Showing papers on "Stackelberg competition published in 1990"

A Branch and Bound Algorithm for the Bilevel Programming Problem

Abstract: The bilevel programming problem is a static Stackelberg game in which two players try to maximize their individual objective functions. Play is sequential and uncooperative in nature. This paper presents an algorithm for solving the linear/quadratic case. In order to make the problem more manageable, it is reformulated as a standard mathematical program by exploiting the follower's Kuhn–Tucker conditions. A branch and bound scheme suggested by Fortuny-Amat and McCarl is used to enforce the underlying complementary slackness conditions. An example is presented to illustrate the computations, and results are reported for a wide range of problems containing up to 60 leader variables, 40 follower variables, and 40 constraints. The main contributions of the paper are in the step-by-step details of the implementation, and in the scope of the testing.

A solution method for the linear static Stackelberg problem using penalty functions

Abstract: A new solution technique is presented for the linear constrained static Stackelberg problem. For a given value of x, the leader's decision vector, the follower is at its rational reaction set when the duality gap of the second-level problem becomes zero. The outer problem is solved by appending to the leader's objective, a function that minimizes the duality gap of the follower's problem. This structure leads to the decomposition of the composite problem into a series of linear programs leading to an efficient algorithm. It is proved that optimality is reached for an exact penalty function, and the method is illustrated with some examples. >

On the Numerical Solution of a Class of Stackelberg Problems

Abstract: This study tries to develop two new approaches to the numerical solution of Stackelberg problems. In both of them the tools of nonsmooth analysis are extensively exploited; in particular we utilize some results concerning the differentiability of marginal functions and some stability results concerning the solutions of convex programs. The approaches are illustrated by simple examples and an optimum design problem with an elliptic variational inequality.

Stackelberg Leadership as a Natural Solution Under Cost Uncertainty

Abstract: This paper analyzes a differentiated duopoly model with cost uncertainty in an environment where information sharing is prohibited. The duopolists can commit themselves to be a Stackelberg leader or follower at the time when they know the distribution, but not the actual values, of their own and the rival's costs. In a natural Stackelberg situation, the firms agree on the assignment of roles and neither prefers the (Bayesian) Nash equilibrium. An natural Stackelberg situation is shown to be possible under quantity (but not price) competition. Total expected welfare is higher in the natural Stackelberg situation than in the Nash equilibrium. Copyright 1990 by Blackwell Publishing Ltd.

Sequential provision of public goods

Abstract: I consider the private provision of public goods when agents are able to make sequential contributions rather than simultaneous contributions. I show that this tends to exacerbate the free-rider problem in the sense that the amount of the public good provided under sequential contribution is always less than under simultaneous contribution.

Entry-Deterrence in Stackelberg Perfect Equilibria

Abstract: This paper examines entry deterrence in a duopoly where the postentry game is Stackelberg. It is argued that, in reality, firms can use a broader range of precommitments than is allowed for in the literature. This paper permits such precommitments and analyzes the perfect equilibria. It also allows for the fact that there may be fixed costs associated not only with entry, but with beginning production. Several interesting possibilities are explained, including the existence of excess capacity and the holding of inventories even in the absence of any uncertainty. Copyright 1990 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Innovation, Market Structure, and Welfare: A Stackelberg Model

Abstract: A Stackelberg model of production with process innovations is introduced. The leader invests in RD followers conduct no R&D but are able to benefit from the leader's research. It is found that the leader invests less in R&D as the fringe expands or as spillovers from research increase. The output and R&D of the Stackelberg industry fall short of the social optimum. When the Stackelberg leader is more efficient than the fringe, a few firms generate more social welfare than a large number of firms under high technological opportunity. As the technological opportunity diminishes, the welfare differences between market structures are reduced. The findings of this article lend support to the Schumpeterian hypothesis.

Closed-form solution for discrete-time linear-quadratic Stackelberg games

Abstract: A method is proposed for solving the two-point boundary-value problem occurring in discrete-time linear-quadratic Stackelberg games. It is shown that, for open-loop information structure, the necessary conditions can be ordered to form a symplectic matrix. The solution is then obtained by exploiting the properties of such a matrix.

