Showing papers on "Stackelberg competition published in 1984"

Game theory and transportation systems modelling

Abstract: In this paper, correspondences are drawn between two game theory models (Nash noncooperative and Stackelberg games) and some problems in transportation systems modelling. An example of each is described in detail, namely the problem of carriers competing for intercity passenger travel and the signal optimization problem. The discussion serves to underline differences between two categories of transportation problems and introduces the game theory literature as a potential source of solution algorithms. Also it is shown that inner-outer iterative techniques for Stackelberg type problems cannot be expected to converge to the solution, and an approximate formulation of these problems is introduced which appears to be more readily solvable.

A Multiple Leader Stackelberg Model and Analysis

Abstract: This paper presents a new multiple leader-follower model that is a consistent extension of Stackelberg's leader-follower duopoly. The development contrasts with other existing extensions by demonstrating how the leader-firms can utilize the true reaction curve of the follower-firms; it also provides sufficient conditions for some useful convexity and differentiability properties of this function. For the proposed model, we conduct a static analysis and discuss the existence, uniqueness, and computation of an equilibrium solution, as well as study certain issues regarding the relative profits of leader and follower-firms. Since the Cournot oligopoly and the Stackelberg leader-follower models are special cases of this model, the analysis in this paper hopefully provides some further insights about these types of models.

A solution method for the static constrained Stackelberg problem via penalty method

Abstract: This note presents a new solution method for the static constrained Stackelberg problem. Through our approach, the Stackelberg problem is completely transformed into a one-level unconstrained problem such that the newly introduced overall augmented objective function is minimized with repect to the leader's and the follower's variables jointly. It can be proved that a sequence of solutions to the transformed problems converges to the solution of the original problem, when the penalty parameters are updated.

Stackelberg Differential Games in Economic Models

Abstract: and overview.- Game theory and economics.- Mathematical formulation of differential games.- Solutions of hierarchical differential games.- Regional investment allocation problem.- Stackelberg games in linear programming context.- Application to a world industrialization model.- Econometric models: Adaptive games.

Stackelberg strategies and incentives in multiperson deterministic decision problems

Abstract: Discrete and continuous-time two-person decision problems with a hierarchical decision structure are studied, and the applicability and appropriateness of a function-space approach in the derivation of causal real-time implementable optimal Stackelberg (incentive) strategies under various information patterns are discussed. Results on existence and derivation of incentive strategies for dynamic games formulated in abstract inner-product spaces, in the absence of any causality restriction on the leader's policies, are presented; these results are extended and specialized in two major directions: (1) discrete-time dynamic games, and (2) derivation of causal, physically realizable optimum affine Stackelberg policies for both discrete and continuous-time problems.

Cooperative and Non-Cooperative Differential Game Solutions to an Investment and Pricing Problem

Abstract: A monopoly possesses a finite stock of a resource and wishes to determine an optimal pricing policy. The competitive fringe invests in production capacity and wishes to select an optimal investment rate. Demand towards the monopoly depends on price as well as on the sales rate of the competition. Modelling the situation as a differential game, non-cooperative (Nash and Stackelberg) and cooperative (Pareto) equilibria are determined. Owing to the special structure of the game, these solutions can be found in closed form.

Derivation of necessary and sufficient conditions for single-stage Stackelberg games via the inducible region concept

Abstract: The inducible region is defined as the collection of all the possible outcomes. It is typically a subset of the entire decision space. The best the leader can obtain is then the optimal outcome in this inducible region. Necessary and sufficient conditions are derived by first delineating the inducible region, and then obtaining a leader's optimal strategy, if it exists. If not, an e-strategy always exists, provided that the leader's Stackelberg cost is bounded.

Three-level Stackelberg decision problems

Abstract: Three-level Stackelberg decision problems are studied by using the inducible region concept. Through a systematic derivation, it is identified that the leader's control has dual purposes, which in general are not separable. A special class of problems is then considered, where explicit results are obtained.

Linear-quadratic reversed Stackelberg differential games with incentives

Abstract: In this technical note the linear-quadratic Stackelberg differential game with reversed information structure is considered. The leader is confined to stroboscopic (or snap-decision) strategies and necessary and sufficient conditions are then given for the leader to be able to impose, with the help of side payments, the (optimal) team solution.

Patterns of Power: Bargaining and Incentives in Two-Person Games

Abstract: We introduce the concept of a strategic dictator and use it to analyze patterns of power in two-pperson games that arise naturally in bargaining, arbitration, and incentive problems, a strategic dictator is an agent who has the power to ensure that at Nash equilibrium outcome is his or her preferred outcome. but who may have to lie in order to do this. We discuss applications of our analysis to Stackelberg and Cournot Duopolists. to bargaining situations, and to the existence of appropriate incentive systems.

