Showing papers on "Stackelberg competition published in 2005"

Competitive pricing of mixed retail and e-tail distribution channels

Abstract: In addition to regular retail distribution channels, a firm nowadays can avail themselves of such information technology (IT) as the Internet to distribute products directly “on line” (referred to as an “e-tail” distribution channel). The mix of retailing with e-tailing has added a new dimension of competition to the firm's distribution channels. The central issue of this competition is the competitive pricing policies between retail and e-tail distribution channels. In this paper, we consider the price competition between these two channels under two market game settings: the Bertrand and the Stackelberg price competition models. In the Bertrand competition, the manufacturer and retailer simultaneously select e-tail and retail price, respectively, while in Stackelberg competition, the manufacturer as a leader selects the e-tail price, then the retailer selects retail price. We obtain both the Bertrand and Stackelberg equilibrium pricing policies, and compare the profit gains under these two competitions. Based on our results, we propose an appropriate strategy for the manufacturer to adopt when adding an e-tail channel. We also show that an optimal wholesale price exists under a different market structure that could be used to encourage the retailer to accommodate the additional e-tail channel.

Game Theoretic Applications in Supply Chain Management: A Review

Abstract: Recent emphasis on competition and cooperation in supply chains has resulted in the resurgence of game theory as a relevant tool for analyzing such interactions in a supply chain. This paper presents a review of more than 130 papers concerned with game theoretical applications in supply chain management (SCM). We first give a brief summary of the basic solution concepts in non-cooperative and cooperative games such as Nash and Stackelberg equilibria, Nash arbitration scheme and cooperation with sidepayments. the core, the Shapley value and nucleolus. Our review of supply chain-related game theoretical applications is presented in five areas: (i) Inventory games with fixed unit purchase cost, (ii) Inventory games with quantity discounts, (iii) Production and pricing competition, (iv) Games with other attributes, (v) Games with joint decisions on inventory, production/pricing and other attributes. The paper concludes with a summary of our review, suggestions for potential applications of game theory...

The Water-Filling Game in Fading Multiple Access Channels

Abstract: We adopt a game theoretic approach for the design and analysis of distributed resource allocation algorithms in fading multiple access channels. The users are assumed to be selfish, rational, and limited by average power constraints. We show that the sum-rate optimal point on the boundary of the multipleaccess channel capacity region is the unique Nash Equilibrium of the corresponding water-filling game. This result sheds a new light on the opportunistic communication principle and argues for the fairness of the sum-rate optimal point, at least from a game theoretic perspective. The base-station is then introduced as a player interested in maximizing a weighted sum of the individual rates. We propose a Stackelberg formulation in which the base-station is the designated game leader. In this set-up, the base-station announces first its strategy defined as the decoding order of the different users, in the successive cancellation receiver, as a function of the channel state. In the second stage, the users compete conditioned on this particular decoding strategy. We show that this formulation allows for achieving all the corner points of the capacity region, in addition to the sum-rate optimal point. On the negative side, we prove the non-existence of a base-station strategy in this formulation that achieves the rest of the boundary points. To overcome this limitation, we present a repeated game approach which achieves the capacity region of the fading multiple access channel. Finally, we extend our study to vector channels highlighting interesting differences between this scenario and the scalar channel case.

The generalized nash equilibrium model for oligopolistic transit market with elastic demand

Abstract: This paper presents a bilevel transit fare equilibrium model for a deregulated transit system. In the upper-level problem, the transit competition is portrayed as an n-player, non-cooperative game by changing the fare structure of each of a set of transit lines separately so as to maximize the profit of each transit operator within the oligopolistic market. We show that there exists a generalized Nash game between transit operators, which can be formulated as a quasi-variational inequality problem. In the lower-level problem, the passengers' response to the equilibrium fare structure of the transit operators is represented by the stochastic user equilibrium transit assignment model with elastic OD demand. As a result, the bilevel transit fare equilibrium problem is presented in the Stackelberg form and solved by a heuristic solution algorithm based on a sensitivity analysis approach. A numerical example is given to illustrate the competition mechanism on the transit network and some useful findings are presented on competitive operations. (c) 2004 Elsevier Ltd. All rights reserved.

