Showing papers on "Stackelberg competition published in 2001"
TL;DR: A model to study and analyze the benefit of coordinating supply chain inventories through the use of common replenishment epochs or time periods for a one-vendor, multi-buyer supply chain for a single product is proposed.
287 citations
TL;DR: In this article, the authors compare Stackelberg and Cournot duopoly markets with quantity competition, and find that both of them yield higher outputs than Cournot markets and, thus, higher efficiency.
Abstract: We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.
182 citations
06 Jul 2001
TL;DR: It is proved that it is NP-hard to compute the optimal Stackelberg strategy and simple strategies with provable performance guarantees are presented and given.
Abstract: We study the problem of optimizing the performance of a system shared by selfish, noncooperative users. We consider the concrete setting of scheduling jobs on a set of shared machines with load-dependent latency functions specifying the length of time necessary to complete a job; we measure system performance by the total latency of the system.Assigning jobs according to the selfish interests of individual users (who wish to minimize only the latency that their own jobs experience) typically results in suboptimal system performance. However, in many systems of this type there is a mixture of “selfishly controlled” and “centrally controlled” jobs; as the assignment of centrally controlled jobs will influence the subsequent actions by selfish users, we aspire to contain the degradation in system performance due to selfish behavior by scheduling the centrally controlled jobs in the best possible way.We formulate this goal as an optimization problem via Stackelberg games, games in which one player acts a leader (here, the centralized authority interested in optimizing system performance) and the rest as followers (the selfish users). The problem is then to compute a strategy for the leader (a em Stackelberg strategy) that induces the followers to react in a way that (at least approximately) minimizes the total latency in the system.In this paper, we prove that it is NP-hard to compute the optimal Stackelberg strategy and present simple strategies with provable performance guarantees. More precisely, we give a simple algorithm that computes a strategy inducing a job assignment with total latency no more than a constant times that of the optimal assignment of all of the jobs; in the absence of centrally controlled jobs and a Stackelberg strategy, no result of this type is possible.
178 citations
TL;DR: In this article, the authors examined dynamic advertising and promotion strategies in a marketing channel where the retailer promotes the manufacturer product and the manufacturer spends on advertising to build a stock of goodwill.
Abstract: This paper examines dynamic advertising and promotion strategies in a marketing channel where the retailer promotes the manufacturer product and the manufacturer spends on advertising to build a stock of goodwill We assume that sales depend on goodwill and promotion activities and that there are decreasing marginal returns to goodwill Two scenarios are studied First, the manufacturer and retailer determine noncooperatively their respective strategies Second, the game is played a la Stackelberg with the manufacturer as the leader who supports partially the cost of the promotion activities of the retailer In both cases, stationary Markovian strategies are characterized These scenarios are examined also in the absence of decreasing marginal effect of goodwill on sales The results show that, whether or not the goodwill stock has a decreasing marginal effect on sales, the cooperative advertising program is a coordinating mechanism in the marketing channel, ie, both players receive higher payoffs
153 citations
TL;DR: It is suggested that manufacturer's leadership reduces inefficiency in a channel and is more beneficial to the consumer.
Abstract: This paper provides an answer to the question who should, if any, lead a marketing channel? We consider a channel consisting of one manufacturer and one retailer where each player controls his advertising rate and margin. Supposing that advertising has a carry over effect on demand, we adopt a dynamic model. Nash and Stackelberg equilibria are characterised and outcomes compared with an efficient coordinated solution. Our findings suggest that manufacturer's leadership reduces inefficiency in a channel and is more beneficial to the consumer.
110 citations
Posted Content•
TL;DR: In the presence of output subsidization, the optimal output subsidy is identical and profits, output and social welfare are also identical irrespective of whether a public firm moves simultaneously with n private firms or acts as a Stackelberg leader or all firms, public and private, behave as profit-maximizers as discussed by the authors.
Abstract: In the presence of output subsidization, the optimal output subsidy is identical and profits, output and social welfare are also identical irrespective of whether (i)a public firm moves simultaneously with n private firms or (ii) it acts as a Stackelberg leader or (iii) all firms, public and private, behave as profit-maximizers.
94 citations
TL;DR: In this article, the authors show that the profitability of merger in markets with quantity competition does not only depend on cost conditions but also on the market structure and on the involved firms' "strategic power".
75 citations
TL;DR: An interactive algorithm of the model for solving multi-objective decision-making problems and reflecting the interactive natures among the decision makers is developed.
