Showing papers on "Stackelberg competition published in 1985"
01 Dec 1985
TL;DR: The concept of sequential Stackelberg equilibrium is introduced in the general framework of dynamic, two-person games defined in the Denardo contracting operator formalism and can be related to previous results obtained by Başar and Haurie (1984).
125 citations
TL;DR: In this paper, the authors describe two simple results in the theory of Cournot equilibria, namely, the effect of taxation in a Cournot industry and the conditions under which conditions an equilibrium will implicity maximize an objective function.
125 citations
01 Jan 1985
75 citations
TL;DR: In this article, a simple two-stage model of research and development is described, in which the winner of the research stage has the option of moving first in the development stage.
73 citations
TL;DR: In this article, a rational expectations model of a securities market is developed in which one agent, the monopolist, behaves like a Stackelberg leader and other agents behave competitively.
Abstract: A rational expectations model of a securities market is developed in which one agent, the monopolist, behaves like a Stackelberg leader and other agents behave competitively. Two information structures, one in which each agent has identical information and the other in which each agent has independent information are examined. Equilibrium is shown to exist and is characterized in both cases, but monopoly has a significant effect on the equilibrium only in the latter. The optimal strategy of the Stackelberg leader is also studied, and it is shown that he will not randomize his strategy by adding white noise to his demand function, even though this obfuscates the information content of the market price.
51 citations
TL;DR: In this paper, a two-period game where firms can produce inventory in the first period for sale in the second period is analyzed and the existence of the subgame perfect equilibrium is shown.
Abstract: This article analyzes a two-period game where firms can produce inventory in the first period for sale in the second period. We assume that revenues and costs are time invariant and that the firms are symmetric. We focus on the nature and the existence of the subgame perfect equilibrium of this model. We use examples to show that the Nash value functions defined on the joint inventory vector are likely to be ill-behaved. In particular, they need not be concave nor even continuous in the firm's own inventory. As a result, asymmetric equilibrium is possible. When average production costs are falling, single-firm operation can occur in equilibrium. Nonexistence is also a distinct possibility.
34 citations
TL;DR: In this paper, a method to solve the two point boundary value problem (TPBVP) occurring in open-loop Stackelberg strategy for linear-quadratic games is presented.
Abstract: A method to solve the two point boundary value problem (TPBVP) occurring in open-loop Stackelberg strategy for linear-quadratic games is presented. By writing in a special order the necessary conditions that an open-loop Stackelberg solution must satisfy, a Hamiltonian matrix comes out and its properties are exploited to solve the TPBVP. The solution procedure becomes similar to the one used to solve a matrix Riccati equation by the eigenvector method. A simple example is given to illustrate the proposed method.
33 citations
Posted Content•
TL;DR: In this article, a model for dummy endogenous variables is derived from a game theoretic framework where the equilibrium concept used is that of Stackelberg, and the model is applied to a study of husband/wife labor force participation.
Abstract: Following Bjorn and Vuong (1984), a model for dummy endogenous variables is derived from a game theoretic framework where the equilibrium concept used is that of Stackelberg A distinctive feature of our model is that it contains as a special case the usual recursive model for discrete endogenous variables [see eg, Maddala and Lee (1976)] A structural interpretation of this latter model can then be given in terms of a Stackelberg game in which the leader is indifferent to the follower's action Finally, the model is applied to a study of husband/wife labor force participation
21 citations
TL;DR: This paper considers Markovian Stackelberg problems with one leader and N followers and proposes an algorithm to compute optimal affine incentive strategy for the leader and Nash reactions of the followers under the average-cost-per-stage criteria.
13 citations
TL;DR: It is shown that the incentive schemes using information on the follower's strategies depend on an initial state value, which is a sufficient condition for the incentive scheme using theollower's strategy in the linear quadratic differential game with infinite time interval.
Abstract: We deal with Stackelberg games in which a leader has access not only to the state information but also to information on the follower's strategy. We derive sufficient conditions for incentive schemes using information on the follower's strategies in both linear and non-linear differential games, and show that the incentive schemes using information on the follower's strategies depend on an initial state value. We also derive a sufficient condition for the incentive scheme using the follower's strategy in the linear quadratic differential game with infinite time interval.
