Showing papers on "Stackelberg competition published in 1995"

Stable Cartels with a Cournot Fringe

Abstract: The notion of an industry structure characterized by a small group of dominant firms plus a competitive fringe has a long tradition. More recent work explores conditions under which such a pattern constitutes an equilibrium, assuming collusive behavior among one group of firms and price-taking behavior within the fringe [2; 3; 4; 5; 6; 14; 17]. The alternative case of a Courot fringe is analyzed briefly in Spulber [22, 471-73] and more extensively in Martin [14]. Here we adopt the framework of this literature and build on it by analyzing the size and uniqueness of the stable cartel when the fringe is Coumot; endogeneity of Courot versus Bertrand behavior within the fringe, given the stable cartel; possible endogeneity of the Stackelberg sequence of play between the cartel and the fringe; and effects of excludability from the cartel. Welfare effects are also briefly analyzed. Alternatively, cooperation within a cartel is equivalent to the outcome of horizontal mergers in the absence of synergies. As such, this paper presents a contrasting result to the analysis of exogenous Cournot mergers in Salant, Switzer, and Reynolds [18], endogenizes the merger decision, and demonstrates how a theory of mergers can be predicated on a Cournot fringe.

Topological existence and stability for Stackelberg problems

Abstract: The aim of this paper is to study, in a topological framework, existence and stability for the solutions to a parametrized Stackelberg problem. To this end, approximate solutions are used, more precisely, e-solutions and strict e-solutions. The results given are of minimal character and the standard types of constraints are considered, that is, constant constraints, constraints defined by a finite number of inequalities, and more generally constraints defined by an arbitrary multifunction.

Equilibrium Facility Location on Networks

Abstract: 1 Introduction.- 2 Aspatial Stackelberg Nash Cournot Equilibria.- 3 Classical Plant Location on Networks.- 4 Spatial Market Equilibria on Networks.- 5 Sensitivity Analysis of Spatial Market Equilibria on Networks.- 6 A Facility Sizing and Location in Spatial Price Equilibrium Model.- 7 Stackelberg Equilibria on Networks.- 8 A Facility Sizing and Location in Stackelberg Nash Cournot Equilibrium Model.- 9 The Importance of Including Reaction Functions and Analysis of Economic Equilibria in Facility Location Models: An Example.- 10 Dynamic Models: Equilibrium and Disequilibrium Approaches.- 11 Conclusion.- List of Figures.- List of Tables.

A global optimization method for the Stackelberg problem with convex functions via problem transformation and concave programming

Abstract: A global optimization method is proposed for solving the Stackelberg problem through problem transformation and concave programming. The proposed method is applicable to a broad class of the Stackelberg problem, in which each function in upper-level is convex or a difference of two convex functions, and that in lower-level is convex.

Strong-weak Stackelberg Problems in Finite Dimensional Spaces

Abstract: We are concerned with two-level optimization problems called strongweak Stackelberg problems, generalizing the class of Stackelberg problems in the strong and weak sense In order to handle the fact that the considered two-level optimization problems may fail to have a solution under mild assumptions, we consider a regularization involving ǫ-approximate optimal solutions in the lower level problems We prove the existence of optimal solutions for such regularized problems and present some approximation results when the parameter ǫ goes to zero Finally, as an example, we consider an optimization problem associated to a best bound given in [2] for a system of nondifferentiable convex inequalities

Cournot Vs Stackelberg Equilibria With Entrepreneurial and Labour Managed Firms

Abstract: The issue of equilibrium selection in a duopoly game between a profit maximizing and a labour managed firm is addressed under either price or quantity competition with product differentiation. If firms can choose the timing of moves before competing in the relevant market variable, the Bertrand game yields multiple equilibria, while the Cournot game has a unique subgame perfect equilibrium with the profit maximizing firm in the leader’s role and the labour managed firm in the follower’s role. Due to a lower total output, the Cournot-Stackelberg equilibrium yields a lower level of social welfare as compared to the simultaneous equilibrium. This reduces the incentive to transform an LM duopoly into a mixed one.

