Showing papers on "Stackelberg competition published in 1983"

Stackelberg-Nash-Cournot Equilibria: Characterizations and Computations

Abstract: The supply side of an oligopolistic market supplying a homogeneous product noncooperatively is modeled. In this market, there is one leader and N followers. The followers operate under the Cournot assumption of zero conjectural variation and are accordingly called Cournot firms. The leader, called a Stackelberg firm, specifically takes into account the reaction of the Cournot firms to its output. For this situation, we study the behavior and implications of the joint Cournot reaction curve as generated by plausible economic market assumptions. In particular, we study the existence and uniqueness of a Stackelberg-Nash-Cournot equilibrium. In addition, we prescribe an efficient algorithm to determine a set of equilibrating output quantities for the firms.

International R&D Rivalry and Industrial Strategy

Abstract: This paper presents a theory of government intervention which provides an explanation for "industrial strategy" policies such as R&D or export subsidies in imperfectly competitive international markets. Each producing country has an incentive to try to capture a greater share of rent-earning industries using subsidies, but the subsidy-ridden international equilibrium is jointly suboptimal. The equilibrium in the strategic game involving firms and governments is modelled as a three stage subgame perfect Nash equilibrium. The assumption that the government is the first player in this game allows it to influence equilibrium industry outcomes by altering the set of credible actions open to firms.

A Stackelberg solution of dynamic games

Abstract: The paper proposes a formulation of e-Stackelberg and Stackelberg strategies for a large class of dynamic closed-loop games, discusses the interpretation of the leader's strategy as the formalization of the intuitive notion of incentives or threats, and considers limitations of the Stackelberg solution concept which, within the dynamic context, are applicable only in situations where the realization of a leader's strategy is ensured by a binding contract. The solution method is based on the idea of discontinuous strategies assuming that the leader punishes the follower by minimizing his payoff if the latter does not comply with the policy selected for him by the leader.

The transition to nondepletable energy

Abstract: As depletable energy becomes increasingly scarce and expensive, energy markets will turn to a multitude of nondepletable sources of energy. The rate at which this transition occurs will depend on the quantities of fuels available, production costs, government policies, and the choices of major producers. In this paper, we analyze the transition to nondepletable fuels, first in the context of a social planning model, then using a Stackelberg model to represent the dynamic game between owners of depletable and nondepletable fuels. We show that the pace of capacity expansion in the nondepletable sector has a strong influence on socially optimal energy prices and production rates. With the Stackelberg model, we characterize the strategy a market-dominating producer of depletable energy will use against the nondepletable sector. Numerical implementations of this model allow us to compare the socially optimal and market-determined outcomes. Our results show how a dominant depletable-energy producer can manipulate the nondepletable sector by pricing at the marginal cost of backstop output during an early phase of resource depletion.

Stochastic Stackelberg games: Nonnested multistage multiagent incentive problems

Abstract: Recent progress in Stackelberg dynamic games concentrates on either the deterministic situations or partially nested stochastic problems. In this paper, a class of "nonnested' stochastic Stackelberg dynamic games, namely LOG additive incentive problems, is solved. By explicitly introducing two essential ideas-"matching answers" and "GPD phenomenon," each incentive problem can be converted into a set of decoupled inverse team problems (ITP's). The solution of each ITP can then be found by solving a set of linear algebraic equations if it exists. Moreover, it is shown that, for a wide class of problems, if there exist more agents, then it is more advantageous to the leader in the sense that he has more free parameters to manipulate. Therefore, the leader can always induce the agents' cooperation as a team by means of incentives if there are enough agents. Application to a class of stochastic closed-loop dynamic Stackelberg games is also given. Since typically there exist a large number of free parameters in our solution, adequate parameters can then be chosen to make the incentive scheme satisfy additional useful properties such as balanced budget and noise robustness. These topics are treated in the Appendices.

Team-optimal closed-loop Stackelberg strategies for systems with slow and fast modest†

Abstract: This paper discusses team-optimal closed-loop Stackelberg strategies for systems with slow and fast modes. It is established that the cost functions of the players in the pure slow and the full-order games have the same value in the limit as the small singular perturbation parameters tends to zero. It is shown that if the leader bases the design of his approximate strategy on the slow subsystem, while the follower bases his design on the full-order system, then the resulting solution is ill-posed. Moreover, if the fast information is incorporated in the approximate strategy of the leader, then it is shown that the singular perturbation technique of constructing approximate strategies by composing the slow and fast strategies is ill-posed and cannot be used in this problem. A new design methodology to construct approximate Stackelberg strategies by solving reduced-order problems, which have the same information structure as the full-order one, is presented. It is shown that the conditions for existenco and...

Stackelberg Duopoly with an Illyrian and Profit-Maximising Firm

Abstract: Illyrian labour-managed firms may have positively-inclined Cournot reaction functions. Consequently, in a ' * mixed " duopoly a determinate equilibrium can result in which the profit-maximising firm leads and the labour-managed firm follows. A simple example demonstrates this.

Optimal and Near-Optimal Incentive Strategies in the Hierarchical Control of Markov Chains

Abstract: This paper considers Markovian Stackelberg problems with one leader and N followers. Firstly, an algorithm is proposed to compute optimal affine incentive strategy for the leader and Nash reactions of the followers, for general finite state Markov cahins, under the average-cost-per-stage criteria. Next, this algorithm is analyzed in the context of weakly-coupled Markov chains to compute near-optimal strategies from a reduced-order aggregate model. The robustness of the near-optimal solution is established, and the multimodel feature of the computational algorithm is highlighted.

