Showing papers on "Stackelberg competition published in 1986"
TL;DR: In this paper, the authors compare how much profit an owner of a patent can realize by licensing it to an oligopolistic industry producing a homogeneous product, by means of a fixed fee or a per unit royalty.
Abstract: We compare how much profit an owner of a patented cost-reducing invention can realize by licensing it to an oligopolistic industry producing a homogeneous product, by means of a fixed fee or a per unit royalty. Our analysis is conducted in terms of a noncooperative game involving n + 1 players: the inventor and the n firms. In this game the inventor acts as a Stackelberg leader, and it has a unique subgame perfect equilibrium in pure strategies. It is shown that licensing by means of a fixed fee is superior to licensing by means of a royalty for both the inventor and consumers. Only a "drastic" innovation is licensed to a single producer.
657 citations
TL;DR: In this paper, the authors consider the von Stackelberg duopoly model and show that the duopolists will agree over the choice of leader if they have downward-sloping reaction functions and similar profit functions.
Abstract: Under what circumstances will firms agree on the choice of roles of leader and follower in the von Stackelberg duopoly model? A key determinant is the slope of the firms' reaction function (in either price or quantity space). The duopolists will disagree over the choice of roles if they have downward-sloping reaction functions. Each will prefer to be the leader. They will also disagree if they have upward-sloping reaction functions and similar profit functions. Each will prefer that the other be the leader. Preferences between von Stackelberg and Cournot outcomes are also considered.
265 citations
TL;DR: A formal description of the network design problem with continuous decision variables representing link capacities can be cast into a framework of multilevel programming and various suboptimal procedures to solve it are developed.
Abstract: Recently much attention has been focused on multilevel programming, a branch of mathematical programming that can be viewed either as a generalization of min-max problems or as a particular class of Stackelberg games with continuous variables The network design problem with continuous decision variables representing link capacities can be cast into such a framework We first give a formal description of the problem and then develop various suboptimal procedures to solve it Worst-case behaviour results concerning the heuristics, as well as numerical results on a small network, are presented
216 citations
TL;DR: The authors analyzes the choice of contract (sales or rental) of a durable-goods monopolist facing a threat of future entry, and shows that the threat of entry alters that preference.
Abstract: This article analyzes the choice of contract (sales or rental) of a durable-goods monopolist facing a threat of future entry. Although in the absence of such a threat a monopolist would prefer to rent his entire output, we show that the threat of entry alters that preference. There is an optimal preentry contract mix, involving both rental and sales. If both firms behave as Cournot duopolists after entry, the optimal choice of preentry contracts enables the erstwhile monopolist to gain the same profits as he would if he behaved as a von Stackelberg leader.
86 citations
01 Jan 1986
TL;DR: In this paper, the authors present a tutorial on dynamic and differential games and apply them to macroeconomics, including game theory models of fisheries management and optimal dynamic pricing in an Oligopolistic Market.
Abstract: 1. A Tutorial on Dynamic and Differential Games.- 2. On Expectations, Information and Dynamic Game Equilibria.- 3. On Affine Incentives for Dynamic Decision Problems.- 4. On the Computation of Equilibria in Discounted Stochastic Dynamic Games.- 5. Some Economic Applications of Dynamic Stackelberg Games.- 6. Applications of Dynamic Game Theory to Macroeconomics.- 7. Optimal Strategic Monetary Policies in Dynamic Interdependent Economies.- 8. Optimal Dynamic Pricing in an Oligopolistic Market: A Survey.- 9. Dynamic Advertising and Pricing in an Oligopoly: A Nash Equilibrium Approach.- 10. Game Theory Models of Fisheries Management - A Survey.- 11. Common-Property Exploitations under Risks of Resource Extinctions.
48 citations
01 Jan 1986
TL;DR: A general formulation of dynamic and differential games is given, which includes both discrete and continuous time problems as well as deterministic and stochastic games.
Abstract: A general formulation of dynamic and differential games is given, which includes both discrete and continuous time problems as well as deterministic and stochastic games. Solution concepts are introduced in two categories, depending on whether the dynamic game is defined in normal or extensive form. For the former, we present the Nash, Stackelberg and Consistent Conjectural Variations (CCV) equilibria, with considerable discussion devoted to the CCV solution, including comparisons with other more specific definitions found in the literature. For games in extensive form, we discuss the feedback solution concepts, and elaborate on the time consistency issue, which is currently of major interest in the economics literature. The chapter concludes with a discussion which puts into proper perspective the topics and contributions of the ten papers to follow, and their relationships with each other.
39 citations
TL;DR: In this paper, the authors modify the Cournot and Stackelberg models to allow the firms to sell less than they have produced and to store the unsold portion of their output as inventory.