Abstract: Furthering a prior research on two-person bi-level multi-objective decision-making problems of the leader-follower Stackelberg game, we present an extended model of bi-level multi-objective decision-making with multiple interconnected decision makers at the lower level. In the model, the upper level decision maker acts as a leader and the lower level decision makers behave as the followers, and inter-connections and interactions exist among these followers in decision-making scenarios. Following the rules of leader-follower Stackelberg game, we develop an interactive algorithm of the model for solving multi-objective decision-making problems and reflecting the interactive natures among the decision makers. Finally, the authors exemplify the model and algorithm, and draw a conclusion on points of contributions and the significance of this study in decision-making and support. Copyright © 2001 John Wiley & Sons, Ltd.
74 citations
TL;DR: This paper applies efficient algorithms to a set of numerical examples to quantify the supply chain inefficiencies due to functional segregation or uncoordinated decision making in a decentralized channel, and gains insight into systematic differences in the associated pricing and operational patterns.
Abstract: This paper integrates pricing and replenishment decisions for the following prototypical two-echelon distribution system with deterministic demands. A supplier distributes a single product to multiple retailers, who in turn sell it to consumers. The retailers serve geographically dispersed, heterogeneous markets. The demand in each retail market arrives continuously at a constant rate, which is a general decreasing function of the retail price in the market. The supplier replenishes its inventory through orders (purchases, production runs) from a source with ample capacity. The retailers replenish their inventories from the supplier. We develop efficient algorithms to determine optimal pricing and replenishment strategies for the following three channel structures. The first is the vertically integrated channel, where the system-wide pricing and replenishment strategies are determined by a central planner whose objective is to maximize the system-wide profits. The second structure is that of a vertically integrated channel in which pricing and operational decisions are made sequentially by separate functional departments. The third channel structure is decentralized, i.e., the supplier and the retailers are independent, profit-maximizing firms with the supplier acting as a Stackelberg game leader. We apply our algorithms to a set of numerical examples to quantify the supply chain inefficiencies due to functional segregation or uncoordinated decision making in a decentralized channel. We also gain insight into systematic differences in the associated pricing and operational patterns.
68 citations
TL;DR: In this article, the existence and uniqueness results for a hierarchical or Stackelberg equilibrium in a two-player differential game with open-loop information structure were derived for games with a rather nonconflicting structure of their cost criteria.
Abstract: We present existence and uniqueness results for a hierarchical or Stackelberg equilibrium in a two-player differential game with open-loop information structure. There is a known convexity condition ensuring the existence of a Stackelberg equilibrium, which was derived by Simaan and Cruz (Ref. 1). This condition applies to games with a rather nonconflicting structure of their cost criteria. By another approach, we obtain here new sufficient existence conditions for an open-loop equilibrium in terms of the solvability of a terminal-value problem of two symmetric Riccati differential equations and a coupled system of Riccati matrix differential equations. The latter coupled system appears also in the necessary conditions, but contrary to the above as a boundary-value problem. In case that the convexity condition holds, both symmetric equations are of standard type and admit globally a positive-semidefinite solution. But the conditions apply also to more conflicting situations. Then, the corresponding Riccati differential equations may be of H?-type. We obtain also different uniqueness conditions using a Lyapunov-type approach. The case of time-invariant parameters is discussed in more detail and we present a numerical example.
66 citations
TL;DR: In this article, a cost structure that can be used for decentralized control of a multi-echelon inventory system with a central warehouse and a number of retailers is proposed. But it does not consider the effect of policy changes at other installations, since the cost structure satisfies a rationality constraint.
Abstract: We provide a cost structure that can be used for decentralized control of a multi-echelon inventory system with a central warehouse and a number of retailers. This cost structure means that the warehouse, in addition to its local costs, pays a penalty cost for a delay at the warehouse to the retailer facing the delay. A basic assumption is that each installation starts with an initial policy concerning e.g., inventory control and transportation. The installations then play a Stackelberg game with the warehouse being the leader. By minimizing its local costs according to the suggested cost structure, an installation can reduce its costs. The total system costs are then reduced by the same amount. No installation needs to face higher costs due to policy changes at other installations, since the cost structure satisfies a rationality constraint. If an installation applies its initial policy the local costs are the same as in the initial state, even if the other installations change their policies. If the game is played repeatedly the system will approach a Nash equilibrium but not necessarily the centralized optimal solution. As an example we consider a system with one-for-one ordering retailers.
TL;DR: This method uses the concepts of tolerance membership function and multi-objective optimization (MOO) (at each level) to develop a fuzzy max — min decision model for generating Pareto optimal (satisfactory) solution for BLN — MODM problem.
