Showing papers on "Stackelberg competition published in 1989"
01 Jan 1989
TL;DR: In this article, the optimal behavior of a public firm in a market where there are also n private firms is studied. And the optimal strategy of a welfare maximizing firm is to act as if it wanted to maximize its profit.
Abstract: A study of the optimal behavior of a public firm in a market where there are also n private firms. The public firm aims at maximizing a social welfare function while the private firms aim at maximizing profit. The authors compare four possible regimes: (1) the public firm is a welfare maximizing Stackelberg leader; (2) it is a welfare maximizing Cournot-Nash player; (3) it is a profit maximizer (pure oligopoly); and (4) the whole industry is under government control (nationalization). When the number of firms is sufficiently large, the optimal strategy of a welfare maximizing firm is to act as if it wanted to maximize its profit. Copyright 1989 by Royal Economic Society.
624 citations
TL;DR: In this paper, the authors develop a differential game model of duopoly, in which firms incur costs associated with how fast they change their level of output, and demonstrate that the limit game in which the speed of adjustment parameter approaches zero does not tend toward the static Cournot equilibrium.
97 citations
TL;DR: In this article, a generalization of Gordon-Schaefer's fishery resource model to a duopoly is presented, and the resulting noncooperative game is solved analytically as well as numerically by using the equilibrium concepts of Nash and Stackelbewrg.
73 citations
TL;DR: In this article, the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game was considered and a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems was presented.
Abstract: We consider the Stackelberg problem corresponding to a two-player game in which one of the two players has the leadership in playing the game We present a general approach for approximating the considered hierarchical programming problem by a sequence of two-level optimization problems From a practical point of view, we also give some results for asymptotically Stackelberg approximating sequences and for problems with perturbed constraints
60 citations
TL;DR: In this paper, Daughety showed that the Cournot-Nash equilibrium is consistent and the Bertrand and Cournot equilibria are not inconsistent. But they are not consistent with the consistent-conjectures hypothesis.
Abstract: Preface Part 1. Introduction: 1. Introduction, purpose, and overview Andrew F. Daughety Part II. Background: 2. Of the competition of producers Augustin Cournot (translation by Nathanial T. Bacon) 3. Review of Walras's Theorie mathematique de la richesse sociale and Cournot's Reserches sur les principles mathematiques de la theorie des richesses Joseph Bertrand (translation by James W. Friedman) 4. Non-cooperative games John Nash Part III. Examining Cournot's Model: 5. On the existence of Cournot equilibrium William Novshek 6. Collusive behavior in non-cooperative epsilon-equilibria of oligopolies with long but finite lives Roy Radner 7. A non-cooperative equilibrium for supergames James W. Friedman 8. Reconsidering Cournot: the Cournot equilibrium is consistent Andrew F. Daughety 9. An experimental test of the consistent-conjectures hypothesis Charles A. Holt 10. Quantity precommitment and Bertrand competition yield Cournot outcomes David M. Kreps and Jose A. Scheinkman 11. On the efficiency of Bertrand and Cournot equilibria with product differentiation Xavier Vives 12. Price competition vs. quantity competition: the role of uncertainty Paul Klemperer and Margaret Meyer Part IV. Applications: 13. Cournot and Walras equilibrium William Novshek and Hugo Sonnenschein 14. Duopoly information equilibrium: Cournot and Bertrand Xavier Vives 15. Information transmission - Cournot and Bertrand equilibria Esther Gal-Or 16. Uncertainty resolution, private information aggregation, and the Cournot competitive limit Thomas R. Palfrey 17. Losses from horizontal merger: the effects of an exogenous change in industry structure on Cournot-Nash equilibrium Stephen W. Salant, Sheldon Switzer, and Robert J. Reynolds 18. Delegation and the theory of the firm John Vickers 19. A study of cartel stability: the Joint Executive Committee, 1880-1886 Robert H. Porter 20. Oligopoly and financial structure: the limited liability effect James A. Brander and Tracy R. Lewis.
59 citations
01 Jan 1989
TL;DR: A two-level optimization problem corresponding to a two-player game in which player 1 has the leadership in playing the game is considered and an optimal strategy is chosen knowing that player 2 will react by playing optimally and that his choice cannot be affected by player 1.