A game theoretical analysis of the quantity discount problem with perfect and incomplete information about the buyer's cost structure

Abstract: In this paper, we analyze the quantity discount problem by considering the competitive nature of the problem and the informational structure regarding the buyer's cost structure. We formulate the problem as two-person nonzero-sum game and analyze the seller's optimal quantity discount schedule and the buyer's optimal order quantity by using Stackelberg equilibrium. We show that it is always possible for the seller and the buyer to gain from quantity discount. However, a quantity discount schedule under which the buyer orders more than his EOQ at the discounted price is necessary for the seller and the buyer to gain. The optimal quantity discount schedule when the seller knows the buyer's cost parameters is given by a single break point. When the seller does not know the buyer's cost parameters, an optimal quantity discount schedule may not exist. Two approaches have been developed for the seller to offer quantity discount in this case. The application of our analysis is discussed. Our results can be especially useful when the seller has many buyers.

Weak stackelberg problem and mixed solutions under data perturbations 1 1this paper is based upon a communication presented at the 14th symposium on mathematical programming with data perturbation, Washington D.C. 1992. This research has been supported by M.U.R.S.T Roma, Italia.$ef:

Abstract: A two-level optimization problem corresponding to a Stackelberg game in which one of the two players has the leadership in playing the game is considered First, a review of previous results about existence and stability of solutions and approximate solutions is presented in the case in which the solutions set to the lower level problem is a singleton, as well as in the case in which the response function of the follower is multi-valued Then, when some like convexity assumption on the lower level problem is not satisfied, different mixed extensions of the problem are considered and existence and stability of e-mixed solutions introduced by the authors are investigated with respect to perturbations on the data

Optimun and Revenue Maximizing Trade Taxes in a Multicountry Framework

Abstract: The traditional literature derives optimum and revenue-maximizing export taxes within two-country models. with one exporter and one importer (Johnson 1950-51, Tower 1977). In reality, most products, including primary products. are exported by several countries. In this paper, we present a theory of trade taxes in a three-country framework. This enables us to deal with strategic interactions among exporting countries. We show that (i) if one of the countries is a Stackelberg leader, both countries improve their welfare relative to Nash equilibrium, and in the symmetric case, the follower's welfare is higher than that of the leader; (ii) the revenue-maximizing Nash tax is larger than the optimum tax for each country; and (iii) welfare may be higher in the revenue-maximizing Nash equilibrium than in the welfare-maximizing Nash equilibrium, a result which cannot arise in two-country models.

When is a Stackelberg Equilibrium Pareto Optimum

Abstract: Bi-level optimization problems arise in hierarchical decision making, where players of different ranks are involved. The situation is described by the so-called Stackelberg game. The players of lower rank, called followers, react to decisions made by the first rank player, also called the leader. Situations similar to this arise for instance in mixed economies, land-use, traffic signal setting and in the particularly well-known network design problem. Previously, solution techniques based on the replacement of the bi-level problem by a bi-criteria one were proposed. However, it was shown subsequently, by the means of counter examples, that the bi-level problem is not equivalent to the bi-criteria formulation. In this note we demonstrate that the bi-criteria approach is not necessarily obsolete. We derive conditions under which we show that a Stackelberg equilibrium is indeed a Pareto optimum.

Management of Effluent Discharges: A Dynamic Game Model

Abstract: This paper is concerned with the problem of the management of effluent dumped into a stream by identifiable polluters. The problem involves a Regional Council which imposes environmental levies on the polluters whose economic activity, otherwise beneficial for the region, results in pollution of the stream. The model for the problem of effluent management is formulated as a dynamic game between the Regional Council and the polluters. The game is “played” in discrete time. The players in the game are the polluters ( “followers” ) and the Council (the “leader”). This formulation leads naturally to a Stackelberg concept of the solution for the game at hand. Because of the obvious difficulties implied by this solution concept, an equilibrium will be sought through the use of an applicable Decision Support Tool wherever an analytical solution appears intractable.

Reputation and Equilibrium Selection in Games with a Patient Player

Abstract: A single long-run player plays a simultaneous-move stage game against a sequence of opponents who play only once, but observe all previous play. Let the “Stackelberg strategy” be the pure strategy to which the long-run player would most like to commit himself. If there is positive prior probability that the long-run player will always play the Stackelberg strategy, then his payoff in any Nash equilibrium exceeds a bound that converges to the Stackelberg payoff as his discount factor approaches one. When the stage game is not simultaneous move, this result must be modified to account for the possibility that distinct strategies of the long-run player are observationally equivalent. (This abstract was borrowed from another version of this item.) (This abstract was borrowed from another version of this item.)