Abstract: This paper studies a bi-level non-linear multi-objective decision making (BLN — MODM) problem with linear (or nonlinear) constraints, and in which the objective function at each levels are nonlinear functions, which are to be maximized. The BLN-MODM problem can be thought of as a static version of the Stackelberg leader-follower game in which a Stackelberg strategy is used by the leader (or the higher — level decision maker (HLDM)), given the rational reaction of the follower (or the lower-level decision maker (LLDM)). From this point of view, this paper proposes a two-planner bi-level multi-objective decision-making model and solution method for solving this problem. This method uses the concepts of tolerance membership function and multi-objective optimization (MOO) (at each level) to develop a fuzzy max — min decision model for generating Pareto optimal (satisfactory) solution for BLN — MODM problem. The HLDM specifies his/her objective functions and decisions with possible tolerances, which are described by membership functions of fuzzy set theory. Then, the LLDM uses this preference information for HLDM and solves his/her problem subject to the HLDMs’ restrictions. An illustrative numerical example is given to demonstrate the obtained results.
Proceedings Article•
01 Jan 2001
TL;DR: It is shown that the two round Stackelberg strategy (denoted 2SS) always dominates the one round scheme and is considered to be an extension of the above results to special graphs, and special kind of latency functions.
Abstract: We continue the study initiated in [Ro01] on Stackelberg Scheduling Strategies. We are given a set of n independent parallel machines or equivalently a set of n parallel edges on which certain flow has to be sent. Each edge e is endowed with a latency function l{sub e}({center_dot}). The setting is that of a non-cooperative game: players choose edges so as minimize their individual latencies. Additionally, there is a single player who control as fraction ?? of the total flow. The goal is to find a strategy for the leader (i.e. an assignment of flow to indivual links) such that the selfish users react so as to minimize the total latency of the system. Building on the recent results in [Ro01, RT00], we show the following: 1. We devise a fully polynomial approximate scheme for the problem of finding the cheapest Stackelberg Strategy: given a performance requirement, our algorithm runs in time polynomial in n and {var_epsilon} and produces a Stackelberg strategy s, whose associated cost is within a 1 + {var_epsilon} factor of the optimum stackelberg strategy s*. The result is extended to obtain a polynomial-approximation scheme when instances are restricted to layered directed graphs in which each layer has a bounded number of vertices. 2. We then consider a two round Stackelberg strategy (denoted 2SS). In this strategy, the game consists of three rounds: a move by the leader followed by the moves of all the followers folowed again by a move by the leader who possibly reassigns some of the flows. We show that 2SS always dominates the one round scheme, and for some classes of latency functions, is guaranteed to be closer to the global social optimum. We also consider the variant where the leader plays after the selfish users have routed themselves, and observe that this dominates the one-round scheme. Extensions of the results to the special case when all the latency functions are linear are also presented. Our results extend the earlier results and answer an open question posed by Roughgarden [Ro01].
27 May 2001
TL;DR: This paper presents the discussion and comparison of the different optimization strategies and their associated evolutionary tools for the multi-point design optimization of a multi-element airfoil system during landing and taking off operations of an aircraft.
Abstract: This paper presents the discussion and comparison of the different optimization strategies and their associated evolutionary tools for the multi-point design optimization of a multi-element airfoil system during landing and taking off operations of an aircraft. New optimization algorithms based on binary coded genetic algorithms (GAs) coupling with game theory, such as Nash GAs (N-GAs) and Stackelberg GAs (S-GAs), are introduced and implemented to optimize the position of slat and flap of a high lift system operating simultaneous at taking off and landing conditions. A cheap nondifferentiable CFD solver coupling an inviscid panel approach with laminar or turbulent boundary layers and wake is used to solve the flow field around this system. Numerical results are compared with different strategies which demonstrates the flexible capability and robustness of such algorithms for multi-objective and multidisciplinary optimization problems in aerodynamics.
TL;DR: In this paper, the authors explore possible strategic interactions between the state and local community in games of tropical forestland appropriation and show that the local response to more state deforestation depends on the costs, market and behavioral assumptions, and less on the structure of the game.
