Showing papers on "Stackelberg competition published in 1999"
TL;DR: In this article, the authors consider a two-stage serial supply chain with stationary stochastic demand and fixed transportation times, and compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs, i.e., the optimal solution.
Abstract: We investigate a two-stage serial supply chain with stationary stochastic demand and fixed transportation times. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost, e.g. the upper stage (the supplier) may dislike backorders at the lower stage (the retailer). We consider two games. In both, the stages independently choose base stock policies to minimize their costs. The games differ in how the firms track their inventory levels (in one, the firms are committed to tracking echelon inventory; in the other they track local inventory). We compare the policies chosen under this competitive regime to those selected to minimize total supply chain costs, i.e., the optimal solution. We show that the games (nearly always) have a unique Nash equilibrium, and it differs from the optimal solution. Hence, competition reduces efficiency. Furthermore, the two games' equilibria are different, so the tracking method influences strategic behavior. We show that the system optimal solution can be achieved as a Nash equilibrium using simple linear transfer payments. The value of cooperation is context specific: In some settings competition increases total cost by only a fraction of a percent, whereas in other settings the cost increase is enormous. We also discuss Stackelberg equilibria.
541 citations
TL;DR: In this article, the authors consider a two-stage game in which each player can either commit to a quantity in stage 1 or wait till stage 2, and they show that committing is more risky for the high cost firm and that, consequently, risk dominance considerations, as in Harsanyi and Selten (1988), allow the conclusion that only the low cost firm will choose to commit.
198 citations
TL;DR: In this article, Stackelberg's classical critique of the Cournot duopoly, in the framework of endogenous timing for two-player games, was revisited, and different sets of minimal conditions, directly on the demand and cost functions, yielding respectively the simultaneous and the two sequential modes of play.
196 citations
TL;DR: In this paper, an approach to providing flexibility in resolving the conflicts between the interests of multiple disciplines is proposed, which integrates the robust design concept into the existing game protocol, in particular the Stackelberg leader/follower protocol, where the solution for the design parameters which involve the coupled information between multiple players (disciplines) are developed as a range of solutions rather than a single point solution.
Abstract: The interdisciplinary nature of complex systems design presents challenges associated with computational burdens and organizational barriers as these issues cannot be resolved with faster computers and more efficient optimization algorithms. There is a need to develop design methods that could model different degrees of collaboration and help to resolve the conflicts between different disciplines. In this paper, an approach to providing flexibility in resolving the conflicts between the interests of multiple disciplines is proposed. We propose to integrate the robust design concept into the existing game protocol, in particular the Stackelberg leader/follower protocol. Specifically, the solution for the design parameters which involve the coupled information between multiple players (disciplines) are developed as a range of solutions rather than a single point solution. This additional flexibility provides more freedom to the discipline that takes the role of follower while the performance of the discipline that takes leader's role is stable within a tolerable range. The method is demonstrated by a passenger aircraft design problem. NOMENCLATURE
141 citations
92 citations
TL;DR: In this paper, the Stackelberg common agency game is used to model the separation of powers between two regulators, and the authors show that when regulators have a limited ability to commit, this static cost of regulators separation becomes a dynamic benefit.
85 citations
TL;DR: In this article, the authors discuss the element of cooperation between firms in the form of information exchange through communication into the Hotelling spatial competition model and show that subgame perfect equilibrium in a two-stage game can be achieved in a wide range from minimum differentiation to maximum differentiation, depending upon the relative strength of the cooperation effect over the competition effect.
74 citations
TL;DR: In this article, the authors considered a multiobjective two-level linear programming problem in which the decision maker at each level has multiple-objective functions conflicting with each other.
Abstract: In this paper, we consider a multiobjective two-level linear programming problem in which the decision maker at each level has multiple-objective functions conflicting with each other The decision maker at the upper level must take account of multiple or infinite rational responses of the decision maker at the lower level in the problem We examine three kinds of situations based on anticipation of the decision maker at the upper level: optimistic anticipation, pessimistic anticipation, and anticipation arising from the past behavior of the decision maker at the lower level Mathematical programming problems for obtaining the Stackelberg solutions based on the three kinds of anticipation are formulated and algorithms for solving the problems are presented Illustrative numerical examples are provided to understand the geometrical properties of the solutions and demonstrate the feasibility of the proposed methods
73 citations
TL;DR: In this article, the subgame perfect equilibrium for a two-stage game where the central government is the Stackelberg leader and controls pollution taxes is shown to correspond to the Nash equilibrium in a game where regional governments control both policy instruments.