Dynamic Game Theoretic Model of Multi-Layer Infrastructure Networks

Abstract: Due to similarities in terms of network structure and interactions among them, most infrastructure systems can be viewed as coupled layers of a generalized transportation network in which the passenger, freight, data, water, and energy flows are the commodities in the different layers. The coupling is due to the varying degrees of interactions among these layers in terms of shared physical networks, budgetary constraints, socio-economic environments, environmental concerns, information/other resources, and in particular, functional interdependencies. However, these interactions are normally ignored in the engineering planning, design and analysis of infrastructure systems. Identifying and understanding these interactions using a holistic perspective can lead to more efficient infrastructure systems. This paper presents a preliminary network flow equilibrium model of dynamic multi-layer infrastructure networks in the form of a differential game involving two essential time scales. In particular, three coupled network layers—automobiles, urban freight and data—are modeled as being comprised of Cournot-Nash dynamic agents. An agent-based simulation solution structure is introduced to solve the flow equilibrium and optimal budget allocation problem for these three layers under the assumption of a super authority that oversees investments in the infrastructure of all three technologies and thereby creates a dynamic Stackelberg leader-follower game.

The generalized Stackelberg equilibrium of the all-pay auction with complete information

Abstract: We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts ’early’ and a group of players who choose ’late’. Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses ’late’, whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost.

Optimal Trade and Privatization Policies in an International Duopoly with Cost Asymmetry

Abstract: This paper examines optimal trade and privatization policies in a mixed duopoly in which a pubic home firm competes with a more efficient foreign firm. The home firm is a Cournot competitor or a Stackelberg leader. The home government chooses the degree of privatization and import tariff to maximize national welfare. The paper examines the policy effects on industry equilibrium with general demand and cost structures and shows that the optimal level of privatization depends crucially upon the strategic substitutability-complementarity assumption. It further shows that if both policies are used under linear demand and quadratic costs, the equilibrium prices, firms' outputs, welfare and tariff rates are the same under Cournot and Stackelberg competition, and price equals the home firm's marginal cost. Neither full nationalization nor full privatization is optimal under Cournot, but full nationalization is always optimal under Stackelberg competition. If only one policy is used, a reduction in government's ownership of the public firm under Cournot competition and constant marginal costs calls for a higher optimal tariff rate. This result does not carry over to the case of increasing marginal costs, although the optimal tariff is lower under full nationalization than under full privatization.

Licensing contract in a stackelberg model

Abstract: We study optimal linear licensing and its social welfare implications when the innovator (patentee) is an insider that can make capacity/output commitment so as to act as a Stackelberg leader in the output market. We show that (i) the patentee’s profit-maximizing licensing contract is a royalty; (ii) the optimal royalty rate is greater than the cost reduction attained by the licensed technology and is increasing in the number of competitors; (iii) optimal licensing maximizes the likelihood of technology transfer, may reduce social welfare and always makes consumers worse off; and (iv) the innovator benefits from capacity commitment, and the more competitive the output market, the greater the gains it makes by licensing. The opposite holds for consumers. 1I ntroduction Patent licensing is quite widespread and takes place in almost all industries. The common modes of patent licensing are a royalty per unit of output produced with the patented technology, and/or a fixed fee. The patent licensing literature has analyzed the patentee’s profitmaximizing (optimal) licensing contract for two general cases: one, where the patentee is outside the market of operation, i.e. the patentee is not a competitor in the product market; the other where the patentee is inside the market of operation and naturally becomes a competitor in the product market.