The Incidence of Entry in 3 Oligopoly Models

Abstract: Three of the least satisfactory features of oligopoly theory are that the beliefs of firms are frequently arbitrary, that the solution concept (which reflects these beliefs) used is taken as exogenous, and that its role in conditioning the results is neglected. The first criticism has been resolved to a large extent in the recent "Consistent Conjectures" literature (Bresnahan, 1981; Perry, 1981; Ulph, 1983; for critical views, see Laitner, 1980, or Boyer and Moreaux, 1983), which characterizes equilibria having the property that firms hold locally correct conjectures about rivals' reactions. Yet, however satisfactory they are on the question of arbitrariness, Consistent Conjectures unfortunately run afoul of the exogeneity criticism, for it is by no means clear how firms come to possess the information needed to form such beliefs. Quite clearly, the complete answer to the exogeneity question lies in models of information acquisition and evaluation by firms; nevertheless, it would be unwise to abandon static models wholesale, for they can be useful if supplemented by a set of comparative static exercises revealing how variations in the solution concept itself conditions the results. This paper advances the case for such a "comparative statics with respect to solution concept" primarily by discussing a somewhat unusual illustration. Much recent work has been devoted to entry and its effects on market performance, but relatively little is known about how putative entrants are attracted to the market, how much entry occurs in particular types of markets, how fast it occurs, how incumbents anticipate putative entrants, and their speed of reaction. Thus, while we have some feel for how variations in solution concept affect the market share or profits of a given set of firms in post-entry equilibria (e.g. Shubik, 1980; Ulph and Folie, 1980; Dixit, 1980; Spulber, 1981), we have very little in the way of answers to questions like: "Is there more entry when firms 'play' Cournot than when one firm acts as a Stackelberg leader vis-a-vis the rest?" or "Does successful entry and even displacement of relatively "inefficient" incumbents occur more or less rapidly when firms behave as Cournot than when industry conduct is described by some other solution concept?" Such questions are natural, for example, if one is interested in the persistence of market power and its speed (if any) of decline. Section II contains some slightly startling results which emerge from considering what is very much a special case of an entry process. While the main interest in the results arises because they underline, in a particularly emphatic manner, the sort of interesting phenomena that can be revealed by such comparative static exercises, I shall, in Section III, pursue these results as having interest in their own right and speculate on their robustness to various extensions of the model. Section I commences the whole discussion with some methodological remarks.

Policy solutions for a linked model for two common market countries

Abstract: Mini-Interplay consists of two linked macroeconometric policy models for the Federal Republic of Germany and the Netherlands. The policy evaluation problem is formulated as a linear quadratic difference game. Algorithms are given for stagewise solutions with a pure feedback information structure for three solution concepts: the “noncooperative” Nash, the “hierarchical” Stackelberg and the “cooperative” Pareto concept. The set of Pareto solutions is parametrized by the weighing factor of the two cost functionals. The preferences are chosen such that acceptable Nash and Stackelberg solutions result. It is tried to meet the target paths of the objective variables or to do better under the restriction that the use of instrumental variables stays within acceptable bounds. The mostly unrealistic symmetry of the quadratic cost-functionals is taken into account. Those end-costs of the Pareto solutions which are individually rational with respect to the end-costs of the Nash solution form possible outcomes of a bargaining game. Following the axiomatic approach Nash and Kalai-Smorodinsky arbitration schemes are applied to arrive at acceptable Pareto solutions. Unfortunately, the corresponding weighing factors are not invariant under equivalent cost-functional representations.

Stackelberg strategies in discrete linear quadratic problems

Abstract: Linear closed-loop Stackelberg strategies in sequential decision-making problems for linear time-invariant discrete systems and trace criteria which may be interpreted as the expected value of quadratic criteria are considered. Necessary conditions for the solution are developed and an algorithm of the multi-level Stackelberg problem is presented. An example for a two-level problem is presented to illustrate the proposed numerical algorithm

Fees Versus Royalties and the Private Value of a Patent

Abstract: We compare how much profit an owner of a patented cost-reducing invention can realize by licensing it to an oligopolistic industry producing a homogeneous product, by means of a fixed fee or a per unit royalty. Our analysis is conducted in terms of a noncooperative game involving n + 1 players: the inventor and the n firms. In this game the inventor acts as a Stackelberg leader, and it has a unique subgame perfect equilibrium in pure strategies. It is shown that licensing by means of a fixed fee is superior to licensing by means of a royalty for both the inventor and consumers. Only a "drastic" innovation is licensed to a single producer.(This abstract was borrowed from another version of this item.)

Decentralized linear-quadratic differential games with incentives12

Abstract: In this paper we consider linear-quadratic differential games and the problem of decentralized hierarchical control is studied within the framework of Stackelberg games with reversed information structure. The leader is then confined to stroboscope (or snap-decision) strategies and necessary and sufficient conditions are given for the leader to be able to impose, with the help of side-payments, the (optimal) team solution. The theory is illustrated by a ‘debt-servicing’ example and by an example of economic stabilization.