Showing papers on "Stackelberg competition published in 2003"

Nash-Cournot Equilibria in Power Markets on a Linearized DC Network with Arbitrage: Formulations and Properties

Abstract: Extending a prior arbitrage-free model of Hobbs (2001), this article presents two models of an electric power market with arbitrage on a linearized DC network with a affine price functions The two models represent a decentralized system involving bilateral contracts between producers and consumers in which the system operator's role is limited to providing transmission services The two models differ in how arbitrage is handled In the first model, the producers anticipate the effect of arbitrage upon prices at different locations (Stackelberg assumption), and therefore treat the arbitrage amounts as decision variables in their profit maximization problems In the second model, the firms take the arbitrage quantities as inputs in their problems (Cournot assumption), and the arbitrager solves a separate profit maximization problem that takes the electricity prices and the transmission costs as inputs In each model, we adopt a Nash-Cournot equilibrium as the solution concept for the game among producers We show that the resulting equilibrium problems can be formulated as monotone mixed linear complementarity problems Based on such a formulation, we obtain existence,uniqueness,and various quantitative properties of the equilibrium solutions to the models It is also demonstrated that these two models of a bilateral market yield the same prices, producer outputs, and profits as a model of Cournot competition in a “Poolco” system,in which a system operator runs a centralized auction and buys all production, and then resells it to consumers This result implies that Cournot competition among producers yields the same outcomes for two distinct market designs Finally, we present a numerical example to illustrate the theoretical results

Stackelberg Mixed Duopoly with a Foreign Competitor

Abstract: We investigate Stackelberg mixed duopoly models where a state-owned public firm and a foreign private firm compete We examine a desirable role (either leader or follower) of the public firm We also consider endogenous roles by adopting the observable delay game of Hamilton and Slutsky (1990) We find that, in contrast to Pal (1998) discussing a case of domestic competitors, the public firm should be the leader and that it becomes the leader in the endogenous role game We also find that in contrast to Ono (1990) eliminating a foreign firm does not improve domestic welfare in mixed oligopolies

Stackelberg Mixed Duopoly with a Foreign Competitor

Abstract: We investigate Stackelberg mixed duopoly models where a state-owned public firm and a foreign private firm compete. We examine a desirable role (either leader or follower) of the public firm. We also consider endogenous roles by adopting the observable delay game of Hamilton and Slutsky (1990). We find that, in contrast to Pal (1998) discussing a case of domestic competitors, the public firm should be the leader and that it becomes the leader in the endogenous role game. We also find that in contrast to Ono (1990) eliminating a foreign firm does not improve domestic welfare in mixed oligopolies.

Analysis of a Decentralized Production-Inventory System

Abstract: We model an isolated portion of a competitive supply chain as aM/M/1 make-to-stock queue. The retailer carries finished goods inventory to service a Poisson demand process, and specifies a policy for replenishing his inventory from an upstream supplier. The supplier chooses the service rate, i.e., the capacity of his manufacturing facility, which behaves as a single-server queue with exponential service times. Demand is backlogged and both agents share the backorder cost. In addition, a linear inventory holding cost is charged to the retailer, and a linear cost for building production capacity is incurred by the supplier. The inventory level, demand rate, and cost parameters are common knowledge to both agents. Under the continuous-state approximation where theM/M/1 queue has an exponential rather than geometric steady-state distribution, we characterize the optimal centralized and Nash solutions, and show that a contract with linear transfer payments replicates a cost-sharing agreement and coordinates the system. We also compare the total system costs, the agents' decision variables, and the customer service levels of the centralized versus Nash versus Stackelberg solutions.

Endogenous Role in Mixed Markets: A Two-Production-Period Model

Abstract: In this paper, I investigate endogenous roles in a mixed duopoly, where private and state-owned public firms compete, by allowing two production periods. I find that many equilibria exist, including the Cournot-type equilibrium and one Stackelberg-type equilibrium where the public firm becomes the follower. However, another Stackelberg-type equilibrium where the public firm becomes the leader does not exist. If small inventory costs are introduced, the unique equilibrium outcome becomes the Stackelberg type where the public firm is the follower.

