Showing papers on "Stackelberg competition published in 1998"

Stackelberg-Nash equilibrium for multilevel programming with multiple followers using genetic algorithms

Abstract: Multilevel programming offers a means of studying decentralized noncooperative decision systems. Unfortunately, multilevel programming is lacking efficient algorithms due to its computational difficulties such as nonconvexity and NP-hardness. This paper will design a genetic algorithm for solving Stackelberg-Nash equilibrium of nonlinear multilevel programming with multiple followers in which there might be information exchange among the followers. As a byproduct, we obtain a means for solving classical minimax problems. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed genetic algorithm.

Pricing Strategy and Financial Policy

Abstract: Recent empirical evidence indicates that capital structure changes affect pricing strategies. In most cases, prices increase following the implementation of a leveraged buyout of a major firm in an industry, with the more leveraged firm in the industry charging higher prices on average. Notable exceptions exist, however, when the leverage increasing firm's rival is relatively unlevered. The first observation is consistent with a model where firms compete for market share on the basis of price. The second observation can be explained within the context of a Stackelberg model where the relatively unlevered rival acts as the Stackelberg price leader.

The chaotic duopolists revisited

Abstract: The adjustment process of three oligopolists is studied, under Cournot and Stackelberg action. It is demonstrated that with an iso-elastic demand function and constant marginal costs, the system can result in periodic or in chaotic behaviour. In particular, the case with two identical and one different oligopolists is focused, which turns into a virtual duopoly, though displaying a wider set of bifurcations than can occur in genuine duopoly.

Game-Theoretic Formulations of Interaction Between Dynamic Traffic Control and Dynamic Traffic Assignment

Abstract: The dynamic traffic control problem and the dynamic traffic assignment problem are integrated as a noncooperative game between a traffic authority and highway users. The objective of the combined control-assignment problem is to find a mutually consistent dynamic system-optimal signal setting and dynamic user-optimal traffic flow. The combined control-assignment problem is first formulated as a one-level Cournot game: the traffic authority and the users choose their strategies simultaneously. The combined control-assignment problem is subsequently formulated as a bi-level Stackelberg game. The traffic authority is the leader; it determines the signal settings in anticipation of the users' reactions. The users are followers who choose their routes after the signal settings have been determined. Finally, the system-optimal control-assignment problem is formulated as a Monopoly game. The sole player—the traffic authority—determines both signal settings and traffic flows to achieve a dynamic system-optimal so...

Empirical Analysis of Competitive Product Line Pricing Decisions: Lead, Follow, or Move Together?

Abstract: Researchers have recently developed models for determining which market conduct best describes observed data. We apply these techniques from the "new empirical industrial organization" literature to the competitive product line pricing decision, where a firm strategically prices its brands when determining the profit-maximizing conduct in the market. Demand, cost, and market structure are estimated endogenously. Empirical results from analyzing price competition in the laundry detergent market between Procter and Gamble selling Tide and EraPlus, and Lever Brothers offering Wisk and Surf, indicate that each firm positions its strong brand as a Stackelberg leader, with the rival's minor brand being the follower.

Dynamics of a Cournot Game with n-Competitors

Abstract: The dynamical system of n competitors in a Cournot game is derived. The stability of its fixed point (Nash equilibrium) is studied. The effect of a modification of the price–demand relation is pointed out.