Game Models of Environmental Policy in an Open Economy

Abstract: In this paper we study some aspects of the question of international environmental regulation from a game theoretic perspective. We address two broad questions. First, we examine the circumstances under which the pursuit of unilateral environmental policy by a country in a Stackelberg game will make that country worse off. Second, we study the effects of environmental regulation by means of alternate price control instruments in a Stackelberg game where there is transboundary pollution. We find that there are plausible theoretical circumstances in which the pursuit of unilateral environmental policy is not a good idea. Further, we show that in choosing between alternate pollution control instruments, national governments typically face a tradeoff between instruments which correct more distortions but are costly to implement and instruments which correct fewer distortions but are less costly to implement. In particular, we obtain a dominance result for a tariff policy; this result favors the use of tariffs from an informational standpoint alone.

International Trade in Exhaustible Resources: A Cartel-Competitive Fringe Model

Abstract: Author(s): Karp, Larry; Tahvonen, Olli | Abstract: We characterize the open-loop and the Markov perfect Stackelberg equilibria for a differential game in which a cartel and a fringe extract a nonrenewable resource. Both agents have stock dependent costs. The comparison of initial market shares, across different equilibria, depends on which firm has the cost advantage. The cartel's steady state market share is largest in the open loop equilibrium and smallest in the competitive equilibrium. The initial price may be larger in the Markov equilibria, so a decrease in market power may make the equilibrium appear less competitive. The benefit to cartelization increases with market share.

International Trade in Exhaustible Resources: A Cartel-Competitive Fringe Model

Abstract: We characterize the open-loop and the Markov perfect Stackelberg equilibria for a differential game in which a cartel and a fringe extract a nonrenewable resource. Both agents have stock dependent costs. The comparison of initial market shares, across different equilibria, depends on which firm has the cost advantage. The cartel's steady state market share is largest in the open loop equilibrium and smallest in the competitive equilibrium. The initial price may be larger in the Markov equilibria, so a decrease in market power may make the equilibrium appear less competitive. The benefit to cartelization increases with market share.

Team-Optimal Closed-Loop Stackelberg Strategies for Discrete-Time Descriptor Systems

Abstract: In this paper we investigate the team-optimal closed-loop Stackelberg strategies for discrete-time descriptor systems. We show that the closed-loop no-memory information on the descriptor variables is sufficient for the leader to design the team-optimal feedback closed-loop Stackelberg strategies for a general class of linear-quadratic Stackelberg games. Sufficient conditions for the existence of such strategies are derived. A recursive scheme is presented to determine the team-optimal feedback closed-loop Stackelberg strategies. A numerical example is solved to illustrate the validity of the sufficient conditions.

International Trade in Exhaustible Resources: A Cartel-Competitive Fringe Model - eScholarship

Abstract: We characterize the open-loop and the Markov perfect Stackelberg equilibria for a differential game in which a cartel and a fringe extract a nonrenewable resource. Both agents have stock dependent costs. The comparison of initial market shares, across different equilibria, depends on which firm has the cost advantage. The cartel's steady state market share is largest in the open loop equilibrium and smallest in the competitive equilibrium. The initial price may be larger in the Markov equilibria, so a decrease in market power may make the equilibrium appear less competitive. The benefit to cartelization increases with market share.

Sequential stability of regularized constrained stackelberg problems

Abstract: We are concerned with constrained Stackelberg problems, corresponding to nonzero-sum non-cooperative games, in which the constraints of the leader depend on the reaction set of the follower supposed not to be a singleton, generalizing the case considered in [2,10]. In [1], existence and approximation results have been given by considering regularized problems. Here our aim is to give stability results for such regularized problems under data perturbations, generalizing those presented in [9]

A Characterization of the Food Industries

Abstract: This paper investigates consistency in the context in which conjectural variation have been applied to the food industries. This is a homogeneous-product, quantity-setting model in which firms are identical. Previous contributions in the American Journal of Agricultural Economics use the model in a hybrid form, which is part conjectural variations and part Cournot. Stackelberg (1934) and Leontief (1936) provide the foundations for a pure, conjectural variations approach. When the model is applied in its correct form, the following conclusions are obtained; An identical-finns, restricted-entry equilibrium yields a consistent conjecture. It is the monopolistic conjecture. When entry is endogenous, consistency requires ,firm output to contract with new entry and expand with exit, but there exists no conjecture that is consistent with equilibrium. Consequently, the restricted-entry equilibrium, in which firms have monopolistic conjectures, is unique. It predicts unambiguous grounds for public intervention in the food system, the premise for which should be tested.