The Stackelberg equilibrium applied to AC power systems-a noninterior point algorithm

Abstract: The electric utility deregulation process and the introduction of competition among its participants introduced the notion of equilibria models adapted to the energy market. Among them, the Stackelberg equilibrium represents a monopolist approach, defined by a hierarchical structure, with a dominant firm acting in a privileged position and a group of subordinated ones acting as followers. Its application to AC power systems can be modeled as a bilevel mathematical problem, and represented by its Karush Kuhn Tucker (KKT) formulation. This paper presents a noninterior point algorithm to solve this Stackelberg equilibrium, considering the electrical power system as an interconnected network through its transmission system. Numerical examples with a 24 bus and the IEEE-118 bus systems illustrated the leader participant behavior and showed the market power exercised by them, which is increased in the presence of tighter transmission capacity constraints. The numerical examples also showed the robustness and efficiency of the proposed algorithm.

Hotelling competition on quality in the health care market

Abstract: This paper aims to theoretically analyse recent health system reforms. Generally patients are free to choose, within the region they live in, the best provider among the private "accredited" and public ones. The criterion patients use to choose the provider which fits their expectations best is not, at least in a tax financed system, the price of the treatment since patients do not pay directly for the treatment they receive. Crucial in determining their choice is the quality level and the provider spatial location. In a normative perspective we want to analyse hospitals' Nash/Counot and Stackelberg equilibriums in a Hotelling spatial competition scenario. Because of asymmetric information, patients could be unable to observe the true quality provided. Thus the demand for health care services is assumed to depend on a perceived quality (different from true quality). New equilibrium outcomes are investigated when patient choice is affected by uncertainty.

The Effects of Information on Strategic Investment and Welfare

Abstract: A model is considered where two firms compete in investing in a risky project. At certain points in time the firms obtain imperfect information about the profitability of the project. We impose that investing first can be beneficial because a Stackelberg advantage, and thus a higher market share, is obtained. On the other hand, investing as second implies that one can benefit from an information spillover generated by the investment of the other firm. Consequently, in equilibrium there is either a preemption situation or a war of attrition. In case no investment takes place during the war of attrition, this war of attrition can turn into a preemption situation. One counterintuitive result is that welfare can be negatively affected by signals becoming more informative or by occuring more frequently. Furthermore, simulations indicate that duopoly leads to higher welfare than monopoly when signals are less informative, wheras the opposite holds if there is more or better information.

Cournot Vs Stackelberg Equilibria with a Public Enterprise and International Competition

Abstract: This paper examines the validity of alternative assumptions about public enterprise strategies in the presence of both domestic and international competition. It extends the quantity-setting game to a preplay stage and endogenizes the firms' order of moves to show that i) Cournot competition is not the subgame perfect Nash equilibrium of the extended game, ii) the only SPN equilibria are sequential and iii) for some values of structural parameters, public Stackelberg leadership is the unique SPN equilibrium solution of the game. This has a significant consequence for debates over privatisation because with a public Stackelberg leadership game, there is no distortionary effect associated with the operation of a public enterprise in the domestic market.

All Stackelberg Location Equilibria in the Hotelling's Duopoly Model on a Tree with Parametric Prices

Abstract: The sequential Hotelling's duopoly model on a tree was studied by Eiselt (1992), who developed conditions for the existence of location equilibria when location decisions are nodes and prices are parametric In this paper, this competition model is also analyzed, but considering that locations for the two firms can be any pair of points on the tree, nodes or points in the edges First, a condition is given under which both the leader and the follower get a positive profit In this setting, the problem of finding optimal locations for each of them is studied with different and equal prices In both cases, the set of optimal locations for the follower is generated for any location of the leader as well as the set of optimal locations for the leader As a consequence the entire set of Stackelberg solutions to this competition model is obtained

Allowing for Two Production Periods in the Cournot Duopoly: Experimental Evidence

Abstract: In this study behavior in a Cournot duopoly with two production periods (the market clears only after the second period) is compared to behavior in a standard one-period Cournot duopoly. Theory predicts the endogenous emergence of a Stackelberg outcome in the two-period market. The results of the experiments, however, reveal that in both markets (roughly) symmetric outcomes emerge and that, after a short adaptation phase, average industry output in the two-period markets is the same as in the standard one-period markets.