Optimal flow control and fairness in communication networks--a game theoretic perspective

Abstract: The problem of defining an optimum flow control strategy in a multiclass telecommunication networks environment is addressed in this thesis. Several classes of users compete for the resources of a network trying to optimize their performance. From the point of view of game theory, which is the natural setting, there is a precise way of treating this problem. This is not just an artifact, the advantage is that it leads to some precise answers to the problem of optimal, fair flow control schemes which are not only powerful but beautiful in their simplicity as well. Using power as the performance criterion, the performance of the system and of the individual users is obtained. When there is no distinction between the classes a system optimization point is defined. When classes act independently and optimize their performance without having knowledge of the objectives of the other classes, then the Nash equilibrium is calculated. When one of the classes has a priority of information and acts knowing the reactions of the other classes than the Stackelberg equilibrium is proposed as the appropriate operation point. Convergence properties of the greedy algorithm to a Nash equilibrium are analysed. A complete analysis for the synchronous and asynchronous algorithms that converge to Nash equilibria is given. In the cooperative case Pareto optimality is defined as the appropriate flow control notion. Pareto optimal algorithms are given for the single queue case and the association between Pareto optimality and the product of powers is presented. When a throughput delay criterion is used Pareto optimality results in multiobjective programming and the Stackelberg equilibrium results in a multilevel program. Through a transformation of variables both problems are transformed to their equivalent linear versions. An interconnection between these methods and the optimization of a weighted criterion is shown. The Nash arbitration scheme is presented as the appropriate way to define a unique fair strategy. The Jacksonian network with loop-free routing is the model used in this chapter. It is shown that the product of powers provides a unique Pareto point that is fair to all the classes. In the case of delay constraints a modified version of the throughput delay criterion is presented. Uniqueness of the fair point is also shown in this case.

Stackelberg price leadership in the linear heterogeneous duopoly

Abstract: We consider for the linear heterogeneous duopoly with substitutive goods and with price strategies the situations in which one firm, firm 1 say, prefers to be price leader, whereas firm 2 prefers to be price follower Conditions that necessarily hold in that case are derived and interpreted in economic terms These conditions characterize the powerful position of firm 1 relative to firm 2 on the market

Optimal dynamic taxation with respect to firms

Abstract: In this paper we develop a framework for determining optimal profit taxation in a market economy with value-maximising firms, which face costs of adjustment for investment. The government chooses this tax rate in such a way that the utility of the consumer, which depends on public and private consumption will be maximised. The private consumption is financed by wage income and dividend, while public consumption is financed by tax revenues. We show that there is a dynamic trade-off between public consumption now and in the future. Two possible solutions are derived. The first solution, which is the formal outcome of an open-loop Stackelberg equilibrium of a game between government and firms, is time-inconsistent and is only credible, if there is commitment or if there are reputational forces. The second solution, which corresponds to a feedback Stackelberg equilibrium, is time-consistent, but yields a lower value of steady-state utility.

Three essays on strategic trade policy : precommitment, time consistency, and effects of a ratio quota

Abstract: This dissertation investigates the strategic behavior of firms under imperfect competition in international trade;We utilize the Spencer-Brander multi-stage game in which two firms; one foreign and one domestic, compete as Cournot rivals in a third country. A three-stage game is characterized as: (1) one home government sets subsidies on both export and investment, (2) firms choose the levels of investment, and (3) firms choose output levels. We show that it is not generally optimal to choose investment levels that minimize costs in a Spencer-Brander model. Precommiting both investment and output levels by a home government (as a normal Stackelberg leader) is shown to yield a solution superior to the Spencer-Brander outcome;However, neither of these precommitment models is time consistent because the ex ante subsidy in a precommitment model is larger than that which appears optimal ex post. We show that the time consistent solution can dominate the precommitment solutions, a result that is at odds with the conventional wisdom concerning the inferiority of the time consistent solution. This result emerges because neither precommitment solution is made optimally contingent on foreign investment;We examine the effects of a ratio VER (voluntary export restraints). We claim that under the implementation of a ratio VER, the strategic behavior of firms is most appropriately modeled as simultaneous play, not as Stackelberg leadership for the home firm. Under simultaneous play, we show that (1) there is no equilibrium in pure strategies, and (2) the unique mixed strategy exists with the domestic firm's randomization of its production. In comparing tariffs and quotas, we find that the foreign firm prefers a VER to a tariff system, when the two are chosen such that the home firm's profits under a VER are the same as under a tariff system.

