Showing papers on "Stackelberg competition published in 2000"

Manufacturer-Retailer Channel Interactions and Implications for Channel Power: An Empirical Investigation of Pricing in a Local Market

Abstract: The issue of "power" in the marketing channels for consumer products has received considerable attention in both academic and practitioner journals as well as in the popular press. Our objective in this paper is to provide an empirical method to measure the power of channel members and to understand the reasons demand factors, cost factors, nature of channel interactions for this power. We confine our analysis to pricing power in channels. We use methods from the game-theory literature in marketing on channel interactions to obtain the theoretical framework for our empirical model. This literature provides us a definition of power-one that is based on the proportion or percentage of channel profits that accrue to each of the channel members. There can be a variety of possible channel interactions between manufacturers and retailers in channels. The theoretical literature has examined some of these games. For example, Choi 1991 examines how channel profits for manufacturers and retailer vary if channel interactions are either vertical Nash, or if they are Stackelberg leaderfollower with either the manufacturer or the retailer being the price leader. Each of these three channel interaction games has different implications for profits made by manufacturers and retailers, and consequently for the relative power of the channel members. In contrast to the previous literature that has focused largely on the above three channel interaction games, our model extends the game-theoretic literature by allowing for a continuum of possible channel interactions between manufacturers and a retailer. Furthermore, for a given product market, we empirically estimate from the data where the channel interactions lie in this continuum. More critically, we obtain measures of how channel profits are divided between manufacturers and the retailer in the product market, where a higher share of channel profit is associated with higher channel power. We then examine how channel power is related to demand conditions facing various brands and cost parameters of various manufacturers. In going from game-theory-based theoretical models of channel interactions to empirical estimation, we use the "new empirical industrial organization" framework Bresnahan 1988. As part of this structural modeling framework, we build retail-level demand functions for the various brands manufacturer and private label in a given product category. Given these demand functions, we obtain optimal pricing rules for manufacturers and the retailer. In determining their optimal prices, manufacturers and the retailer account for how all the players in the channel choose their optimal prices. That is, we account for dependencies in decision making across channel members. These dependencies are characterized by a set of "conduct parameters," which are estimated from market data. The conduct parameters enable us to identify the nature of channel interactions between manufacturers and the retailer along the continuum mentioned previously. In addition to the demand and conduct parameters, manufacturers' marginal costs are also estimated in the model. These marginal cost estimates, along with the manufacturer prices and retail prices available in our dataset, enable us to compute the division of channel profits among the channel members. Hence, we are able to obtain insights into who has pricing power in the channel. In the empirical application of the model, we analyze a local market for two product categories: refrigerated juice and tuna. In both categories, there are three major brands. The difference between them is that the private label has an insignificant market share in the tuna category. Our main empirical results show that the usual games examined in the marketing literature do not hold for the given data. We also.nd that the retailer's market power is very significant in both these product categories, and that the estimated demand and cost parameters are consistent with the estimated pattern of conduct between the manufacturers and the retailer. Given the evidence from the trade press of intense manufacturer competition in these categories, as well as the "commodity" nature of these products, the result of retailer power appears intuitive.

Market Information and Firm Performance

Abstract: The value of new information depends on how accurate the information is, but it may also depend on the characteristics of the firm and the nature of the industry it operates in. We develop a game-theoretic model to understand how firm and industry characteristics moderate the effect of market information on firm profits. Our results suggest that information is more valuable when product substitutability is higher, suggesting that information is of greater value in more competitive industries. Our results also suggest that although industry size does not affect the value of information, information is more valuable for larger firms. We find that, except under some conditions, more precise market information has a greater impact on profits in a Stackelberg mode of conduct than in a Bertrand-Nash mode.

Improving a supplier's quantity discount gain from many different buyers

Abstract: We consider the pricing and inventory decisions of a vendor who supplies a single product to multiple heterogeneous buyers. The problem is analyzed as a Stackelberg game in which the vendor acts as the leader by announcing its pricing policy to all the buyers in advance and the buyers act as followers by choosing their order quantity and the sassociated purchasing price independently under the vendors' pricing scheme. We propose in this paper a pricing policy for the vendor that offers price discounts based on the percentage increase from a buyers' order quantity before discount. The proposed policy is defined as a discrete all-unit quantity discount schedule with many break points. We show that: (I) the proposed policy offers a higher price discount to a buyer ordering a larger quantity and hence complies with general fair trade laws; (ii) an explicit solution is obtained for the vendors' optimal decision; and (iii) although suppliers in reality normally offer price discounts based on a buyers' unit increase in order quantity, the proposed policy is superior for the vendor when there are many different buyers. Other benefits of the proposed pricing policy are demonstrated by numerical examples.