Equilibrium problems with equilibrium constraints: stationarities, algorithms, and applications

Abstract: An equilibrium problem with equilibrium constraints (EPEC) is a member of a new class of mathematical programs that often arise in engineering and economics applications. One important application of EPECs is the multi-leader-follower game in economics, where each leader is solving a Stackelberg game formulated as a mathematical program with equilibrium constraints (MPEC). Motivated by applied EPEC models for studying the strategic behavior of generating firms in deregulated electricity markets, the aim of this thesis is to study theory, algorithms, and new applications for EPECs. We begin by defining EPEC stationarity concepts. We then propose a sequential nonlinear complementarity (SNCP) method for solving EPECs and establish its convergence. We present the numerical results of the SNCP method and give a comparison with two best-reply iterations, nonlinear Jacobi and nonlinear Gauss-Seidel, on a set of randomly generated test problems. The computational experience to date shows that both the SNCP algorithm and the nonlinear Gauss-Seidel method outperform the nonlinear Jacobi method. We investigate the issue of existence of an EPEC solution in Chapter 4. In general, an EPEC solution may not exist because of nonconvexity of the associated MPECs. However, we show that the existence result can be established for the spot-forward market model proposed by Allaz and Vila or the two-period Cournot game studied by Saloner. We observe that the mathematical structure of the spot-forward market model is similar to that of the multiple leader Stackelberg model analyzed by Sherali when new variables are introduced for spot market sales. Consequently, we are able to adapt Sherali's analysis to establish the existence of a forward market equilibrium for M asymmetric producers with nonidentical linear cost functions. In Chapter 5, we present a novel MPEC approach for solving the static moral-hazard problem in economics. We consider deterministic contracts as well as contracts with action and/or compensation lotteries and formulate each case as an MPEC. We propose a hybrid procedure that combines the best features of the MPEC approach and the LP lottery approach. Numerical results on an example show that the hybrid procedure outperforms the LP lottery approach in both computational time and solution quality in terms of the optimal objective value.

Optimal Trade and Privatization Policies in an International Duopoly with Cost Asymmetry

Abstract: This paper examines optimal trade and privatization policies in a mixed duopoly in which a pubic home firm competes with a more efficient foreign firm. The home firm is a Cournot competitor or a Stackelberg leader. The home government chooses the degree of privatization and import tariff to maximize national welfare. The paper examines the policy effects on industry equilibrium with general demand and cost structures and shows that the optimal level of privatization depends crucially upon the strategic substitutability-complementarity assumption. It further shows that if both policies are used under linear demand and quadratic costs, the equilibrium prices, firms' outputs, welfare and tariff rates are the same under Cournot and Stackelberg competition, and price equals the home firm's marginal cost. Neither full nationalization nor full privatization is optimal under Cournot, but full nationalization is always optimal under Stackelberg competition. If only one policy is used, a reduction in government's o...

Predicting Competitive Response to a Major Policy Change: Combining Game-Theoretic and Empirical Analyses

Abstract: This research uses Procter & Gamble's value pricing initiative as a context for testing whether actual competitor and retailer response to a major policy change can be predicted using a game-theoretic model We first estimate demand functions for P&G and competitor brands from the period before value pricing was initiated We then formulate a dynamic manufacturer-retailer Stackelberg model that includes P&G, a national-brand competitor, and a retailer The model takes P&G's move as given and prescribes the price and promotion response of the competitors and the retailer We substitute the estimated demand parameters into the model to obtain prescriptions for each competitor and the retailer, and see whether these prescriptions are related to the actual response We find that the dynamic game-theoretic model calibrated with empirical estimates of demand parameters has significant predictive power We also test the predictive power of two benchmark models The first is based on the reaction function approach of Leeflang and Wittink Leeflang, Peter S H, Wittink, Dick R 1992 Diagnosing competitive reactions using aggregated scanner data Internat J Res Marketing9 39-57, and the second is a simplification of our dynamic model where the retailer is not strategic The dynamic game-theoretic model performs better than either benchmark

The Generalized Stackelberg Equilibrium of the All-Pay Auction with Complete Information

Abstract: We characterize the equilibrium of the all-pay auction with general convex cost of effort and sequential effort choices. We consider a set of n players who are arbitrarily partitioned into a group of players who choose their efforts 'early' and a group of players who choose 'late.' Only the player with the lowest cost of effort has a positive payoff in any equilibrium. This payoff depends on his own timing vis-a-vis the timing of others. We also show that the choice of timing can be endogenized, in which case the strongest player typically chooses 'late,' whereas all other players are indifferent with respect to their choice of timing. In the most prominent equilibrium the player with the lowest cost of effort wins the auction at zero aggregate cost.