37 citations
01 Jan 1986
TL;DR: Construction of optimal incentive strategies for continuous time two-person game problems described by integral convex cost criteria is considered and they are represented by means of Stieltjes measures.
Abstract: Construction of optimal incentive strategies for continuous time two-person game problems described by integral convex cost criteria is considered. The strategies are affine in the data available and they are represented by means of Stieltjes measures.
36 citations
TL;DR: Canzoneri and Gray as discussed by the authors consider alternative strategic monetary policies within the context of two economies subject to a mutual oil disturbance, where both economies are subjected to stochastic demand and supply shocks and expectations are rational.
Abstract: Western economies have become increasingly interdependent during recent years An important consequence of this is that the effects of macroeconomic policies within these economies have become more closely related A policy implemented in one country will generate effects abroad, while the impacts of this policy on the domestic economy are modified by the behaviour and policies of the foreign economies with which it is interacting Thus policy making in a multicountry context necessarily involves strategic behaviour Analysis of strategic behaviour within the context of international macroeconomic policy began with the pioneering work of Hamada (1976), who investigated this question under the assumptions of Cournot and Stackelberg behaviour His analysis is based on a fixed exchange rate regime and the objective function involves the tradeoff between inflation and the balance of payments More recently, Canzoneri and Gray (1 985) consider alternative strategic monetary policies within the context of two economies subject to a mutual oil disturbance1 This paper continues the analysis of strategic monetary policy The framework it employs is a two country stochastic macro model in which both economies are subjected to stochastic demand and supply shocks and expectations are rational2 The policy makers in the two countries seek to optimise their respective objective functions, which are taken to be functions of unanticipated movements in output and in the consumer price index The model begins by determining the usual Cournot and Stackelberg equilibria for this model However, these represent just two possible equilibria, and a number of alternatives are also considered In particular, in the derivation of the Cournot equilibrium, each agent takes the behaviour of his opponent as given, and therefore assumes that his rival does not react to his actions On the other hand, each agent is shown to respond in accordance with a reaction function, so that ex post, the assumption of no response is incorrect By contrast, we also consider a Consistent Conjectural Variations equilibrium (CCV) in which each policy maker, in determining his own actions, correctly conjectures the response of his opponent The requirement of con
32 citations
TL;DR: In this article, the authors construct a model of long-term bilateral competition between the supplier of an exhaustible resource and a consuming country capable of producing a perfect substitute for the resource.
Abstract: We construct a model of long-term bilateral competition between the supplier of an exhaustible resource and a consuming country capable of producing a perfect substitute for the resource. The technology for producing the substitute is known, and the strategy of the consuming country is to choose an investment program for installing the substitute. We derive equilibrium configurations of investment and extraction for the case of linear demand under three scenarios: (1) the resource supplier is a von Stackelberg leader; (2) the consuming country is a von Stackelberg leader; and (3) buyers and sellers of the resource engage each other period by period. A comparison of these cases reveals incentives for long-term commitment on the part of one or both parties and also suggests that there may be gains from strategic intervention into resource markets by governments of consuming nations.
27 citations
TL;DR: In this article, the authors examined Stackelberg price leadership in a spatially competitive model with infinitely many stores on an infinite line, and showed that collusion of two stores makes a difference to prices only if the colluding stores are nearest neighbors.
01 Jan 1986
TL;DR: In this paper, a dynamic inflationary model is developed for two interdependent symmetric economies, where the objective of each policy maker is to trade off in an intertemporally optimal way the rate of inflation and unemployment in his economy.
Abstract: This paper applies the framework of dynamic game theory to the analysis of a number of issues in international policy making First, a dynamic inflationary model is developed for two interdependent symmetric economies, where the objective of each policy maker is to trade off in an intertemporally optimal way the rate of inflation and unemployment in his economy Then, the equilibrium is studied under a variety of behavioral assumptions These include principally feedback Nash equilibrium, feedback Stackelberg behavior, and feedback consistent conjectural variations equilibrium, all under the feedback information pattern and with discounted objective functions defined on an infinite time horizon These solutions are subsequently computed for different sets of numerical values assigned to some key parameters in the model, and compared with results obtained in a previous work using a static model
TL;DR: In this article, a general dynamic model of fishing under harvest share contracts is developed, where the reason for a share contract to exist is the avoidance of transaction costs and a detailed analysis of the effectiveness of different regulation policies is presented.