44 citations
TL;DR: The paper studies off-line computation of the Stackelberg solution in a repeated game framework, utilizing the Genetic Algorithm, and shows that an evolutionary mutation probability is preferable to a fixed one as usually assumed.
Abstract: The paper studies off-line computation of the Stackelberg solution in a repeated game framework, utilizing the Genetic Algorithm. Simulations are conducted with a numerical linear quadratic example and a Fish War game example. Furthermore, it is shown that an evolutionary mutation probability is preferable to a fixed one as usually assumed.
39 citations
TL;DR: In this paper, an experiment designed to assess the effects of advance-production decisions on posted-offer market performance is reported, where sellers made binding production commitments prior to posting prices, an alteration that shifts the unique stage-game Nash equilibrium from the competitive to the Cournot outcome.
Abstract: An experiment designed to assess the effects of advance-production decisions on posted-offer market performance is reported. Six of the twelve triopolies were conducted under standard posted-offer rules. In the remaining markets sellers made binding production commitments prior to posting prices, an alteration that shifts the unique stage-game Nash equilibrium from the competitive to the Cournot outcome. As predicted, advance-production decisions raised prices and lowered output. Nevertheless, stable Cournot outcomes were never observed.
Journal Article•
TL;DR: In this article, a model of an oligopolistic market with a homogeneous product is examined, where each subject uses a conjecture about the market response to variations of its production volume, depending upon both the current total volume of production at the market and the subject's contribution into it.
TL;DR: The problem is set up as a Stackelberg differential game in which the government is identified as an open-loop equilibrium, supposing that the government can credibly precommit to its subsidy and buying program.
Journal Article•
TL;DR: In this article, the authors model the decision problem of a firm wishing to allocate a fixed budget among several activities, so as to maximize the expected profit from the activities it captures.
Abstract: Firms who are involved in R&D activities are often “racing” against competitors to become the first to attain the desired breakthrough. The goal might indeed be to “beat” the competitors in as many such R&D races as possible. However, when resources are limited, and competitors' budget allocation to these R&D activities unknown, the challenge becomes to devise a method of allocating R&D budgets to activites in a strategically “optimal” way. We model the decision problem of a firm wishing to allocate a fixed budget among several activities, so as to maximize the expected profit from the activities it captures. The probability of capturing an activity is an increasing function of one's allocation to it, and a decreasing function of the competitor's allocation. For a specific plausible capture-probability function, we find the optimal allocation between two activities conditional on the competitor's allocation (the “reaction curve”). Nash and Stackelberg equilibria for that model are then characterized. We also briefly explore the implications of more general, or different, capture-probability functions.
TL;DR: In this paper, the authors consider a duopolistic market where ex ante identical firms sequentially position their products prior to competing on prices and show that the unique equilibrium outcome involves (1) firms choosing Stackelberg pricing over Bertrand-Nash pricing; and (2) the positioning first mover acting as the price leader.
Abstract: Prior empirical work shows that different markets are characterized by different pricing patterns, such as Bertrand-Nash pricing or Stackelberg leader-follower pricing. The author considers a duopolistic market where ex ante identical firms sequentially position their products prior to competing on prices (in a single- or multiperiod setting) and show that the unique equilibrium outcome involves (1) firms choosing Stackelberg pricing over Bertrand-Nash pricing; and (2) the positioning first mover acting as the price leader. An attractive property of this model is that the ex post larger firm acts as the price leader, which is consistent with prior empirical evidence. Copyright 1999 by University of Chicago Press.
Posted Content•
01 Jan 1999
TL;DR: In this paper, the optimal taxation with an imperfect labor market was analyzed and the Nash equilibrium was compared with the alternative of the Stackelberg leadership of the government, where the structure of the game had only a minor impact on the optimal choice of the tax on capital.