Capacity precommitment as a barrier to entry: A Bertrand-Edgeworth approach

Abstract: With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need time to build, that is, cannot adjust capacity instantaneously in the post-entry game. This approach produces a simple and intuitive set of equilibrium behaviors and generates clear predictions about when these different outcomes are likely to arise. Our model also departs substantially from the existing literature in concluding that sunkness of capacity costs is neither necessary nor sufficient for capacity to have precommitment value.

Environmental Taxation and Strategic Commitment in Duopoly Models

Abstract: In this paper, we address the issue of optimalenvironmental taxation under imperfect competition.The problem is analysed for three different types ofduopoly models, the Cournot open and closed loopmodels, and the Stackelberg model. We explicitlyanalyse the role of strategic behaviour. Each firm hasto make a choice of output level and of the level ofa strategic variable. The choice of this strategicvariable affects both marginal cost and emissions. Wecompare the properties of these three duopoly models,and derive and compare optimal environmental taxes. Weshow that whether the optimal tax is lower or higherthan marginal environmental costs depends on theinformation transmission and the effect of thestrategic variable on marginal costs. In addition, thedifferences in market shares, and the influence of thetax on the cost structure play important roles, indetermining optimal emission taxes.

Ordinal games and generalized Nash and Stackelberg solutions

Abstract: The traditional theory of cardinal games deals with problems where the players are able to assess the relative performance of their decisions (or controls) by evaluating a payoff (or utility function) that maps the decision space into the set of real numbers. In that theory, the objective of each player is to determine a decision that minimizes its payoff function taking into account the decisions of all other players. While that theory has been very useful in modeling simple problems in economics and engineering, it has not been able to address adequately problems in fields such as social and political sciences as well as a large segment of complex problems in economics and engineering. The main reason for this is the difficulty inherent in defining an adequate payoff function for each player in these types of problems. In this paper, we develop a theory of games where, instead of a payoff function, the players are able to rank-order their decision choices against choices by the other players. Such a rank-ordering could be the result of personal subjective preferences derived from qualitative analysis, as is the case in many social or political science problems. In many complex engineering problems, a heuristic knowledge-based rank ordering of control choices in a finite control space can be viewed as a first step in the process of modeling large complex enterprises for which a mathematical description is usually extremely difficult, if not impossible, to obtain. In order to distinguish between these two types of games, we will refer to traditional payoff-based games as cardinal games and to these new types of rank ordering-based games as ordinal games. In the theory of ordinal games, rather than minimizing a payoff function, the objective of each player is to select a decision that has a certain rank (or degree of preference) taking into account the choices of all other players. In this paper, we will formulate a theory for ordinal games and develop solution concepts such as Nash and Stackelberg for these types of games. We also show that these solutions are general in nature and can be characterized, in terms of existence and uniqueness, with conditions that are more intuitive and much less restrictive than those of the traditional cardinal games. We will illustrate these concepts with numerous examples of deterministic matrix games. We feel that this new theory of ordinal games will be very useful to social and political scientists, economists, and engineers who deal with large complex systems that involve many human decision makers with often conflicting objectives.

Computational methods through genetic algorithms for obtaining Stackelberg solutions to two-level mixed zero-one programming problems

Abstract: In this paper, we develop computational methods for obtaining Stackelberg solutions to two-level mixed zero-one programming problems in which the decision maker at the upper level controls zero-one variables and the decision maker at the lower level controls real variables. To illustrate two-level mixed zero-one programming problems, we formulate a facility location and transportation problem as a two-level mixed zero-one programming problem. We develop computational methods through genetic algorithms for obtaining Stackelberg solutions. To demonstrate the feasibility and efficiency of the proposed methods, computational experiments are carried out and comparisons between the methods based on the branch-and-bound techniques and the proposed methods are provided.

A Stackelberg price leadership model with application to deregulated electricity markets

Abstract: This paper presents a Stackelberg price leadership model for simulating deregulated electricity markets consisting of one or a few large producers and a larger number of fringe producers. It is assumed that the large producer(s) would adopt oligopoly strategy using their market power while the small producers would use Bertrand-like strategy. The model is a multi-objective profit maximization program. The multi-objectives are converted into the same number of partial Lagrangian functions with power production and supply as the control variables. A set of KKT conditions is then derived considering the game strategies of the producers. Test results show that the model successfully produces a total profit that is greater than that profit from a welfare maximization model but is less than that from a collusion model. Producers who adopt Cournot strategy are better off with higher profits as compared with marginal cost pricing.