Probabilistic prospects of Stackelberg leader and follower

Abstract: In this paper, we consider the family of allm×n bimatrix games, whose payoff entries are the players' orderings of the outcomes, and count the fraction of games whose Stackelberg solution is the leader'sh th best outcome and the follower'sk th best outcome (h,k≤mn). We conclude that the average leader and follower enjoy symmetric prospects, and that the advantage lies not in the leadership role, but in the relative size of the player's strategy space.

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.

Sufficient conditions for the team-optimal closed-loop Stackelberg strategies in linear differential games with time-delay

Abstract: In this paper, the sufficient conditions for constructing a team-optimal closed-loop Stackelberg strategies are derived in linear differential games with time-delay. The obtained conditions are the natural extension of the results derived by Basar and Olsder (1980) in linear differential games to linear differential games with time-delay

A Stackelberg equilibrium for continuous-time differential games

Abstract: The paper is concerned with the construction of Stackelberg strategies for differential continous-time leader-follower games, where the leader has access to the closed-loop information. The proposed approach utilizes the methodology of sequential strategies, developed originally for the zero-sum differential games, to derive a method for computing the upper bound for the leader's payoffs and obtain sufficient conditions for the existence of equilibrium.

A Two-Stage Model of Research and Development With Endogenous Second Mover Advantages

Abstract: This paper describes a simple two-stage model of research and development, in which the ‘winner’ of the research stage has the option of moving first in the development stage. Some unexpected results emerge: in equilibrium, the leader in the development stage invests less than each follower, and is consequently least likely to collect the patent. Moreover, the leader receives a lower expected payoff than each of the followers. Thus there are endogenous second-mover advantages. Using a game of timing (in which the identity of the Stackelberg leader is determined) to link the two stages, I find that firms face quite different incentives in the research stage. Although the leader invests less than each follower in the research stage as well, the leader enjoys higher expected revenue from the complete (two-stage) game than does each follower. The equilibrium is inefficient because there is a lag between the time at which research is completed and the time at which development is begun, and because aggregate investment is inefficiently (asymmetrically) distributed across firms.

An equilibrium theory for multi-person decision making with multiple probabilistic models: Part II: Asymmetric mode of decision making

Abstract: This paper develops an equilibrium theory for two-person two-criteria stochastic decision problems with static information patterns and an asymmetric mode of decision making, wherein the decision makers have different probabilistic models of the underlying process. The objective functions are quadratic and the decision spaces are general inner-product spaces. Firstly, a set of sufficient conditions is obtained for existence and uniqueness of Stackelberg equilibria, and a uniformly convergent iterative scheme is developed, whereby the equilibrium policy of the leader can be obtained by evaluating a number of conditional expectations. When the probability measures are Gaussian, the equilibrium solution is shown to be generically non-linear, with the linear structure prevailing only in some special cases which are delineated in the paper.

Dynamic, Hierarchical Decision Problems,

Abstract: : A hierarchical decision problem with one leader and a continuum of followers is investigated The problem is formulated as a stochastic Stackelberg game with nonnested information structure, and studied by using the Inducible Region concept For the single-stage case, it is shown that the inducible region can be delineated, and the optimal Stackelberg strategy can be constructed These results are then extended to the two-stage case Although the problem is formulated in a pricing context in terms of companies and customers, the formulation can be interpreted differently to model Command Control and Communications Systems related problems (Author)

A STACKELBERG EQUILIBRIUM FOR CONTIW@l?S-TII?E DIFFERENTIAL GAMES

Abstract: The paper is concerned with the construction of Stackelberg strategies for differential continous-time leader-follower games, where the leader has access to the closed-loop information. The proposed approach utilizes the methodology of sequential strategies, developed originally for the zero-sum differential games, to derive a method for computing the upper bound for the leader's payoffs and obtain sufficient conditions for the existence of equilibrium.

Conflict, Cooperation and Social Preference Functions

Abstract: In this paper, game theoretic solution concepts are applied to a dynamic linear-quadratic econometric decision model with more than one decision maker. Noncooperative Nash- and Stackelberg-, and cooperative Nash-Harsanyi-solutions are given. The cooperative Nash-Harsanyi solution concept allows the determination of a social preference function which reflects the individual objectives of the single decision makers with a fair weight. The theoretical discussion will be closed by a numerical illustration.

.LV EQUILIBRILT THEORY FOR MLZTI-PERSOK DECISIOS MAKISG WITH MLZTIPLE PROBABILISTIC MODELS Part 11. Asymmetric Mode of Decision Making'

Abstract: This paper develops an equilibrium theory for two- persontwecriteria stochastic decision problems with static information patterns and an asymmetric mode of decision making, wherein the decision makers have dif- ferent probabilistic models of the underlying process. The objective functions are quadratic and the decision spaces are general inner-product spaces. Firstly, a set of sufficient conditions is obtained for existence and uniqueness of Stackelberg equilibria, and a uniform- ly convergent iterative scheme is developed, whereby the equilibrium policy of the leader can be obtained by evaluating a number of conditional expectations. When the probability measures are Gaussian, the equilibrium solution is shown to be generically non- linear, with the linear structure prevailing only in some special cases which are delineated in the paper.

Pricing Problems with a Continuum of Customers: Solution of a Class of Non-Nested, Stochastic Stackelberg Games via the Inducible Region Approach

Abstract: Pricing problems are formulated as non-nested, stochastic Stackelberg games, and studied by using the inducible region concept. It is shown that the inducible region can indeed be delineated, and the optimal pricing scheme can be constructed.