Abstract: This paper analyses optimal taxation with an imperfect labor market. Unemployment results from the market power of a monopoly union that determines the wage unilaterally. The government provides a public good and raises revenue by taxing rent, labor and capital income. Labor is immobile while capital is internationally traded. This paper focuses on the interaction between government and union. The Nash equilibrium is compared with the alternative of the Stackelberg leadership of the government. While the structure of the game has only a minor impact on the optimal choice of the tax on capital, the tax on labor depends critically on the structure of the interaction. Employment is lower when the government acts as a Stackelberg leader.
TL;DR: The asymptotic behavior of difference equations appearing in the necessary optimality conditions of noncooperative open loop Nash and Stackelberg games and the properties of the solutions of the corresponding algebraic Riccati-type equations are studied.
01 Sep 1999
TL;DR: In this article, the authors analyze a Cournot duopoly model with finitely repeated competition, where each firm is allowed to hold inventories for a period, and when there are more than two periods, inventory-holdings encourage firms to take collusive actions.
Abstract: This paper analyses a Cournot duopoly model with finitely repeated competition. Each firm is allowed to hold inventories for a period. When there are more than two periods, inventory-holdings encourage firms to take collusive actions. By holding large inventories, a firm can commit to large sales in the next period, giving inventories a strategic value. When a firm deviates from collusion, the strategic value of inventories allows the non-defecting firm to become the Stackelberg leader in future markets, forcing the defecting firm to become the Stackelberg follower. Collusive sales can be attained with this threat of punishment.
TL;DR: In this paper, conditions for a leader to be more advantageous than a follower in Stackelberg duopoly with symmetric firms and without product differentiation were derived, and the equilibria in Cournot duopolies were compared under a set of reasonable assumptions.
Abstract: First, conditions are derived for a leader (or a follower) to be more advantageous than a follower (or a leader) in Stackelberg duopoly with symmetric firms and without product differentiation. Second, the equilibria in Cournot and Stackelberg duopolies are compared under a set of reasonable assumptions. If the reaction function slopes upward, the Cournot duopolists' profits turn out to be lower than those of both the Stackelberg leader and follower, and the equilibrium industry output is smaller in Stackelberg duopoly than in Cournot duopoly.
JEL Classification Numbers: D21, D43, L13.
TL;DR: Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved and they have a stick and carrot structure.
Abstract: This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary, and there is only one seller in the market in infinitely many periods.
TL;DR: In this article, the endogenous choice of timing in a vertically differentiated duopoly where quality improvement requires a fixed convex cost is discussed, and it is shown that only simultaneous equilibria can arise.
TL;DR: Within the framework of a standard discrete time Linear‐Quadratic DynamicReversed Stackelberg game, the best possible open‐loop cheating strategy for an unscrupulous leader is derived.
Abstract: The distinctive characteristic of a “Reversed Stackelberg Game” is that the leader playstwice, first by announcing his future action, second by implementing a possibly differentaction given the follower's reaction to his announcement. In such a game, if the leader usesthe normal Stackelberg solution to find (and announce) his optimal strategy, there is a strongtemptation for him to cheat, that is, to implement another action than the one announced. Inthis paper, within the framework of a standard discrete time Linear‐Quadratic DynamicReversed Stackelberg game, we discuss and derive the best possible open‐loop cheatingstrategy for an unscrupulous leader.
Posted Content•
TL;DR: This article showed that the Klein-Monti model of bank behavior does not necessarily hold in oligopolistic Cournot or Stackelberg generalizations, since introducing asymmetries in the cost functions of the banks, or in their way of conduct, may imply counterintuitive effects on the individual banks' volumes of loans and deposits.
Abstract: The well-known Klein-Monti model of bank behavior considers a monopolistic bank. We demonstrate that this model’s results on the comparative static effects of a change in the exogenous interbank market interest rate do not necessarily hold in oligopolistic Cournot or Stackelberg generalizations. Introducing asymmetries in the cost functions of the banks, or in their way of conduct, may imply counterintuitive effects on the individual banks’ volumes of loans and deposits. Keywords: Bank behavior, Cournot oligopoly, Stackelberg oligopoly
TL;DR: In this paper, a theoretical and econometric model is developed in order to identify simultaneously the behaviour of the firms and the degree to which regulation constrained the price, considering collusive market-sharing arrangements involving asymmetric firms, and the less collusive outcomes of Cournot and Stackelberg, together with their constrained counterparts.