"Your Reputation Is Who You're Not, Not Who You'd Like To Be''

Abstract: We construct a model in which a firm's reputation must be built gradually, is managed, and dissipates gradually unless appropriately maintained. Consumers purchase an experience good from a firm whose unobserved effort affects the probability distribution of consumer utilities. Consumers observe private, noisy signals (consumer utilities) of the behavior of the firm, yielding a game of imperfect private monitoring} The standard approach to reputations introduces some "good" or "Stackelberg" firms into the model, with consumers ignorant of the type of the firm they face and with ordinary firms acquiring their reputations by masquerading as Stackelberg firms. In contrast, the key ingredient of our reputation model is the continual possibility that the ordinary or "competent" firm might be replaced by a "bad" or "inept" firm who never chooses the Stackelberg action. Competent firms then acquire their reputations by convincing consumers that they are not inept. Building a reputation is an exercise in separating oneself from inept firms who one is not, rather than pooling with Stackelberg firms who one would like to be. We investigate how a firm manages such a reputation, showing, among other features, that a competent firm may not always choose the most efficient effort level to distinguish itself from an inept one.

Is Channel Coordination All it is Cracked Up to be

Abstract: A fundamental task for supply-chain managers is to determine wholesale-prices. Such determination is a core theme in the marketing science literature on distribution channels?which seems to have concluded that channel coordination?setting wholesale-prices to maximize total channel profit?is "good." This judgement is based on analyses of bilateral monopoly models, within which profit may be redistributed to the benefit of all channel members. However, many manufacturers deal with multiple, competing retailers. The pure logic of bilateral monopoly models holds in the presence of multiple retailers if and only if the manufacturer can price discriminate between retailers. Although mechanisms for price discrimination exist, in many situations they are infeasible, illegal or both. When retailers compete there are two feasible and legally permissible methods of achieving channel coordination: a quantity-discount schedule or a menu of two-part tariffs. (The latter is derived in detail in this paper.) A feasible and legally permissible alternative to channel coordination is for the manufacturer to utilize a sophisticated Stackelberg two-part tariff. While such a tariff cannot coordinate the channel, it is the best of all possible two-part tariffs from the viewpoint of maximizing manufacturer profit. Manufacturers are ultimately interested in their own profitability; it follows that channel coordination is manufacturer-optimal only if it generates at least as great a level of profit for the manufacturer as does non-coordination. In this paper we determine if a channel coordinating wholesale-price strategy manufacturer profit-dominates a sophisticated Stackelberg two-part tariff. We show that the optimal policy is dependent on (a) the retailers' fixed costs, (b) the relative size of the retailers and (c) the degree of inter-retailer competition. We conclude that, from the perspective of a manufacturer, channel coordination is often undesirable relative to utilizing a non-coordinating, sophisticated Stackelberg price-strategy. Therefore, channel coordination can no longer be regarded as the ultimate goal toward which supply-chain managers should uncritically strive.

Cournot Competition in the Electricity Market with Transmission Constraints

Abstract: This paper studies the market power of generators in the electricity market when transmission capacity is scarce. We consider a simple world of two generators providing electricity to their consumers through a single transmission line. In the literature, different Cournot equilibrium concepts have been developed. This paper applies these concepts and explains the implicit assumptions on the behavior of the System Operator made in those papers. We show that these implicit assumptions are not realistic. For an alternative role of the System Operator, we solve the Cournot equilibrium and compare the outcome. Furthermore, we show that the axiomatic equilibrium concept of Smeers and Wei (1997) is linked with the model of Oren (1997) and can also be defined as a Nash Equilibrium.

Differential game-theoretic thoughts on option pricing and transaction costs

Abstract: This paper investigates some differential game applications to option pricing mechanisms and related problems. Two players, an investor and "Nature", play a zero-sum game. The usual uncertainty modelling (log-normality for instance) in systems describing the price evolution of stocks is replaced by "Nature", a player who counteracts the investor as much as possible. A relationship between a restricted version of the Black-Scholes and the Hamilton-Jacobi-Bellman partial differential equations is given. This paper, is a first step to possibly solve various option pricing problems (with constraints and/or transactions costs for instance) by means of the available numerical software for optimal control problems. In the second part of the paper, another model, now with three players, is considered. The third player is the bank interested in maximising its own profits by choosing the right formula for transaction costs. Thus a three-person nonzero-sum game, with a special kind of Stackelberg information structure, results. Some simple examples hint in the direction that the bank will be a clear winner.