Abstract: A two-level optimization problem corresponding to a two-player game in which player 1 has the leadership in playing the game is considered. Let K 1 and K 2 be the sets of admissible strategies for the two players. Player 1 (called the leader) and player 2 (called the follower) must select strategies v 1 ∈ K 1 and v 2 ∈ K 2 respectively, in order to minimize their objective functionals J 1 and J 2. It is supposed that player 1 knows everything about player 2 but player 2 knows only the strategy announced by player 1. So, more precisely, player 1 chooses first an optimal strategy knowing that player 2 will react by playing optimally and that his choice cannot be affected by player 1. This concept, introduced by Von Stackelberg in 1939 [24] in the context of static economic competition has been presented in a control theoretic framework by Chen and Cruz (1972) and Simaan and Cruz (1973). A great deal of papers have been devoted to these problems in static and dynamics games (a good list of references can be found in [3], particularly on dynamic cases, and in [1] for application to economic models).
51 citations
TL;DR: In this article, the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behavior in a continuous-time econometric model of the Italian economy, and the case for cooperation is analyzed by considering the Nash and the Kalai-Smorodinsky bargaining models.
Abstract: In this paper the interaction between the Treasury and the central bank is examined in the case of both cooperative and non-cooperative behaviour. Differential games are used in the framework of a continuous-time econometric model of the Italian economy. The Nash and the Stackelberg non-cooperative equilibrium solutions are computed, and the case for cooperation is analysed by considering the Nash and the Kalai-Smorodinsky bargaining models. It is shown that, in the Italian case, the government has a stronger bargaining position than the central bank. A comparison is then made between the different solutions to show that the drawbacks that emerge from non-cooperation are not simply those depending on the players' payoffs. Other features are in fact considered which constitute a further argument for policy co-ordination.
49 citations
01 Jan 1989
TL;DR: In this article, the effects of tariffs and quotas in the presence of quantity-setting international duopolists were compared, and it was shown that a quota will induce a switching of the domestic conjectural variation and is not equivalent to a tariff.
Abstract: This paper compares the effects of tariffs and quotas in the presence of quantity-setting international duopolists. With the Cournot-Nash case, a tariff is equivalent to a quota; but with the Stackelberg and consistent conjecture cases, a quota will induce a switching of the domestic conjectural variation and is found to be not equivalent to a tariff. Copyright 1989 by Royal Economic Society.
38 citations
13 Dec 1989
TL;DR: Stackelberg games and their resulting nonconvex programming problems can be used to model the behavior of independent decision-makers acting within a hierarchy.
Abstract: Stackelberg games and their resulting nonconvex programming problems can be used to model the behavior of independent decision-makers acting within a hierarchy. An examination is made of the formation of coalitions within such organizations of optimizers for a large class of hierarchical problems. The mathematical characteristics of these games and the implications of their solutions are considered. >
29 citations
TL;DR: In this article, the authors present a positive theory of diffusion of technology and examine a two-period model where firms face a tradeoff between early adoption and possibly reaping first mover advantages on one hand and deferring the adoption decision until after all the uncertainty is resolved but face the possibiity of being a follower in the market.
15 citations
TL;DR: In this article, the authors characterize the equilibria of Stackelberg duopolies with differentiated products, where the firms are fighting either in prices and quantities or in price and serving capacities.
Abstract: In this paper, the authors characterize the equilibria of Stackelberg duopolies with differentiated products, where the firms are fighting either in prices and quantities or in prices and serving capacities. It is shown that in the price-quantity case there is always rationing by the leader, but in the price-serving capacity case the leader is rationing only if the goods are close substitutes. Hence, rationing may appear as an equilibrium results. This kind of equilibrium is specific to the Stackelberg competition. Rationing never appears in a duopoly (with the same strategy spaces) where the firm moves are simultaneous. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
TL;DR: In this article, the behavior of firms in the Cournot-Nash model is examined under uncertainty in market demand and in their production, and 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).
TL;DR: In this paper, the authors study Stackelberg games with incomplete information and show the existence of an expected payoff maximizing, incentive compatible strategy for the leader given the follower's reaction function.
Abstract: We study Stackelberg games with incomplete information in a general setting. In particular, we deduce the follower's reaction function, a set-valued function of the leader's action choice and a parameter specifying the follower's payoff type (a parameter about which the leader has only incomplete information), and using a generalized version of Komlos' Theorem due to Balder (1987), we show the existence of an expected payoff maximizing, incentive compatible strategy for the leader given the follower's reaction function.
TL;DR: In this paper, the authors discuss gains and losses from cartelization in markets for exhaustible resources in the absence of binding future contracts and show that the appropriate solution is a feedback Stackelberg equilibrium, in which time consistency is imposed, and it is well known that not only can the dominant firm be worse off in such a feedback equilibrium than it is in the open-loop equilibrium but it can also be worse than in a competitive equilibrium.