Sluggish Demand, Price Expectations And Monopolistic Resource Extraction

Abstract: This paper integrates intertemporal decision making of consumers and a resource monopoly. This analysis accounts for another dynamic and traditionally omitted factor, namely sluggish demand. This is characteristic for many resource markets, e.g. for primary energy carriers. A Stackelberg differential game describes the interaction between the consumers and the producer. In particular, it will be shown, that the volatility of resource prices depends on the shape of the equilibrium demand curve and not on the type of consumer expectations; i.e. price volatility may happen even if consumers know this predatory strategy. Moreover, the monopolist charges higher prices compared with the static demand framework.

Entry deterrence: The case of a buyer with market power

Abstract: The model considers a seller operating under the threat of an arbitrarily large number of unknown potential entrants and facing a strategic buyer. It is shown that the seller's Nash best response function slopes downward in price-output space, while that of the buyer slopes upward. The Nash equilibrium may be associated with a lower probability of entry than the equilibrium at which the buyer behaves non-strategically. With the buyer as the Stackelberg leader, the price is shown to decrease relative to that at the Nash equilibrium, but the probability of entry may rise or fall.

Patents, market structure and welfare : a theoretical investigation into new dimensions of the patent system

Abstract: Chapter I: The relationship between inventor and the Patent Office is modelled as a 'patent regulation game' and it is shown that the conventional wisdom that the P.O. always maximizes welfare by playing the Stackelberg leader is incorrect. Other solution concepts are explored and it is found that, because of the patent life constraint, a reversal of roles may be beneficial. The result that social welfare can be maximized by the P.O. being a Stackelberg follower survives (albeit for a narrower range of values of the key parameters) even if the P.O.-leader is endowed with the additional instrument of a compulsory royalty rate. Chapter II: A new twist is added to the debate on the Schumpeterian competition hypothesis, by considering the structure of the final-product market as a policy Instrument, set by the Patent Office by manipulating patentability standards. It is found that for a vast range of demand functions and under constant returns to scale, a patentability standard that allows for more than one patent to be granted within a given product/process class is welfare superior to the monopoly-generating first-past-the-post current system. If patent life is beyond the P.O.'s control and/or there are increasing returns, no patentability standard is unambiguously preferable. Chapter III: When Research and Development are modelled as two analytically distinct stages, the choice between patentability standards (whether to grant patents to research prototypes or to fully-developed products) is shown to affect the allocation of resources between Research and Development. It is shown that under a single-patent regime, granting patents to research prototypes is unambiguously welfare-improving, whereas under a multiple-patent regime a change to patents being granted to fully-developed products and the attending increase in market uncertainty may raise welfare. Chapter IV: The economics of the 'integer constraint' is analysed and it is found that proper treatment of the indivisibility of firms may reverse the qualitative conclusions of interger-unconstrained models. As an example, a product quality oligopoly model is examined and it is shown that not only the Chamberlinian excess entry result does not apply but also that a free-entry oligopoly and a socially managed industry may produce goods of identical quality, irrespective of the values of cross-derivatives deemed crucial in the literature. Moreover, the integer constraint is shown to provide an explanation for a positive correlation between profitability and concentration in a Cournot oligopoly model with free entry.

Optimal tariff coalitions, an econometric analysis

Abstract: This paper analyzes protectionism in a game theoretic context. Non-cooperative equilibrium solutions are calculated for three players, the E.E.C., the U.S. and the Pacific Basin on the basis of the Project LINK model. These are confronted with cooperative scenarios based on bargaining theory. Coalitions of two players against the third are examined in a Nash and Stackelberg equilibrium framework. The numerical results are summarized in qualitative propositions.

Robust lyapunov games and policy co-ordination

Abstract: This paper extends the robust Lyapunov stabilization approach developed by Leitmann and coworkers to discrete-time, uncertain two-players games. The games are uncertain in the following sense. None of the players knows exactly the constraints facing it or its opponent. Possibly, even the opponent's strategies are not exactly known. However, each player is assumed to know with certainty that the true game lies within a known, bounded class of games. Nash and Stackelberg solutions to the uncertain Lyapunov games are derived, and their basic properties are investigated.