Continuous-Time Option Games: Review of Models and Extensions Part 1: Duopoly under Uncertainty

Abstract: The theory of option games being the combination of two successful theories, namely real options and game theory, has a great potential to applications in many real situations. Although the option games literature is very recent, it has been experimenting a fast growth in the last five years. It considers in the same model, besides the key factors for investment decisions such as uncertainty, flexibility, and timing, the effect of competition with the possible strategies for each firm. This paper reviews a selected literature on continuous-time models of option games and provides some new insights and extensions. This review is divided into two parts or two papers. In this paper we analyze models of duopoly under uncertainty – both symmetrical and asymmetrical. First we present a brief survey of option games with a summary of possible equilibriums in duopoly - like Cournot and Stackelberg, and types of demand function as well as the effects of this uncertainty on these functions. We discuss concepts like the preemption, non-binding collusion, main and secondary perfect-Nash equilibriums in pure strategies, first mover advantage, situations that mixed strategies are necessary, probability of simultaneous exercise as mistake, effect of the competitive advantage, etc. We show that there are two equivalent ways to calculate both leader and follower values, and two ways to calculate the follower threshold. We also extend the asymmetrical duopoly under uncertainty model analyzed by Joaquin & Buttler by considering issues like mixed strategies in asymmetric duopoly and the value of option to become a leader. In a second paper will be discussed important option games models like oligopoly under uncertainty, war of attrition and other models of positive externalities, models with either incomplete or asymmetric information, the current option-games models limitations, and suggestions for future research.

Cournot and Bertrand Games

Abstract: The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row chooser. Because each player has a table, each thinks of him- or herself as the row chooser and the other as the column chooser. The games may be applied to international trade through the traditional Boeing v. Airbus story or, more currently, through foreign sales corporations. Addition of Bertrand competition allows discussion of price wars, and addition of perfect complements allows discussion of the proposed Microsoft breakup.

Bailouts in a Federation

Abstract: The recent move towards decentralization in countries such as Spain, Hungary, and South Africa and the difficulties that central governments have had in dealing with fiscal irresponsibility on the part of regional governments in countries such as Argentina, Brazil, and India has made the study of transfer systems one of the most important areas of research in federalism today. A model of a federation is developed in which regional governments act as Nash competitors with each other but are first-movers in a Stackelberg game with the central government. The central government finds that it will maximize its expected votes by increasing transfers as regions borrow. This bail out of regional governments creates a regional soft budget constraint and results in two incentive effects, a common pool effect on tax payments and an opportunity cost effect. The soft budget constraint lowers the opportunity cost of borrowing for the region, but also increases the tax-cost since a portion of the borrowing must be paid for through increased taxes. The common property problem associated with tax payments implies that the increased tax cost must be less than the decrease in the opportunity cost (leading to excessive borrowing) unless the central government increases grants to other regions when it institutes a bailout. Somewhat surprisingly, in the latter case the additional increased taxes may increase costs enough to offset the lower opportunity cost resulting from the bailout, leading to efficient borrowing decisions as in the case of a hard budget constraint. The results are also useful for understanding the empirical estimation of soft budget constraints.

On a property of mixed strategy equilibria of the pricing game

Abstract: Before solving a two-stage capacity and pricing game for oligopoly, Boccard and Wauthy (2000) argue that, as under duopoly, at a mixed strategy equilibrium of the pricing game the largest firm's expected profit is the profit accruing to it as a Stackelberg follower when the rivals supply their entire capacity. We point to a serious mistake in their argument and then we see how this important property can be satisfactorily established.

Price Competition between an Internet Firm and a Bricks and Mortar Firm

Abstract: This dissertation uses a vertically differentiated products model to examine price competition between two firms, one Internet and one bricks and mortar, who sell the same physical product. Demand is deterministic and is based on consumers' reservation price curves, which are taken to be linear. Consumers are assumed to have different reservation prices for the two channels, even when buying the same physical product, because of the differences in how individuals value the “total product,” the utility of the product itself plus perceived and actual costs and benefits such as driving time, waiting time for products shipped, search time, and the shopping experience itself. Customers will choose to purchase from the firm that provides them the most economic surplus. Additionally, only a fraction of the population is assumed to both have access to the Internet and be willing to purchase on-line. As a result, there are effectively two market segments: those who will purchase on-line and those who will purchase only at a bricks and mortar store. We solve for each firm's optimal price in both Nash (simultaneous) and Stackelberg (sequential) games. Using the degree of innovation, a concept developed by Schmidt and Porteus (2000b), the resulting market structures are interpreted and the importance of innovation in service execution, cost control, and marketing is discussed. For a fixed degree of innovation and reservation price curve structure in the Nash game, it is demonstrated that as the fraction of consumers willing to purchase on-line increases, the resulting market structure may change. Moreover, at odds with one's expectations, as more people become willing to shop on-line, the Internet firm may actually be worse off, all else equal. The increase in the fraction of on-line shoppers alone is not enough to improve the Internet firm's market position. The leader-follower game is also developed, allowing the comparison of the two Stackelberg equilibria and the simultaneous Nash game equilibrium. A firm is found to be at least weakly better off in the Stackelberg equilibria, assuming s/he gets to choose his/her most preferred role.

