Showing papers on "Stackelberg competition published in 1982"

Existence and derivation of optimal affine incentive schemes for Stackelberg games with partial information: a geometric approach†

Abstract: Through a geometric approach, it is shown that a sufficiently large class of incentive (Stackelberg) problems with perfect or partial dynamic information admits optimal incentive schemes that are affine in the available information. As a byproduct of the analysis, explicit expressions for these affine incentive schemes are obtained, and the general results are applied to two different classes of Stackelberg game problems with partial dynamic information.

The Sustainability Concept under Alternative Behavioral Assumptions

Abstract: The main results of the sustainability literature on natural monopolies (for example, Panzar and Willig (1977)), are shown to depend on the Bertrand conjecture First, for the natural monopoly case we prove that industry configurations that are sustainable in the sense of Willig (1980) are equivalent to special kinds of Bertrand equilibria Second, we show that sustainability under the Bertrand assumption does not necessarily imply sustainability under the Cournot assumption and vice versa The general efficiency results that have been obtained for sustainable configurations no longer hold under the Cournot assumption On the other hand, von Stackelberg behavior guarantees sustainability and an efficient industry structure, though not necessarily efficient pricing Third, under the Bertrand assumption, entry can be deterred if sunk costs comprise a sufficiently large fraction of total costs, but this result fails to hold under the Cournot assumption

Algorithms for static stackelberg games with linear costs and polyhedra constraints

Abstract: Three algorithms for solving the static Stackelberg game with two decision makers, linear costs and polyhedra constraints are presented. The nonconvexity of the Reaction set of the Follower is a major source of difficulty in solving such problems. The algorithms presented are able to bypass this difficulty and find the solution in a finite number of iterations.

Product diversification, entry prevention and limit pricing

Abstract: This article considers a multiproduct market in which an established firm faces an unlimited number of potential competitors, and all firms have identical cost functions exhibiting scale economies. It is shown that, if von Stackelberg leadership is feasible, the established firm's profit-maximizing strategy will always involve entry deterrence. The characteristics of alternative entry deterring policies are outlined. For a two-good model, it is argued that product diversification is a feature of optimal strategies when substitutability in demand between the goods is relatively low. This will (will not) be coupled with limit pricing when fixed costs are low (high).

A minimum sensitivity approach to incentive design problems

Abstract: In this paper we introduce the notion of "robust" incentive schemes in multi-agent decision problems with a hierarchical decision structure, and discuss derivation of such policies by minimizing, in addition to the usual (standard) Stackelberg performance indices, an appropriate sensitivity function. Such an approach has applications in decision problems wherein the leader does not know the exact values of some parameters characterizing the follower's cost functional, and seeks to robustify his optimum policy in the presence of deriations from the nominal values. An in-depth analysis of such incentive design problems is provided, and some concrete analytical results are obtained for general cost functionals with a convex structure. The results are then applied to an incentive design problem arising in economics, leading to some meaningful robust incentive policies.

The Concept of Inducible Region in Stackelberg Games

Abstract: Conceptually, the idea of inducible region holds for general problems. Since necessary and sufficient conditions can be derived for certain class of problems by using this idea, it is hoped that the clarification of the concept could lead to the development of a general theory for Stackelberg games.

Credibility and rationality of players strategies in multilevel games

Abstract: The credibility of threats and the rationality underlying their execution is studied in the context of a Stackelberg game with the reversed information structure, repeated an infinite number of times.

Coalition formation in n-person stackelberg games

Abstract: Stackelberg games and their resulting nonconvex programming problems have been used to model multilevel economic systems. These formulations have suggested that independent players, acting sequentially, may not produce Pareto-optimal decisions. Such systems naturally encourage the introduction of an n-player abstract game which permits coalitions of players to form. This paper examines the mathematical characteristics of these imbedded games and the implications of their solution for the overall problem.

Feedback stackelberg solution in continuous-time multi-level games

Abstract: This paper introduces a "Feedback Stackelberg" solution concept for continuous-time multi-level dynamic optimization problem, and discusses its appropriateness for decision making and optimization in the presence of hierarchy.

Optimization in Multilevel Systems

Abstract: The multilevel programming problem is a collection of nested optimization problems where the constraint region of the first is implicitly determined by the solution to the second and so on. Alternatively, the problem may be viewed as an n-person, nonzero sum game with perfect information in which the players move sequentially. When only two players are involved a generalized, static Stackelberg game results. This paper first presents the geometric properties of the linear bilevel program and then offers an extension for the multilevel case. For either, the solution is shown to occur at a vertex of the original polyhedral constraint set. A set of first order necessary conditions is then developed for the general problem and an algorithm proposed for the linear version.

On Dynamic, Deterministic, Stackelberg Games

Abstract: By using a simple example, this paper illustrates a new process for solving general multi-stage Stackelberg games. This gives a distinct picture of the problem, and many peculiar phenomena reveal themselves. In particular, new perspectives of the principle of optimality are discussed.

Incentive stackelberg strategies for deterministic multi-stage decision processes

Abstract: In this paper, we formulate a general incentive Stackelberg dynamic game problem with informational advantage to the leader at each stage of the decision process, which involves partial observation of the follower's decisions. Under a feedback Stackelberg solution concept adapted to this information pattern, some general results on the existence and construction of optimal incentive strategies are obtained, and the derivation of optimal affine policies is discussed. The paper also deals with the global Stackelberg solution in discrete and continuous-time games, and obtains conditions for the existence of causal, physically realizable solutions, in terms of the gradients of the cost functionals evaluated at the optimum operating point.

Optimal strategies for space-dependent discrete-time dynamic games†

Abstract: Optimal strategies are provided for discrete-time dynamic games having space-dependent states and parameters. The Nash strategy is first considered with open-loop, closed-loop, open/closed-loop and periodic state information schemes. Then, using the Nash solution, the strategies for the non-inferior and minimax criteria are discussed. Finally, the Stackelberg criterion is employed and two algorithms are given, namely for the Stackelberg feedback and Stackelberg closed-loop schemes. An illustrative example is included.

A complete solution for two-person, single-stage, deterministic, stackelberg game

Abstract: A method is presented to solve two-person, single-stage, deterministic, Stackelberg games. The approach lies on the delineation of the inducible region. If the leader is extremely powerful, he can induce the follower to do whatever he desires. However, the leader in general can only induce the follower's behavior to "certain extent" due to limited information, control, etc. In other words, there exists a region inside which the leader can induce the follower's behavior. Thus, the best the leader can do is to minimize his cost inside this region. In this paper, we delineate precisely the inducible region, and obtain a leader's optimal strategy, if it exists. In case that a Stackelberg strategy does not exist, we show that an ?-Stackelberg strategy always exists.

Deterministic multi-stage decision pr~cesses~

Abstract: In this paper, we formulate a general incentive Stackelberg dynamic game problem with informational advantage to the leader at each stage of the decision process, which involves partial observation of the follower's decisions. Under a feedback Stackelberg solution concept adapted to this information pattern, some general results on the existence and construction of optimal incentive strategies are obtained, and the derivation of optimal affine policies is discussed. The paper also deals with the global Stackelberg solution in discrete and continuous-time games, and obtains conditions for the existence of causal, physically realizable solutions, in terms of the gradients of the cost functionals evaluated at the optimm operating point.