Technology Transfer in a Stackelberg Structure: Licensing Contracts and Welfare

Abstract: We study the question of optimal licensing contracts in a leadership structure and discuss the welfare implications. We assume that the size of the innovation is exogenous and the patent holder is a competitor in the product market. Then welfare depends on the types of contracts available and on the ownership of patents. In particular, we examine whether a leader's innovation is considered to be socially more valuable than a follower's innovation. We show that there are situations when a follower's innovation generates larger welfare. Given the private incentives for innovation, a licensing policy may induce the desired firm to win the patent race.

Playing Cournot although they shouldn't - Endogenous timing in experimental duopolies with asymmetric cost

Abstract: In this note, we experimentally investigate the extended game with action commitment in a Cournot duopoly with asymmetric cost. Risk dominance considerations allow to select a unique equilibrium in which the low-cost firm is the Stackelberg leader. The data, however, do not support the theory as simultaneous-move play is modal. Average output choices are in line with the Cournot equilibrium. This suggests that Cournot is a much more robust predictor for competition in markets than theory suggests.

An Econometric Analysis of Brand-Level Strategic Pricing Between Coca-Cola Company and PepsiCo.

Abstract: We investigate market structure and strategic pricing for leading brands sold by Coca-Cola Company and PepsiCo. in the context of a flexible demand specification (i.e., nonlinear AIDS) and structural price equations. Our flexible and generalized approach does not rely upon the often used ad hoc linear approximations to demand and profit-maximizing first-order conditions, and the assumption of Nash-Bertrand competition. We estimate a conjectural variation model and test for different brand-level pure strategy games. This approach of modeling market competition using the nonlinear Full Information Maximum Likelihood (FIML) estimation method provides insights into the nature of imperfect competition and the extent of market power. We find no support for a Nash-Bertrand or Stackelberg Leadership equilibrium in the brand-level pricing game. Results also provide insights into the unique positioning of PepsiCo.'s Mountain Dew brand.

Technology Transfer in a Stackelberg Structure: Licensing Contracts and Welfare

Abstract: We study the question of optimal licensing contracts in a leadership structure and discuss the welfare implications. We assume that the size of the innovation is exogenous and the patent holder is a competitor in the product market. Then welfare depends on the types of contracts available and on the ownership of patents. In particular, we examine whether a leader's innovation is considered to be socially more valuable than a follower's innovation. We show that there are situations when a follower's innovation generates larger welfare. Given the private incentives for innovation, a licensing policy may induce the desired firm to win the patent race.

Urban transport pricing reform with two levels of government

Abstract: This paper analyses two challenges in the reform of urban transport pricing. The first challenge is the construction of an optimal package of urban transport pricing instruments assuming one benevolent government level that maximizes overall welfare. We examine the welfare gains from implementing in succession better parking prices, improved public transport prices and time varying tolling. It is found that parking and tolling are the most important elements of the optimal package and that the alternative policy instruments are sub-additive in their benefits. The second problem studied is the use of these pricing instruments by different government levels. We examine a case where an urban government controls parking fees and the regional government controls the tolling. Although both government levels have different objective functions, we find that the overall efficiency losses in the Nash and Stackelberg equilibria are limited.

An MPCC approach for stochastic Stackelberg–Nash–Cournot equilibrium

Abstract: In this article, we investigate a Stochastic Stackelberg–Nash–Cournot Equilibrium problem by reformulating it as a Mathematical Program with Complementarity Constraints (MPCC). The complementarity constraints are further reformulated as a system of nonsmooth equations. We characterize the followers’ Nash–Cournot equilibria by studying the implicit solution of a system of equations. We outline numerical methods for the solution of a stochastic Stackelberg–Nash–Cournot Equilibrium problem with finite distribution of market demand scenarios and propose a discretization approach based on implicit numerical integration to deal with stochastic Stackelberg–Nash–Cournot Equilibrium problem with continuous distribution of demand scenarios. Finally, we discuss the two-leader Stochastic Stackelberg–Nash–Cournot Equilibrium problem.