Endogenous Co‐Leadership When Demand is Uncertain

Abstract: Consider an oligopolistic industry where production is time-consuming, so that each firm needs to make quantity commitment by producing before the market opens. If demand uncertainty resolves some time before the market arrives, then those firms who produce early behave as simultaneous leaders (co-leaders), whilst those who wait until demand becomes observable will be followers. We discover that, in an n-firm oligopoly, the equilibrium number of co-leaders tends to be in excess of their socially optimal number, albeit both numbers monotonically decrease in the magnitude of demand uncertainty relative to the expected level of demand. We also find that, with demand uncertainty and the possibility of Stackelberg behaviour, whether the excess entry theorem applies depends upon the number of existing followers.

Time-to-Market Capability as a Stackelberg Growth Option

Abstract: This paper examines the decision to invest in logistics, market profiling and distribution capabilities that allows a firm to seize market share by being able to deliver a product ahead of competitors. This has the strategic effect of restraining competitors behavior, and may justify the early commitment of such investment eve when waiting offers some option value due to uncertainty on demand. We show that the value of time-to-market investment is unambiguously increasing in such uncertainty. Finally, we show that when all competitors share this investment opportunity, the resulting lrush to the marketn consumes resources without enhancing profitability.

Interest Group Competition over Policy Outcomes: Dynamics, Strategic Behavior, and Social Costs

Abstract: This paper analyzes a two-period model of interestgroup competition between two groups to affect thepolicy outcome. The paper characterizes the subgameperfect equilibrium and considers the welfareimplications of the model. The subgame perfectequilibrium to this game is allocatively efficient ifand only if the initial equilibrium is allocativelyefficient and interest groups are equally adept atproducing political pressure. When rent seeking isconstitutionally protected, the notion of rent-seekingconstrained efficiency is defined as the cooperativesolution to the rent-seeking game. It is shown that arent-seeking constrained efficient equilibrium isattainable by forcing winners in political competitionto fully compensate losers.

Asynchronous Learning with Limited Information: An Experimental Analysis

Abstract: We present the results of an experiment on learning in a continuous-time low-information setting. For a Cournot oligopoly with differentiated products, a dominance solvable game, we find little evidence of convergence to the Nash equilibrium. In an asynchronous setting, play tends toward the Stackelberg outcome. Convergence is significantly more robust for a "Serial Cost Sharing" game, which satisfies a stronger solution concept of overwhelmed solvability. However, as the number of players grows, this improved convergence tends to diminish. This seems to be driven by high and correlated experimentation or noise and demonstrates that even when play converges, the convergence times may be too long to be of practical significance.

Mixed solutions for weak Stackelberg problems: existence and stability results

Abstract: We are concerned with ∈-mixed solutions for weak Stackelberg problems corresponding to two-player nonzero-sum noncooperative games. Two cases are considered: (i) mixed strategies for only the second player; (ii) mixed strategies for both players. After giving basic results relating convergence of functions and weak convergence of probability measures, we establish existence and stability results for ∈-mixed solutions under general assumptions of minimal character without any convexity assumption. Our results improve previous work of Mallozzi and Morgan (Refs. 1–2).

Infinite hierarchical potential games

Abstract: Hierarchical potential games with infinite strategy sets are considered. For these games, pessimistic Stackelberg equilibria are characterized as minimum points of the potential function; properties are studied and illustrated with examples.

Bargaining equilibrium in a non-stationary environment

Abstract: In this paper we study an alternating-oers bargaining model in which the set of possible utility pairs evolves through time in a non-stationary, but smooth manner. In general there exists a multiplicity of subgame perfect equilibria. However, we show that in the limit as the time interval between two consecutive oers becomes arbitrarily small, there exists a unique subgame perfect equilibrium. Fur- thermore, and more importantly, we derive a powerful characterization of the unique (limiting) subgame perfect equilibrium payos, which should prove especially useful in applications. We then explore the circumstances under which Nash's bargaining solution implements this bargaining equilibrium. Finally, we extend our results to the case when the players have time-varying inside options.

A Two-stage Price-setting Equilibrium Designed in Consideration of Goods Relevance and Strategic Relevance

Abstract: This paper analyses the subgame perfect Nash equilibrium of a two-stage price-setting duopoly. The demand functions are classified into four cases in terms of the goods' relevance and strategic relevance between two firms. All four cases are correlated with two opposite prior commitments that generate kinks in the reaction curve. This paper assumes that only one firm can execute the prior commitments. In the model, we find that the firm can increase its payoff with one of the prior commitments in each of the four cases. We also find that our equilibrium outcomes are different from those of Matsumura (1998) in this Journal, and that they occur at the Stackelberg point in all four cases if, and only if, the firm's reaction curves shift to the Stackelberg point as a result of the prior commitments. As a consequence, the effectiveness of strategic commitments is proved.