The Many Faces of Competition

Abstract: Despite a great deal of theoretical research on competition, there has been limited empirical work assessing the type of competitive interaction that actually exists in the marketplace. The empirical work that has been conducted has suggested that there is significant variation in the type of competitive interaction across categories and across marketing instruments. Consequently, the central objective of this paper is descriptive in nature—what does competition look like? Focusing on the competition that exists across strategic groups (Porter 1985), we categorize competitive interaction between private labels and national brands for each of 58 categories and four marketing instruments. Specifically, we look at five types of competitive interaction. Three, cooperative, non-cooperative, and independent (Nash) are symmetric in nature, while two, leader-follower (Stackelberg) and dominant/fringe-firm, are asymmetric. The empirical results suggest that general comments or assumptions about competitive interaction can produce very misleading conclusions. There is no consistent pattern of competition that exists between private labels and national brands across categories. Further, the pattern of interaction is quite complex, while there is likely to be a significant variation across instruments within a category. National brand leadership is the most common form of interaction for each marketing mix variable. However, it characterizes only 19 out of 58 categories for regular price, and 16, 19, and 15 out of 58 categories for temporary price reduction, feature and display, respectively. Further, the interaction is idiosyncratic to the category, depending heavily upon the demand and competitive characteristics of the category. Implications for both game theorists and for managers are explored.

Perfect versus imperfect observability---An experimental test of Bagwell's result

Abstract: In a seminal paper Bagwell (1995) claims that the first mover advantage, i.e. the strategic benefit of committing oneself to an action before others can do, vanishes completely if this action is only imperfectly observed by second movers. In our paper we report on an experimental test of this prediction. We implement three versions of a game similar to an example^? given by Bagwell, each time varying the quality of the signal which informs the second mover. For experienced players we do not find empirical support for Bagwell's result. Instead, we find some support for the noisy Stackelberg equilibrium emphasised by van Damme and Hurkens (1997).

A Stackelberg model of Social Security acceptance decisions in dual career households

Abstract: The joint Social Security acceptance decisions of husbands and wives are modeled as a Stackelberg game with male leadership. The analysis focuses on whether an individual accepts reduced Social Security retirement benefits prior to age 65 or full benefits at age 65 or older. Full information maximum likelihood estimates are presented for a sample of dual career households from the Retirement History Survey. The results indicate that Social Security acceptance decisions in dual career households depend on several individual and household characteristics as well as financial incentives.

Testing the theory: vertical strategic interaction and demand functional form

Abstract: Formulating theoretical models inevitably requires various simplifications that assist in making analysis tractable and that facilitate deriving closed form solutions. While the strategic insights gained from theoretical models of market phenomena are often quite valuable, testing the theoretical assumptions made in these models can aid in assessing the broader applicability of the conclusions drawn. This is particularly true in the channels area, where the focus of research to date has largely been theoretical in nature. In an initial attempt to examine some of the assumptions made in previous theoretical research (e.g., Jeuland and Shugan 1983, McGuire and Staelin 1983, Choi 1991, Raju, Sethuraman and Dhar 1995), we focus on a limited set of issues. First, we empirically examine the vertical channel assumptions made in two well-cited models of retailer-manufacturer interaction: a) the Choi (1991) Manufacturer-Stackelberg (MS) model, and b) the Raju, Sethuraman and Dhar (1995) Stackelberg model addressing store brands. Specifically, empirical tests are developed for Manufacturer Stackelberg conduct and the use of proportional mark-up rules within the channel. Second, since each of these models assume relatively simple linear demand structures, we examine how well linear demands characterize actual market behavior by comparing them to a flexible non-linear form, the LA/AIDS model. The empirical analysis is conducted using data for six individual categories (milk, butter, bread, pasta, margarine and instant coffee) across 59 local markets in 1991 and 1992. The empirical results generally support the assumptions of proportional mark-up behavior by retailers and Manufacturer Stackelberg conduct (Choi 1991) within the channel. While this lends support to the assumptions made in a number of theoretical models addressing channel behavior, we reject linear demands in a favor of a more flexible non-linear form. When combined with the analytical work of Lee and Staelin (1997), this suggests that additional theoretical and empirical work is needed in order to fully understand the implications of using a linear demand specification.

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.

A Two‐stage Price‐setting Duopoly: Bertrand or Stackelberg

Abstract: This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria

The Core of Games with Stackelberg Leaders

Abstract: This paper considers cooperative game theoretic settings in which forming coalitions can act as Stackelberg leaders. We de�fine a value function which modi�fies the gamma-value function (Hart & Kurz, 1983, Chander & Tulkens, 1997) by letting members of deviating coalitions move �first in choosing a coordinated strategy. We accordingly defi�ne what we call the phi-core, and characterize the phi-core allocations of a cartel formation game and of a public goods economy.