Demand uncertainty and manufacturer returns policies for style-good retailing competition

Abstract: This paper investigates the role of the returns policy in the co-ordination of supply chain: A manufacturer provides a return policy for unsold goods to two competing retailers who face uncertain demand. The problem is described with a game theory structure: The manufacturer, as the Stackelberg leader, first commits a returns price to the retailers under a given wholesale price. Upon receiving this information, two competing retailers, as followers, make decisions for their retail price and order size, in which the process of pricing and ordering is played as Nash equilibrium. Anticipated the retailers’ responses, the manufacturer designs his returns policy. Adopting the classic newsboy problem model framework and using numerical study methods, the study finds that the provision of a returns policy is dependent on the market conditions faced by the retailers. The paper also analyses the impact of demand variability on the decisions of optimal retail price and order quantity and profit reallocation between the manufacturer and the retailers. Finally, it investigates how the competing factor influences the decision-making of supply chain members in response to uncertain demand and profit variability.

Stackelberg Leadership with Demand Uncertainty

Abstract: We consider a simple Stackelberg model with demand uncertainty only for the first mover in order to compare the advantages of leadership and flexibility, and use an example to provide some discussion about the endogenous order of moves in the presence of demand uncertainty. We find that only when the realized demand is in an intermediate zone does the first mover preserve its advantage; when the realized demand is far from its expected value, the second mover obtains higher profit than the leading firm, as the leadership advantage is dominated by the benefit of flexibility when demand fluctuation is significant. Even with this risk of losing flexibility under significant demand variation, for some parameter values in our model the first firm still has incentive to choose Stackelberg rather than Cournot competition.

Quantity discount pricing policies for heterogeneous retailers with price sensitive demand

Abstract: Although quantity discount policies have been extensively analyzed, they are not well understood when there are many different buyers. This is especially the case when buyers face price-sensitive demand. In this paper we study a supplier's optimal quantity discount policy for a group of independent and heterogeneous retailers, when each retailer faces a demand that is a decreasing function of its retail price. The problem is analyzed as a Stackelberg game whereby the supplier acts as the leader and buyers act as followers. We show that a common quantity discount policy that is designed according to buyers' individual cost and demand structures and their rational economic behavior is able to significantly stimulate demand, improve channel efficiency, and substantially increase profits for both the supplier and buyers. Furthermore, we show that the selection of all-units or incremental quantity discount policies has no effect on the benefits that can be obtained from quantity discounts. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005

Labor Supply of Retiring Couples and Heterogeneity in Household Decision-Making Structure

Abstract: This paper analyzes the labor market participation behavior of retiring couples in Norway. To account for the unobserved heterogeneity in decision-making structure within the household, I formulate a mixed model by assuming there are two types of households, the cooperative type and the non-cooperative type. I assume that non-cooperative households behave according to a Stackelberg game with the male as the leader, while cooperative households engage in a cooperative bargaining process. The estimation results show that more than half of the households are of the non-cooperative type.

Shelf-space allocation and advertising decisions in the marketing channel: a differential game approach

Abstract: This paper deals with the issue of shelf-space allocation and advertising decisions in marketing channels. We consider a network composed of a unique retailer offering the products of two competing manufacturers. The retailer controls the amount of shelf-space to allocate to both brands, while the manufacturers make advertising decisions in order to build their brand image (i.e. the goodwill stock). The demand for each brand is affected by its own goodwill level and the shelf-space allocated to the brand at retailer's store. The problem is formulated as a Stackelberg differential game played over an infinite horizon, with the manufacturers as leaders and the retailer as the follower. Stationary feedback equilibria are computed. Our main results indicate that the shelf-space allocated to each brand, manufacturers' advertising strategies at the equilibrium and channel members' value functions are affected by the goodwill levels of both products.