12 citations
TL;DR: In the infinite dimensional case of reflexive Banach spaces, the authors consider an approximation of a constrained Stackelberg problem (two-level optimization problem) by a sequence of twolevel optimization problems and illustrate this approach with a discretization method applied to a class of well-posed control problems
01 Dec 1985
TL;DR: In this article, optimal incentive schemes for continuous time Stackelberg games with linear state dynamics and quadratic cost functionals are constructed, where the leader is assumed to have perfect or partial information on the past values of the state and on those of the follower's decision.
Abstract: Optimal incentive schemes for continuous time Stackelberg games with linear state dynamics and quadratic cost functionals are constructed. The leader is assumed to have perfect or partial information on the past values of the state and on those of the follower's decision. The permissible strategies for the leader are affine in the data available and they are represented by Lebesgue-Stieltjes integrals.
TL;DR: In this article, the authors extend Gerber's seminal paper on chains of reinsurance in three directions: (i) to throw some light on the rationale of finite chains under the Stackelberg equilibria introduced by Gerber, (ii) to propose new non-cooperative equilibrium concepts, of the Cournot type, which allow the first reinsured to transfer more than 50 percent of its risk if the risk aversion is the same for all companies, and (iii) to compare the Pareto optimal and the different equilibrium transfers of risk between reinsurers.
Abstract: The purpose of this paper is to extend Gerber's seminal paper on chains of reinsurance in three directions: (i) to throw some light on the rationale of finite chains under the Stackelberg equilibria introduced by Gerber, (ii) to propose new non-cooperative equilibrium concepts, of the Cournot type, which allow the first reinsured to transfer more than 50 percent of its risk if the risk aversion is the same for all companies, and (iii) to compare the Pareto optimal and the different equilibrium transfers of risk between reinsurers.
TL;DR: In this article, the Stackelberg equilibria of the game under alternative behavioral assumptions about the sequencing of moves are analyzed and the relative gains of the seller and the two buyers are computed for specific numerical examples.
Abstract: This note reexamines a problem of competitive bidding under asymmetrical information about the value of the object which was originally formulated and studied by R. Wilson Wilson, R. B. 1967. Competitive bidding with asymmetric information. Management Sci.13 816-820.. We analyze the Stackelberg equilibria of the game under alternative behavioral assumptions about the sequencing of moves. The relative gains of the seller and the two buyers are computed for specific numerical examples.
19 Jun 1985
TL;DR: In this article, the construction of optimal affine incentive strategies for continuous-time linear-quadratic Stackelberg games is considered, and an optimal incentive strategy for continuous time linear quadratic games is proposed.
Abstract: Construction of optimal affine incentive strategies for continuous-time linear-quadratic Stackelberg games is considered.
TL;DR: A model which determines bus service levels considering users' travel behavior in multi-modal road network is developed and it is proved the convexity of sub-optimization problems and replace them with their Kuhn-Tucker's conditions.
Abstract: In this study, we develop a model which determines bus service levels considering users' travel behavior in multi-modal road network.The model is formulated as the 2-level Stackelberg planning problem. The optimal solutions of the sub-optimization problems represent the network equilibrium conditions by mode (cars, buses) under a given bus service level. The main-optimization problem represents the maximization of the users' benefit in the system under the traffic equilibrium conditions.In order to solve this model, we prove the convexity of sub-optimization problems and replace them with their Kuhn-Tucker's conditions. We also develop both a method by which we solve the 2-level Stackelberg planning problem and an algorithm. In a model network, the applicability of this model is verified.
01 Jan 1985
TL;DR: In this paper, the authors provide a small sample of papers that highlight the various aspects of the duopoly problem, including the nature of the strategies employed, the effects of dynamic considerations, the concept of reaction of one firm to the actions of the other, the importance of information, the influence of entry considerations and others.
Abstract: Ever since Cournot’s (1838) celebrated treatment of the duopoly problem, the model of two firms in an industry has provided an important and fertile ground for the examination of the foundations of market behaviour. The duopoly level is the simplest situation that brings up the fundamental issues involved in formulating the market behaviour of firms and these include the nature of the strategies employed, the effects of dynamic considerations, the concept of ‘reaction’ of one firm to the actions of the other, the importance of information, the influence of entry considerations and others. Such celebrated contributions as Bertrand (1882), Edgeworth (1925), Hotelling (1929), Chamberlin (1933), Stackelberg (1934), Feltner (1949), Mayberry, Shubik and Nash (1953) and Shubik (1955, 1959, 1968, 1974) provide only a small sample of papers that highlight the various aspects of the duopoly problem.