Cost Structures and Nash Play in Repeated Cournot Games

Abstract: This paper reports an experiment designed to assess the effects of a rotation in the marginal cost curve on convergence in a repeated Cournot triopoly Increasing the cost curve's slope both reduces the serially-undominated set to the Nash prediction, and increases the peakedness of earnings We observe higher rates of Nash equilibrium play in the design with the steeper marginal cost schedule, but only when participants are also rematched after each decision Examination of response patterns suggests that the treatment with a steeper marginal cost curve and with a re-matching of participants across periods induces the selection of Nash Consistent responses

Labor market regimes and monetary policy

Abstract: In this paper we propose straightforward extensions of multi-union, monopolistic competition models appearing in the recent literature on the macroeconomic effects of monetary policy. We extend these models from the Stackelberg equilibrium to the Nash equilibrium under variations in labor market regime in order to evaluate propositions about non-neutrality of monetary policy.

Macroeconomic Effects of Sectoral Shocks in Germany, the U.K. and, the U.S

Abstract: Models for non-cooperative as well as cooperative behavior of families are estimated on data from Norway from 1994 to 1998. The models aim at explaining labor supply behavior of married couples the first five months after the husband becomes eligible for early retirement, while the wife is not eligible. Estimates and predictions derived from the different models are compared. Econometric tests find that the Stackelberg model with the male as the leader is the best. Simulations with the estimated models show that taxing pension income the same way as labor income would reduce the propensity to retire early considerably.

On finding curb sets in extensive games

Abstract: We characterize strategy sets that are closed under rational behavior (curb) in extensive games of perfect information and finite horizon. It is shown that any such game possesses only one minimal curb set, which necessarily includes all its subgame perfect Nash equilibria. Applications of this result are twofold. First, it lessens computational burden while computing minimal curb sets. Second, it implies that the profile of subgame perfect equilibrium strategies is always stochastically stable in a certain class of games.

Stackelberg Solutions to Two-Level Linear Programming Problems with Random Variable Coefficients

Abstract: In this paper, to cope with hierarchical decision making problems under uncertainty, we formulate a two-level linear programming problem in which random variable coefficients are involved in objective functions and constraints, and reduce the problem into deterministic problems by using two models. While one of the deterministic problems is a usual two-level linear programming problem, the other is a two-level quadratic one. We present a computational method for obtaining Stackelberg solutions to the reduced deterministic two-level quadratic programming problems.

Game Theory and Applications

Abstract: Preface A Robust Control Approach to Option Pricing: The Uniqueness Theorem Existence & Uniqueness of Nash Equilibria in a Simple Lanchester Model of the Impact of Customer Churn The Game-Theoretical Model of Selection Services in Company with Various Ordering Schemes Numerical Approximation of Nash Equilibria for a Class of Non-Cooperative Differential Games Public Goods in Networks: A Statistical Mechanics Approach Network Congestion, Braess Paradox & Urban Expressway System Game-theoretical Model of Service Quality Choice: Portuguese Mobile Service Market Paul Samuelsons Critique & Equilibriums Concepts in Evolutionary Game Theory Price Stackelberg Competition & Capacity Constrains An Inter-group Conflict Model Integrating Perceptions of Threat & Vested Interest: Extending Rational Choice to Incorporate Psychological Dynamics Product Differentiation in the Presence of Social Interactions of Consumers A Class of Differential Games with Random Terminal Time The Present & Future of Game Theory Index.

Regulating transmission in a spatial oligopoly: A numerical illustration for Belgium

Abstract: This paper introduces strategic behavior of the electricity network operator in a congested network with imperfect competition for generation. It models a two stage Stackelberg game. First, the network operator sets transmission prices, then generators set output and sales. Several scenarios for the generation market structure and the behavior of the network operator are compared numerically. The calibration of the numerical model is based on data of the Belgian electricity market.