Abstract: This paper explores possible strategic interactions between the state and local community in games of tropical forestland appropriation. Three typical cases are discussed, corresponding to a development over time of increased resource competition and market integration. The local response to more state deforestation depends on the costs, market, and behavioral assumptions, and less on the structure of the game (Cournot or Stackelberg). The state fuels local deforestation by providing infrastructure (roads) which reduces the net costs of agricultural expansion, or when markets are imperfect and local behavior determined by survival needs. The game structure is, however, important for total deforestation.This paper explores possible strategic interactions between the state and local community in games of tropical forestland appropriation. Three typical cases are discussed, corresponding to a development over time of increased resource competition and market integration. The local response to more state deforestation depends on the costs, market, and behavioral assumptions, and less on the structure of the game (Cournot or Stackelberg). The state fuels local deforestation by providing infrastructure (roads) which reduces the net costs of agricultural expansion, or when markets are imperfect and local behavior determined by survival needs. The game structure is, however, important for total deforestation.
TL;DR: In this paper, the authors investigated an extension of the linear bilevel programming problem where the objective functions of both players are bilinear and a regularized term is added to the follower objective function to overcome certain discontinuities in the master problem.
Abstract: The bilevel programming problem (BLPP) is equivalent to a two-person Stackelberg game in which the leader and follower pursue individual objectives Play is sequential and the choices of one affect the choices and attainable payoffs of the other The purpose of this paper is to investigate an extension of the linear BLPP where the objective functions of both players are bilinear To overcome certain discontinuities in the master problem, a regularized term is added to the follower objective function Using ideas from parametric programming, the generalized Jacobian and the pseudodifferential of the regularized follower solution function are computed This allows us to develop a bundle trust-region algorithm Convergence analysis of the proposed methodology is given
TL;DR: In this paper, the Stackelberg model is extended to include any number of non-identical firms and demonstrates significant counterintuitive results, such as entry of an additional firm may increase the quantities and/or profits of some existing firms; it may also increase the total industry profit.
Abstract: This paper extends the Stackelberg model to include any number of nonidentical firms and demonstrates significant counterintuitive results. For example, entry of an additional firm may increase the quantities and/or profits of some existing firms; it may also increase the total industry profit.
TL;DR: It is shown that time coordination generally has a substantial benefit for the vendor, although the benefit to the buyers may be limited.
Abstract: We study the coordination of a two-echelon distribution system where a vendor distributes a single product to a set of independent buyers. The problem is analyzed as a Stackelberg game in which the vendor acts as the leader and buyers act as followers. A simple strategy is developed for the vendor to employ a uniform quantity-discount policy to coordinate buyers' replenishment times by the power-of-two policy. Solution procedures are developed for the equilibrium strategy. It is shown that time coordination generally has a substantial benefit for the vendor, although the benefit to the buyers may be limited. Furthermore, uniform quantity discounts to all buyers are normally feasible but not sufficient to achieve perfect channel coordination when buyers act independently. The proposed strategy obtains a high proportion of the maximum benefit under perfect channel coordination.
TL;DR: In this paper, the authors considered an asymmetric duopoly producing a homogeneous commodity and facing a competitive demand, where one of the players maximizes its profit and the other one, being eager to earn hard currencies, maximises its revenue, while the second player is not allowed to sell more than a certain proportion of the quantity sold by its rival.
TL;DR: In this paper, the authors analyzed a model of bargaining in which two parties use a mediator who sequentially makes random proposals until agreement by both parties is reached, and they showed that as the cost of delay shrinks to zero, the subgame perfect payoff converges to the asymmetric Nash bargaining solution with weights determined by the relative discount rates of the players.
Abstract: This paper analyzes a model of bargaining in which two parties use a mediator who sequentially makes random proposals until agreement by both parties is reached. I show that as the cost of delay shrinks to zero, the subgame perfect payoff converges to the asymmetric Nash bargaining solution with weights determined by the relative discount rates of the players. I also establish conditions for the uniqueness of the subgame perfect equilibrium for arbitrary discount rates.
Posted Content•
25 Oct 2001
TL;DR: In this article, the authors investigated the nature of the equilibria arising under spatial differentiation in a duopoly model, where at least one firm maximises value added per worker.
Abstract: The nature of the equilibria arising under spatial differentiation is investigated here in a duopoly model, where at least one firm maximises value added per worker. The study shows that if firms' objectives differ, there exists a subgame perfect equilibrium in pure strategies, which is possibly characterised by asymmetric locations. If both firms are labour-managed, there exists a (symmetric) subgame perfect equilibrium in pure strategies with firms located at the first and third quartiles, if and only if the setup cost is low enough. Otherwise, undercutting is profitable.
TL;DR: This paper provides an explanation for an important institutional feature of staggered time-dependent adjustment rules assumed in a number of macroeconomic models.
