Stackelberg competition

About: Stackelberg competition is a research topic. Over the lifetime, 6611 publications have been published within this topic receiving 109213 citations.

Strategic behavior when allocating indivisible goods sequentially

Abstract: We study a simple sequential allocation mechanism for allocating indivisible goods between agents in which agents take turns to pick items.We focus on agents behaving strategically. We view the allocation procedure as a finite repeated game with perfect information. We show that with just two agents, we can compute the unique subgame perfect Nash equilibrium in linear time. With more agents, computing the subgame perfect Nash equilibria is more difficult. There can be an exponential number of equilibria and computing even one of them is PSPACE-hard. We identify a special case, when agents value many of the items identically, where we can efficiently compute the subgame perfect Nash equilibria. We also consider the effect of externalities and modifications to the mechanism that make it strategy proof.

Pricing and warranty decisions in a two-period closed-loop supply chain

Abstract: For a two-period closed-loop supply chain (CLSC) consisting of a manufacturer and a retailer, Stackelberg game analyses are conducted to examine pricing and warranty decisions under two warranty mo...

Computing the Stackelberg/Nash Equilibria Using the Extraproximal Method

Abstract: In this paper we present the extraproximal method for computing the Stackelberg/Nash equilibria in a class of ergodic controlled finite Markov chains games. We exemplify the original game formulation in terms of coupled nonlinear programming problems implementing the Lagrange principle. In addition, Tikhonov's regularization method is employed to ensure the convergence of the cost-functions to a Stackelberg/Nash equilibrium point. Then, we transform the problem into a system of equations in the proximal format. We present a two-step iterated procedure for solving the extraproximal method: a the first step the extra-proximal step consists of a "prediction" which calculates the preliminary position approximation to the equilibrium point, and b the second step is designed to find a "basic adjustment" of the previous prediction. The procedure is called the "extraproximal method" because of the use of an extrapolation. Each equation in this system is an optimization problem for which the necessary and efficient condition for a minimum is solved using a quadratic programming method. This solution approach provides a drastically quicker rate of convergence to the equilibrium point. We present the analysis of the convergence as well the rate of convergence of the method, which is one of the main results of this paper. Additionally, the extraproximal method is developed in terms of Markov chains for Stackelberg games. Our goal is to analyze completely a three-player Stackelberg game consisting of a leader and two followers. We provide all the details needed to implement the extraproximal method in an efficient and numerically stable way. For instance, a numerical technique is presented for computing the first step parameter λ of the extraproximal method. The usefulness of the approach is successfully demonstrated by a numerical example related to a pricing oligopoly model for airlines companies.

Pricing decisions for substitutable products with horizontal and vertical competition in fuzzy environments

Abstract: This paper considers the pricing decisions of substitutable products which are produced by duopolistic manufacturers respectively and then sold by one common retailer to the consumers. Both the manufacturing cost and the customer demand for each product are characterized as fuzzy variables. Six expected value models are developed to explore the effects of the duopolistic manufacturers’ three pricing strategies (i.e. Bertrand competition, Stackelberg competition, cooperation) and vertical competition between the manufacturers and the retailer on the optimal pricing decisions and channel profit-split of a two echelon supply chain, and the corresponding analytical solutions are derived. Finally, a numerical example is given to illustrate the effectiveness of the proposed models, and to gain additional managerial insights.

Competitive, cooperative and Stackelberg congestion pricing for multiple regions in transportation networks

Abstract: In the previous studies of congestion pricing, it is assumed that the network is managed by a central authority with the objective to enhance the performance of the whole network. In practice, however, a transportation network often covers multiple administrative regions, and the subnetwork in each local region is managed separately by the local transportation authority with perhaps competing objectives. In this article, we propose practical pricing schemes that can take into account competition and/or collaboration between different administrative regions of the network. Both Nash and Stackelberg games are employed to capture the behaviour of local regions. Numerical examples show that local regional pricing may be beneficial or detrimental to the whole network, depending on the structure and O–D pattern of the network. And cooperation among regions in congestion pricing can improve overall system performance in terms of total social welfare.