Abstract: Publisher Summary This chapter discusses gains and losses from cartelization in markets for exhaustible resources in the absence of binding future contracts In modeling, imperfect competition (whether by buyers or sellers) in markets for exhaustible resources, where dynamic analysis is essential, the appropriate equilibrium concept depends crucially on whether it is assumed that agents can make binding commitments about their future behavior In the specific context of a market where there is a dominant firm sharing the market with a fringe of competitive producers, modeling the equilibrium as an open-loop Stackelberg equilibrium yields policies that in general are time inconsistent and so only appropriate if the dominant firm can precommit itself to a path of future outputs or prices In the absence of such commitments, the appropriate solution is a feedback Stackelberg equilibrium, in which time consistency is imposed, and it is well-known that not only can the dominant firm be worse off in such a feedback equilibrium than it is in the open-loop equilibrium but it can also be worse off than in a competitive equilibrium
TL;DR: In this paper, the problem is modelled as an open-loop Stackelberg differential game such that the manager is the leader; the shareholders are followers, playing a Nash game.
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TL;DR: In this article, the binding-contracte open-loop von Stackelberg equilibrium in the cartel-vereus-fringe model of the eupply side of a market for a raw material from an exhaustible natural resource is reconsidered.
Abstract: In this paper the binding-contracte open-loop v~n Stackelberg equilibrium in the cartel-vereus-fringe model of the eupply side of a market for a raw material from an exhaustible natural resource is reconsidered. It is shown that the equilibrium for this model differs from what the previoua literature on this model (e.g. Ulph and Folie (1981), Newbery (1981) and Ulph (1982)) suggests. The equilibrium is solved for by using optimal control techniques and it turns out that the previous literature should be corrected in two respects. Firstl,y, the marginal production costs for the cartel are not treated correctly and secondly, the resulting equilibrium price path may not be continuous, as ia implicitly assumed by previous authors. For some values oi the parameters the equilibrium is still time-inconsistent and thia turns out to be so in almost the same cases as in the previous literature. The time-inconsistency is one reason to reject the open-loop von Stackelberg equilibrium concept for this model. Another reason is that for plausible parameter values the equilibrium price path turns out to be discontinuoue. Especially in markets for raw materials such as crude oil, this will Iead to speculation. In that case the assumption that the demand only depends on the current price level is not valid anymore.
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TL;DR: In this paper, the optimal Stackelberg policy in a model of credibility and monetary policy developed by Cukierman and Meltzer is solved in a linear quadratic form and certainty equivalence does not apply.
Abstract: In this paper we solve for the optimal (Stackelberg) policy in a model of credibility and monetary policy developed by Cukierman and Meltzer. Unlike the (Nash) solution provided by Cukierman and Meltzer, the dynamic optimization problem facing the monetary authority in this case is not of a linear quadratic form and certainty equivalence does not apply. The learning behavior of the private sector (regarding the policymaker's preferences) becomes intimately linked with the choice of the optimal policy and cannot be separated as in the certainty equivalent case. Once the dual effect of the optimal Stackelberg policy is recognized, the monetary authority has an additional channel of influence to consider beyond that taken into account by sub-optimal, certainty equivalent, Nash policy rules.
TL;DR: In this article, the existence and constructions of the optimal affine incentive strategies for both the leader and one of the followers are studied by a vector space approach, and a special class of problems are solved as an application of the theory.
Abstract: In this paper, three-person deterministic Stackelberg game problems with a linear hierarchical decision structure are considered in a general Hilbert space setting. The existences and the constructions of the optimal affine incentive strategies for both the leader and one of the followers are studied by a vector space approach. A special class of problems are solved as an application of the theory, and the explicit optimal affine incentive strategies are obtained.
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TL;DR: In this paper, the authors consider a hierarchical model of spatial electoral competition with two dominant players (incumbents) and one entrant and prove that the equilibrium of this game, called a hierarchical equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points.