Abstract: A general dynamic model of fishing under harvest share contracts is developed. Vessel owners hire fishermen to work on the vessels and pay them a share of the catch and an additional wage. The harvest rate depends on labor input, capital input, and stock level. Neither of the agents is unionized. On each vessel we have a principal agent setting where the crews' labor input decisions and vessel owners' decisions about harvest shares are based on myopic optimization. However, in this first analysis of the model risk is not included in the formulation. The paper concentrates on the incentive effects and in this framework the reason for a sharecontract to exist is the avoidance of transaction costs. In a share contract fishery both labor input and resource use are inefficient. A detailed analysis of the effectiveness of different regulation policies is presented.
01 Dec 1986
TL;DR: By using a kind of non-linear incentive strategy to solve the multi-stage Stackelberg games with partial information, the quantity of threat is calculated and it is shown that the duration of punishment is only on those stages where the follower plays nonoptimally.
Abstract: In this paper we apply a kind of non-linear incentive strategy to solve the multi-stage Stackelberg games with partial information. This strategy depends on a parameter p, as p=?, it becomes the affine strategy. In addition, by using this strategy, we can calculate the quantity of threat and we can show that the duration of punishment is only on those stages where the follower plays nonoptimally. We give illustrative examples and compare the quantity of threat in the case of partial information with that in the perfect information case.
01 Jan 1986
TL;DR: In this paper, a simple linear dynamic macroeconomic model of the trade-off between unemployment and inflation is considered, and the resulting linear quadratic differential game both for the non-cooperative feedback Nash solution and for the set of Pareto-optimal solutions is shown that both solutions lead to constant strategies over the entire infinite time horizon.
Abstract: A simple linear dynamic macroeconomic model of the trade-off between unemployment and inflation is considered. Two policy-making institutions, namely the government and the central bank, can exert influence on this economic system, aiming at reducing the rates of unemployment and of inflation by fiscal and monetary policies, with quadratic costs attached to the use of the respective own control variables; in addition, they give different weights to the target variables, which arc assumed to enter linearly into the objective functions. We solve the resulting linear-quadratic differential game both for the non-cooperative feedback Nash solution and for the set of Pareto-optimal solutions. It is shown that both solutions lead to constant strategies over the entire infinite time horizon. In the non-cooperative case, open-loop Nash, feedback Nash, and Stackelberg equilibria coincide. On the other hand, they do not belong to the set of Pareto-optimal outcomes and are therefore inefficient. Sensitivity analyses are provided for the optimal non-cooperative and cooperative strategies.
TL;DR: In this article, the authors examine the trade policy incentives resulting from these labour asymmetries, focusing on profit shifting tariffs, quotas, and subsidies, using a simple duopoly model.
Abstract: Asymmetries in labour relations can have important effects on imperfectively competitive rivalries between firms Such asymmetries are particularly striking in cross-country comparisons and are therefore of greatest interest in international markets Using a simple duopoly model, we focus on two asymmetries First, one firm may face a noncooperative union and second, institutional factors may allow one firm to commit itself to particular labour input before its rival sets output, giving it a natural Stackelberg leadership role We examine the trade policy incentives resulting from these labour asymmetries, focusing on profit shifting tariffs, quotas and subsidies
TL;DR: In this paper, the authors examine the generality of the proposition (Buiter (I98I)) that innovation-contingent (or feedback or closed-loop) policies are always superior to non-innovation-Contingent policies in the design of stabilisation programs unless (i) they arbitrarily increase the randomness of current and future policy instruments or (ii) the authorities either pursue the wrong objectives or else pursue the right objectives in an inept manner.
Abstract: In the following pages we examine the generality of the proposition (Buiter (I98I)) that innovation-contingent (or feedback or closed-loop) policies are always superior to non-innovation-contingent (or fixed or open-loop) policies in the design of stabilisation programmes unless (i) they arbitrarily increase the randomness of current and future policy instruments or (ii) the authorities either pursue the wrong objectives or else pursue the right objectives in an inept manner. What is at stake here is the general presumption that acting on more information is necessarily beneficial to the economic agent. In order to tackle the question, we bring together two strands of the literature that have so far remained largely separate. First, the optimum-control strand, which discusses policy within a framework where the authorities are assumed to be Stackelberg leaders and the public Stackelberg followers (e.g. Buiter (I98I), Miller (i984)) and in which the proposition under scrutiny has been proved. Second, the recent suggestion by Barro and Gordon (I983 a, b) that the policy game in the absence of pre-commitments may be better approximated by a Nash non-cooperative equilibrium between the authorities and private agents on the grounds that it is the only incentive-compatible notion. In this case, the solution to the game is constructed in such a way that, in equilibrium, each agent is maximising his utility given the strategy chosen by the opponent, i.e. each player has chosen his best reply to the other players' moves. It will be shown here that once a Nash equilibrium is assumed, contingent policies do not dominate fixed policies. In the process, it will also become apparent that once innovation-contingent responses are allowed for, Barro and Gordon's argument against discretionary policy is strengthened: even if the deterministic component of the Nash policy is non-inflationary, its innovationcontingent part is counterproductive. In other words, even if the authorities aim at stabilising output at, and not above, the natural rate (or, equivalently, do not derive utility from positive deviations from the natural rate), the absence of precommitment entails a welfare loss. In section I we briefly discuss the relationship between information and precommitment and rules versus discretion to avoid misunderstanding of the thrust of our analysis. In sections II-IV we demonstrate the central proposition in two different classes of models. First, in models, as in Buiter (i98I), wlhere the decision-takers are restricted to react to exogenous shocks with a one-peried lag. Second, in models (e.g. B. Friedman (I977) and Courakis (I984)) where, while still unable to observe directly the behaviour of the ultimate goal variables,
TL;DR: In this article, the authors considered a two-person non-zero sum bimatrix game with the leader Bonneville Power Administration (BPA) and the follower California utilities (CU), where BPA pursues an iterative tit-for-tat scheme following determination of excess energy magnitude, duration and equilibrium price.