Vertical price leadership within a channel: a cointegration study.

Abstract: This paper is concerned with the question whether or not retailers allow suppliers to set their prices not only on the basis of the costs faced by the suppliers but also on the basis of consumer demand, i.e., whether or not suppliers are able to use foresight (i.e., behave as vertical price leaders in the sense of Stackelberg leadership) by having the economic power and managerial ability to take into account the reactions of the downstream retailers to changes in suppliers' wholesale prices. Using standard theory, long-run price relationships between the stages in the channel are derived. Next, these static price relationships are imposed on a dynamic model to be tested for cointegration and error-correction structure. An empirical application to two Dutch marketing channels for food products gives conceivable results.

Linear Bilevel Programming: Continuous Variables

Abstract: The vast majority of research on bilevel programming has centered on the linear version of the problem, alternatively known as the linear Stackelberg game. In this chapter we present several of the most successful algorithms that have been developed for this case, and when possible, compare their performance. We begin with some basic notation and a discussion of the theoretical character of the problem.

Endogenous timing of investments yields modified Stackelberg outcomes

Abstract: This paper deals with capacity constrained price competition in a duopoly model. The model resembles that in Kreps and Scheinkman (1983), but the timing of the investment/capacity choice is endogenous. In equilibrium, one of the firms will invest to become the Stackelberg leader, although the ratio between the leader's and the follower's capacities is smaller than in the standard Stackelberg outcome. Capacity is built too early, resulting in welfare losses. The leader and the follower will earn equal profits, except when capacity costs are small.

Cournot vs stackelberg: the case of labor-managed duopoly

Abstract: First, the equilibrium properties are compared for general Cournot and Stackelberg two-person games with symmetric payoff functions . Second, labor-managed Cournot and Stackelberg duopoly equilibria are compared. Under our assumptions, the Cournot firm's output is larger than the Stackelberg follower's output, which in turn is larger than the leader's output. Dividend per unit of labor is larger for the Stackelberg follower than for the Stackelberg leader, which in turn gets larger dividend per unit of labor than the Cournot firm .

The Non-Robustness of the Nash-Stackelberg-Hybrid Equilibrium

Abstract: In a simple, standard sequential search model, the Nash-Stackelberg-Hybrid equilibrium is shown, in general, to be non-robust when the assumption that all firms are constrained to operate one outlet is dropped. Unless the firms are constrained from increasing the number of outlets or the price, they will open additional outlets to increase their market power. In a standard duopoly model an equilibrium featuring both firms operating multiple outlets is shown to exist.

Intervening duality based analyses of nonconstant sum bimatrix games

Abstract: The intervening duality idea was introduced in Ryan (1995) with a context of linear programming characterizations of two person constant sum coin tossing games in which two individuals are modelled as playing as if simultaneously against nature and against each other by making themselves dual to the duals of an intervening coin. The purpose of this paper is to extend intervening duality characterizatione, and by that means to model explicitly subjectively interactive processes of specification and solution to non constant sum bimatrix games the Prisoner’s Dilemma and collusion, Stackelberg and Cournot solutions, to the duopoly problem.

The closed-loop implementation of the open-loop stackelberg solution in the linear quadratic problems

Abstract: The present paper deals with the Stackelberg solution of the basic LQ bicriteria dynamic optimization problem. It is shown that the two-point boundary value problem involved in the LQ Stackelberg optimization problem has a Hamiltonian structure. Considering this remarkable structural property, an efficient numerical method for solve it, is presented. The closed-loop implementation of the open-loop Stackelberg strategies is obtained by solving a standard differential Riccati equation associated to an extended ordinary LQ optimization problem (by increasing the system state with an additional multiplier). The proper closed-loop implementation depending only on the system state is possible if a certain differential matrix equation has a continuous solution.