Abstract: In this paper we consider a hierarchical model of spatial electoral competition with two dominant players (incumbents) and one entrant. The incumbents engage in a non-cooperative game against each other and act as Stackelberg leaders with respect to a vote-maximizing entrant. We prove that the equilibrium of this game, called a hierarchical equilibrium, exists and is unique for an arbitrary single-peaked distribution of voters' ideal points. Moreover, we fully characterize the set of equilibrium strategies and show its equivalence to the set of strategies generated by a perfect-foresight equilibrium. Most of the recently developed models of entry in oligopolistic markets and the theory of political competition deal with the case of dominant firms or parties which face a threat of potential entry. These models possess a number of features on which they may be compared and contrasted. The most important of these features are the ways in which the existing parties or firms compete against each other for votes or profits, and types of expectations the incumbents have about the responses of potential entrants to changes in their decisions. In most of the cases an electoral or oligopolistic competition is represented by some type of a non-cooperative game played by parties or firms. In this paper we also consider a non-cooperative model of electoral race where the established parties (incumbents) compete against each other by offering positions ("ideologies") to the population of voters. Given the profile of voters' preferences over the space of "ideologies" (or, issue space), each of the established parties attempts to maximize its vote share. In making their choices, the incumbents, however, anticipate that a new party (an entrant) will join the electoral race. Consistent with the other parties' objectives, the entrant is assumed to maximize its share of voters while taking the incumbents' choices as given. The resulting non-cooperative game possesses, therefore, a structural hierarchy: the established parties behave as Nash players with respect to each other, whereas acting as Stackelberg leaders with respect to the entrant and correctly anticipating its vote-maximizing response to their choices in the issue space. The main purpose of this paper is to study the properties of the game we described and, in particular, to characterize its equilibrium, which we will call "hierarchical equilibrium". Naturally, some assumptions are needed in order to guarantee the existence of the equilibrium. We assume that there are two established parties, the issue space I is the uni-dimensional interval, all voters have symmetric single peaked-peaked preferences over I and the distribution of the voters' ideal points is represented by a quasi-concave continuous density function. Under these rather mild assumptions, we are able to prove the existence and uniqueness of the hierarchical equilibrium and to completely
TL;DR: In this article, the authors analyzed protectionism in a game theoretic context and calculated non-cooperative equilibrium solutions for three players, the E.E.C., the U.S. and the Pacific Basin on the basis of the Project LINK model.
TL;DR: In this article, a Stackelberg Incentive Equilibrium is solved for the widely used Barro-Gordon unemployment-inflation game, and an equibrium incentive strategy (a monetary rule) that leads to a team optimal solution of zero expected inflation and zero actual inflation is obtained.
TL;DR: In this article, the integrated problem of electric generating system development and resource supply is formulated as multi-level multifollower Stackelberg games, where the non-cooperative and cooperative approaches to the public participation are investigated from the point of view of social siting concern.
01 Jan 1989
TL;DR: In this paper, the authors propose an optimal control method to identify the best inflation-output combinations which are compatible with a given empirical model, assuming that the political institutions concerned with planning act in complete agreement.
Abstract: By using optimal control methods, it is possible to identify the best inflation-output combinations which are compatible with a given empirical model. In general, these tradeoffs are calculated on the assumption that optimal policy decisions are centralised; i.e. that the political institutions concerned with planning act in complete agreement. However, this is not the case in many countries where two decision making institutions, the government and the central bank, can co-exist, and manage fiscal and monetary policy separately.
TL;DR: The solution of the specified Stackelberg problem is reduced to the sequential solution of a finite number of standard constrained quadratic programming problems and the iterative selection of solution structures for the follower reaction.
TL;DR: In this paper, a Stackelberg model with two price setting firms producing a differentiated good is analyzed and it is shown how the non-existence problem can be circumvented by either allowing for mixed strategies or positive costs of information acquisition, but in both cases they find a possibility of a non-informationally efficient equilibrium.
21 Jun 1989
TL;DR: In this paper, the Stackelberg approach of game theory is considered for the optimization of two-level singular systems, where the objective function of each local controller assesses the performance of the corresponding subsystem, and the goal function of the central controller is to assess the overall system performance.
Abstract: This paper studies the optimization problem of two-level singular systems. The system considered is composed of N subsystems, and each is a linear singular system controlled by a local controller and a central controller. The objective function of each local controller assesses the performance of the corresponding subsystem, and the objective function of the central controller assesses the performance of the overall system. In this paper, the Stackelberg approach of game thory is considered for the optimization of such a system. The necessary conditions for the existence of open-loop Stackelberg solutions are derived.
TL;DR: In this article, the authors analyze an exhaustible resource market dynamic game between a dominant firm and a price-taking competitive fringe and examine two time consistent equilibria: the feedback Stackelberg equilibrium (FSE) which assumes the dominant firm commits its plan for one period, and the closed-loop Nash equilibrium (CLNE), which assumes no commitment for either agent.
TL;DR: In this paper, the authors developed a framework for determining optimal profit taxation in a market economy with value-maximising firms, which face costs of adjustment for investment, and showed that there is a dynamic trade-off between public consumption now and in the future.
TL;DR: In this paper, the robust Lyapunov stabilization approach was extended to discrete-time, uncertain two-player games, where none of the players knows exactly the constraints facing it or its opponent.
TL;DR: In this article, a Stackelberg game model with ring-like structure is proposed to describe hierarchical decision-making process when the second-level decision maker works according to reward.