Noncooperative game approach for public participation and resource supply in electric generating system development

Abstract: A two-level multifollower Stackelberg game model for electric generating system development and efficient resource utilization is developed. It is assumed that exist plural public groups with different social siting concerns. Interperiod balances in electric generating capacity and resource supply are first investigated. Several fundamental factors such as electric supply, siting concern, and electric cost are then evaluated, where the social negative preference plays the basic role. The integrated problem of resource supply, electric generating system development, and public participation is then formulated as a two-level multifollower Stackelberg game, in which electric generating system development with public participation is investigated at the second level under the first-level resource supply strategy. The model evaluates interactions between the electric supply, resource supply, and social siting concern. Simulation analyses are presented to show the characteristics and effectiveness of the model. >

Nash vs Stackelberg strategies in a capital accumulation game

Abstract: This paper is aimed at giving new insights on the strategic investment problem as formulated by Spence (1979) and Fudenberg & Tirole (1983) [F-T hereafter]. These authors analyse the investment intertemporal strategies simultaneously used by a firm established in a market and by a new entrant when investment is assumed to be irreversible and when there is no capital depreciation through time. The strategic investment level of the established firm is then defined as the minimum initial capital stock which prevents the new entrant to get nonnegative profits in the future. The strategic investment depends on the strategies used in the post-entry game. The analysis of the post-entry game will be made in terms of Differential Games. Two dynamic equilibrium concepts will be discussed: the perfect Nash equilibrium (closed loop) and the Stackelberg equilibrium. Technicalities as well as comparisons with F-T results are given in Thepot (1989). Section 1 is devoted to the definition of the Differential Game; the Nash and the Stackelberg strategies are respectively analyzed in Section 2 and 3.

Optimal pre-commitment in macroeconomic policy: a game theoretic analysis of fiscal policy

Abstract: This paper proposes a new solution to the problem of time inconsistency that arises in dynamic policy games played between the government and the public. In a Stackelberg game, a subgame-perfect equilibria is found in which members of the public employ trigger strategies in response to a sequence of policies chosen by the government. The government's precommitment to a particular policy is determined endogenously as part of its optimal strategy. In a simple political model of fiscal policy, the proposed equilibrium is used to show why a government will tolerate a rise in debt well above its targeted level. Copyright 1990 by Royal Economic Society.

Precommitment and Random Exchange Rates in Symmetric Duopoly: A New Theory of Multinational Production

Abstract: Recent volatility in real exchange rates has renewed interest in the nature of multinational firms. One increasingly common phenomenon involves the foreign sourcing of production, in which certain domestic firms choose to produce part or all of their product abroad and then export the commodity for domestic sale. Multinational production has been rationalized on the basis of inherent asymmetries between firms, such as the possession of certain firm-specific assets or differences between firms in their perceptions of foreign production costs, access to foreign subsidy programs, and the possibility of tariff preemption. Such behavior has also been rationalized in terms of corporate risk-aversion and a desire to hedge real exchange rate risk through the diversification of production locations. This paper presents an entirely novel explanation for the existence of multinational firms and the foreign sourcing of production. Rather than relying on exogenous asymmetries between firms or on assumptions about corporate aversion to risk, this explanation recognizes that exchange rate uncertainty may offer a purely strategic motive for symmetric and risk-neutral domestic oligopolists to precommit to foreign production in order to attain a position of industry leadership. This explanation is presented in the specific context of a two-period model of strategic foreign production by domestic duopolists. Strategically symmetric and risk-neutral firms are confronted by a unique source of uncertainty in the form of a randomly fluctuating exchange rate. Exchange rate uncertainty is resolved, for the purposes of current production decisions, between the two periods. Precommitted foreign production in the first period yields a leadership advantage relative to firms that do not precommit, but this decision must be evaluated against the value of the alternative of remaining flexible to adopt a production plan after the resolution of exchange rate uncertainty. A unique symmetric sequential equilibrium in mixed strategies is determined in this market, allowing a Stackelberg leader to endogenously emerge through a credible precommitment to the foreign sourcing of production.