01 Jan 1986
TL;DR: The Stackelberg equilibrium as mentioned in this paper is a hierarchical equilibrium concept for non-cooperative games, where one or several players have dominant roles vis-a-vis the rest of the players.
Abstract: Two equilibrium concepts are frequently used in connection with noncooperative games. When there is no cooperation among the players and they make decisions independently, the natural solution concept is the Nash equilibrium solution where no single player has an incentive to deviate unilaterally from that solution. On the other hand, when one or several player(s) has (have) dominant role(s) vis-a-vis the rest of the players, one has to introduce a hierarchical equilibrium concept, known as the Stackelberg equilibrium solution.
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TL;DR: The authors analyzes strategic monetary policies using a standard two country stochastic macro model and finds that demand shocks are much less problematical than supply disturbances from the viewpoint of macro stabilization.
Abstract: This paper analyzes strategic monetary policies using a standard two country stochastic macro model Three noncooperative equilibria, namely Cournot, Stackelberg, and Consistent Conjectural Variations, are consideredThe Pareto Optimal equilibrium, where aggregate joint costs are minimizedis also considered, and all strategic equilibria are compared to the perfectly fixed and flexible exchange rate regimes The main conclusions obtained are:(i) Demand shocks are much less problematical than supply disturbances from the viewpoint of macro stabilization; (ii) the gains from cooperation are typically small; (iii) the strategic equilibria all show substantial margins of superiority over the fixed and flexible regimes
TL;DR: In this paper, the closed loop Stackelberg equilibrium is used to determine the optimal time consistent announcement for finite and infinite horizon repeated games, and it is shown under what conditions the optimal announcement belongs to a sequential equilibrium of the game.
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TL;DR: The authors analyzes strategic monetary policies using a standard two country stochastic macro model and finds that demand shocks are much less problematical than supply disturbances from the viewpoint of macro stabilization.
Abstract: This paper analyzes strategic monetary policies using a standard two country stochastic macro model. Three noncooperative equilibria, namely Cournot, Stackelberg, and Consistent Conjectural Variations, are considered.The Pareto Optimal equilibrium, where aggregate joint costs are minimizedis also considered, and all strategic equilibria are compared to the perfectly fixed and flexible exchange rate regimes. The main conclusions obtained are:(i) Demand shocks are much less problematical than supply disturbances from the viewpoint of macro stabilization; (ii) the gains from cooperation are typically small; (iii) the strategic equilibria all show substantial margins of superiority over the fixed and flexible regimes.
01 Jan 1986
TL;DR: In this paper, a Stackelberg game between the monopolist and consumers is considered in the context of durable goods and it is shown that with endogenous scrappage, consumers have a substitution possibility which constrains the profits of a monopolist seller.
Abstract: It is commonly believed that textbook publishers attempt to "kill off" competition from used textbooks through yearly edition changes. In the context of Wicksell's model of durable goods, Peter Swan has shown that such "planned obsolescence" is never optimal: a monopolist seller of durable goods maximizes profits by setting product durability equal to the competitive or socially optimal level, and efficiently extracts consumer surplus through sales price alone. This paper formulates a monopolist seller's choice of price and durability as the solution to a Stackelberg game between the monopolist and consumers. We employ a new equilibrium model of a durable goods market which, unlike Wicksell's model, recognizes that scrappage of durables is endogenously determined. We show that with endogenous scrappage, consumers have a substitution possibility which constrains the profits of a monopolist seller. This constraint on profits causes the monopolist to distort durability from the socially optimal level. We derive conditions under which this distortion takes its most extreme form: the monopolist kills off competition from used durables by producing new assets of zero durability.