and sequential entry and conclude that the possibility of merger generally leads to inefficient location choices and higher transport costs. Levy and Reitzes examine the anticompetitive effects of mergers in Salop's circular model [9; 12]. In this model firms are evenly spread around a circle and then a Bertrand-Nash game is played in prices. They conclude that if two adjoining firms merge, the merged firm will increase prices at both its locations and prices will rise, although to a lesser extent, at all other locations. In related work, McAfee, Simons and Williams study a Cournot-Nash model of horizontal mergers between firms that engage in spatial price discrimination [10]. Their work also yields an estimate of the increases in equilibrium post-merger delivered price. Yet, both of these studies treat firm locations as fixed. This rules out any influence of future possible merger on the location choices of firms. We will show that this influence can be substantial.

Product-line selection, production decisions and allocation of common fixed costs

Product costs are determined in practice for the purpose of pricing, make-buy and product-line decisions. While many costs are directly assignable to individual products, common costs have historically presented a difficult conundrum. A variety of cost allocation methods are used in practice, or have been suggested in the literature, to attach these costs to individual products. While such procedures are theoretically unsupported, they may be able to mimic the “correct” decisions adequately. In this paper, we investigate the efficacy of certain cost allocation schemes in a competitive environment. The schemes are evaluated with reference to a scenario in which there is a single fixed cost incurred in manufacturing any subset of a set of products. Under idealized conditions, a Cournot-Nash model is developed that describes the number of entering firms and the equilibrium price and production levels. Using this as a point of reference, it is shown that by using gross contribution as an allocation basis, optimal product-line decisions are achieved, without distorting the selection of production levels. Moreover, competitive pressure sufficient to drive total net profits close to zero is sufficient to require that any allocation rule supporting optimal product-line decisions yields allocations nearly proportional to gross contributions. An analogy is drawn with the allocation of joint costs to coproducts in a competitive environment, and the corresponding allocation in proportion to net realizable value.

Horizontal Mergers in Spatially Differentiated Noncooperative Markets

The authors present a Cournot-Nash model of horizontal mergers between firms that engage in spatial price discrimination. The model extends the analysis of such mergers as presented in the U.S. Department of Justice's Merger Guidelines. Rather than conclude the evaluation of such a merger with an estimate of the postmerger Hirschman-Herfindahl Index, as is done in the Merger Guidelines, the authors' model yields an estimate of the increases in the equilibrium, postmerger delivered.prices caused by the merger. Copyright 1992 by Blackwell Publishing Ltd.

Horizontal Mergers and Antitrust Policy

The welfare implications of horizontal mergers are examined in the context of the Cournot-Nash model of M. Perry and R. Porter (1985). Horizontal mergers are more likely to be welfare enhancing the more concentrated is the ownership of the nonmerging firms. Mergers that create a new largest firm, or increase the size of the largest firm, reduce welfare. Copyright 1992 by Blackwell Publishing Ltd.

Technology and price in a non-cooperative framework

We consider a Cournot-Nash model to argue that lowering of cost of production for a particular producer might lead to an increase in the price of the commodity. This result has implications for patentship of innovations and technology licensing policies.

Imperfect competition under uncertainty

The behavior of firms in the Cournot-Nash model is examined under uncertainty in market demand and in their production. The emerging result is that if one of the firms is more strongly risk averse than the other its output will increase but total output declines (even when the other is risk neutral). In the Stackelberg model, however, if the follower is risk neutral it might compensate for the decline of output by the leader.