TL;DR: In this paper, the authors explore how harvesting technology can affect firms' internalisation of common pool externalities and the incentives for expanding a firm's size, focusing on supply side non-pecuniary externalities.
Abstract: This paper explores how harvesting technology can affect firms' internalisation of common pool externalities and the incentives for expanding firm's size. Focusing on supply side non-pecuniary externalities, our closed-entry harvesting competition model suggests that when marginal harvesting costs are weakly sensitive to common pool externalities, atomistic competition is likely to remain, other things equal, as the predominant industrial structure in the fishery. The avenue for increasing industrial concentration is modelled via Stackelberg leadership which offers the option of preempting rivals' production. In our static modelling, a fishery subject to Stackelberg signalling results in higher overfishing versus the case of a highly decentralised harvesting sector (proxied by the use of Nash conjectures). Given that static optimising behaviour could be interpreted as a result of entry controls and other fishing regulations being widely perceived as ineffective controls, the obtained overfishing ranking suggests that in fisheries where strategic preemption in production is feasible, but where entry controls and other important regulations on fishing effort are considered to be ineffective, overfishing is likely to remain the predominant outcome, even if other incentives promote evolution towards a more concentrated industry structure. When the fishery is already overpopulated by numerous small firms, whatever advantages large firms may have in terms of profitability, numerous small-scale fishermen tend to make up for in the political arena. This imposes constraints on the politically feasible fishing regulations. We use a second best welfare benchmark to illustrate resulting policy trade-offs.
TL;DR: In this article, the authors use a simple international trade model where governents fix their tariffs in order to maximize social welfare and find that when countries behave in a non-cooperative way this performance leads to tariff dis crimination.
Abstract: This paper shows that preferential trade agreements can emerge in an endogenous way. We use a simple international trade model where govern ments fix their tariffs in order to maximize social welfare. We find that when countries behave in a non co-operative way this performance leads to tariff dis crimination. This result holds whether firms play a Cournot strategy or whether they follow a Stackelberg's leader-follower strategy. This paper also analyzes whether multilateralism and regionalism are complementary or sub stitutive processes. It is concluded that, in spite of the fact that absolute protec tion is reduced as a result of the economic integration process, relative protec tion against the rest of the world increases and, therefore, the two processes
TL;DR: In this article, the authors consider a two-period duopoly game where in the first period the leader produces a good with a given quality and the other firm can only imitate it, and the outcome of this is uncertain: it could either be the case that a good of better quality can be introduced, or that a cost reduction in producing the existing good is attained.
Abstract: The model considers a two-period duopoly game where in the first period the leader produces a good with a given quality and the other firm can only imitate it. It is the Stackelberg case where, in addition, the leader has the choice of the quality of the good and the imitation is costly, but not prohibitively so. Under this assumption quantities and profits in terms of the quality are derived as subgame perfect equilibrium. In the second period there exists the possibility for the leader and/or the follower to make an investment. The outcome of this is uncertain: it could either be the case that a good of better quality can be introduced, or that a cost-reduction in producing the existing good is attained. The former case is a product innovation, whereas the latter case is a process innovation. By solving the game backwards as a function of the quality of the first period, there exists the possibility of an equilibrium where the follower chooses to invest and the leader does not invest .
01 Jan 1999
TL;DR: In this paper, the authors propose a systematic means for achieving a set of overall traffic management or planning goals with respect to the performance of the traffic network through the use of link tolls.
Abstract: The authors propose a systematic means for achieving a set of overall traffic management or planning goals with respect to the performance of the traffic network through the use of link tolls. The primary goals are defined by a set of link flow restrictions. The tolls that achieve these goals are obtained by solving a generalization of the classical user equilibrium model which includes a set of side constraints on the link flows. The set of toll prices obtained is not necessarily unique; this fact enables the traffic planner to choose a toll scheme which satisfies exogenous constraints and which may optimize a secondary goal, such as with respect to the toll itself. The overall model is derived as a special case of a mathematical program with equilibrium constraints (MPEC) describing a Stackelberg game involving the traffic manager and the users of the network. The model is shown to yield valuable information also in the case where the management goals and exogenous toll constraints are inconsistent with each other or with the underlying network.