TL;DR: Based on oligopoly theory, the authors proposes a Stackelberg game model between a BOT investor and an electric utility whereby they can negotiate a long-term energy contract, and asymmetric pricing schemes are taken into account such that a host utility purchases electricity from a bOT company at its avoided cost, and sells its electricity to end users at its average cost.
TL;DR: This article explored the relationship between mergers, welfare, and concentration using a two-stage oligopoly model that generalizes the Cournot and Stackelberg models, and found that most mergers lower welfare and many of these are profitable.
Abstract: This paper explores the relationship between mergers, welfare, and concentration, using a two-stage oligopoly model that generalizes the Cournot and Stackelberg models. This model has been used to show that some profitable mergers raise welfare and that some welfare-lowering mergers are unprofitable. Based on this, one might conclude that policy designed to restrict mergers is unnecessary or even counterproductive. This present paper examines in greater detail the implications of this model and finds that a merger's effects depend not only on the reduction in the number of firms, but also on premerger and postmerger firm behavior. In fact, most mergers lower welfare, and many of these are profitable. Usually, but not always, changes in concentration and welfare are negatively related.
TL;DR: In this paper, the authors re-examine endogenous Stackelberg leader-follower relations by modeling an explicitly dynamic market and find that such a Stackeberg-like equilibrium can arise only when the relative weight of the pre-Stackekelberg first marketing period is sufficiently high, with time preferences being sufficiently strong.
Abstract: This paper re-examines endogenous Stackelberg leader–follower relations by modelling an explicitly dynamic market. We analyze a twice-repeated duopoly where, in the beginning, each firm chooses either a quantity-sticky production mode or a quantity-flexible production mode. The size of the market becomes observable after the first period. In the second period, a firm can adjust its quantity if and only if it has adopted the flexible mode. Hence, if one firm chooses the sticky mode whilst the other chooses the flexible mode, then they respectively play the roles of a Stackelberg leader and a Stackelberg follower in the second marketing period. Somewhat intriguing is the finding that such a Stackelberg-like equilibrium can arise only when the relative weight of the pre-Stackelberg first marketing period is sufficiently high, with time preferences being sufficiently strong.
01 Sep 2001
TL;DR: It is shown that solving the hybrid pursuit game is equivalent to finding a Stackelberg equilibrium solution for a partial information Markov game, which can be solved using dynamic programming.
Abstract: We address the design of optimal strategies for a pursuer trying to catch a moving evader. When the pursuer has available two teams of agents with different capabilities-one that can "search for the evader" and the other one that can "catch the evader"-, the game can be naturally formulated as an optimal control problem on a hybrid system. We show that solving the hybrid pursuit game is equivalent to finding a Stackelberg equilibrium solution for a partial information Markov game, which can be solved using dynamic programming. Since for most realistic situations this approach is computationally very difficult, we propose a two-level suboptimal solution that uses a greedy control for coordinating the agents within each team, and a threshold-based logic for orchestrating the switching between teams. Simulations are included to show the feasibility of the approach.
01 Oct 2001
TL;DR: In this paper, the authors investigated the nature of the equilibria arising under spatial differentiation in a duopoly model, where at least one firm maximises value added per worker.
Abstract: The nature of the equilibria arising under spatial differentiation is investigated here in a duopoly model, where at least one firm maximises value added per worker. The study shows that if firms' objectives differ, there exists a subgame perfect equilibrium in pure strategies, which is possibly characterised by asymmetric locations. If both firms are labour-managed, there exists a (symmetric) subgame perfect equilibrium in pure strategies with firms located at the first and third quartiles, if and only if the setup cost is low enough. Otherwise, undercutting is profitable.
TL;DR: This work considers a firm that wishes to maximise the profits coming from the sale of a new product or technology by determining an optimal price and advertising strategy and a public authority wishing to accelerate and stimulate the adoption of the new product by using a budget to give price subsidies directly to the consumers.
Abstract: We consider a firm that wishes to maximise the profits coming from the sale of a new product or technology by determining an optimal price and advertising strategy. A public authority wishes to accelerate and stimulate the adoption of the new product by using a budget to give price subsidies directly to the consumers. The problem is set up as a Stackelberg differential game.
01 Jan 2001
TL;DR: In this paper, the value of commitment in Stackelberg games where the follower chooses whether to pay some cost e to perfectly observe the leader's action is examined, and it is shown that in the unique case, commitment is worth it.
Abstract: We report on experiments examining the value of commitment in Stackelberg games where the follower chooses whether to pay some cost e to perfectly observe the leader’s action. Vardy (2001) shows that in the unique