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Stackelberg competition

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


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Journal ArticleDOI
07 Dec 2012
TL;DR: In this article, a Stackelberg strategy subject to the evolutionary Stokes equations is studied, considering a Nash multi-objective equilibrium (not necessarily cooperative) for the follower players and an optimal problem for the leader player with approximate controllability objective.
Abstract: Abstract. We study a Stackelberg strategy subject to the evolutionary Stokes equations, considering a Nash multi-objective equilibrium (not necessarily cooperative) for the “follower players” (as they are called in the economy field) and an optimal problem for the leader player with approximate controllability objective. We will obtain the following three main results: the existence and uniqueness of the Nash equilibrium and its characterization, the approximate controllability of the Stokes system with respect to the leader control and the associate Nash equilibrium, and the existence and uniqueness of the Stackelberg-Nash problem and its characterization.

43 citations

Journal ArticleDOI
TL;DR: An interdisciplinary P2P energy sharing framework that considers both technical and sociological aspects is proposed, based on prospect theory and stochastic game theory, in which the prosumers work as followers with subjective load strategies, while an energy sharing provider serves as the leader with a dynamic pricing scheme.
Abstract: Distributed energy resources bring about challenges related to the participation of an increasing number of prosumers with strong social attributes in peer-to-peer (P2P) energy sharing markets, resulting in the increased complexity of socio-technical systems. Previous research has focused on energy sharing analysis based on rational games without considering the social attributes of prosumers, which are not typically used in real scenarios. In this article, an interdisciplinary P2P energy sharing framework that considers both technical and sociological aspects is proposed. It is based on prospect theory (PT) and stochastic game theory, in which the prosumers work as followers with subjective load strategies, while an energy sharing provider (ESP) serves as the leader with a dynamic pricing scheme. A subjective utility model with risk utility (RU) determined by PT is designed for prosumers, and a profit model for dynamic prices is suggested for ESP. Moreover, a solution algorithm that consists of interpolation and curve fitting to obtain the RU function, the aggregation of prosumers to a Markov decision process, and a differential evolution algorithm to solve the game are proposed to solve the problems of the “curse of dimensionality” and discreteness arising from the social attributes of prosumers. Numerical analysis reveals the results of the Stackelberg equilibrium and demonstrates the effectiveness of this method in terms of the social behavior of prosumers, i.e., radicalness when losing and conservatism when gaining.

43 citations

Journal ArticleDOI
TL;DR: It is proved that the problem is APX-hard even if there are only two different red costs, and an approximation algorithm is given whose approximation ratio is at most min {k,1+ln’b,1-ln W}, where k is the number of distinct red Costs, b is thenumber of blue edges, and W is the maximum ratio between red costs.
Abstract: We consider a one-round two-player network pricing game, the Stackelberg Minimum Spanning Tree game or StackMST. The game is played on a graph (representing a network), whose edges are colored either red or blue, and where the red edges have a given fixed cost (representing the competitor's prices). The first player chooses an assignment of prices to the blue edges, and the second player then buys the cheapest possible minimum spanning tree, using any combination of red and blue edges. The goal of the first player is to maximize the total price of purchased blue edges. This game is the minimum spanning tree analog of the well-studied Stackelberg shortest-path game. We analyze the complexity and approximability of the first player's best strategy in StackMST. In particular, we prove that the problem is APX-hard even if there are only two different red costs, and give an approximation algorithm whose approximation ratio is at most $\min \{k,1+\ln b,1+\ln W\}$, where $k$ is the number of distinct red costs, $b$ is the number of blue edges, and $W$ is the maximum ratio between red costs. We also give a natural integer linear programming formulation of the problem, and show that the integrality gap of the fractional relaxation asymptotically matches the approximation guarantee of our algorithm.

42 citations

Journal ArticleDOI
TL;DR: The main determinant of the equilibrium in mature industries is to respond well to the actions of the competing chain rather than to directly maximize the profit of each chain, which means that the equilibrium does not necessarily maximize the profits of the entire industry.
Abstract: Our main objective is to investigate the influence of the bargaining power within a chain on its industry. As a building block, we first discuss the implications of bargaining within a single chain by considering an asymmetric Nash bargaining over the wholesale price (BW). We show that both Manufacturer Stackelberg (MS) and vertical integration (VI) strategies are special cases of the BW contract. We then develop the Nash equilibrium in an industry with two supply chains that use BW. We identify the profit-maximizing (coordinating) bargaining power within this industry. We show that when a chain is not monopolistic, VI does not coordinate the chain and that the MS contract, where the manufacturer has all the bargaining power, is coordinating when competition is intense. We find that the main determinant of the equilibrium in mature industries is to respond well to the actions of the competing chain rather than to directly maximize the profit of each chain. That is, the equilibrium does not necessarily maximize the profit of the entire industry. While a coordination of the industry could then increase the profitability of both chains, such a coordination is likely against antitrust law. Moreover, if one chain cannot change its actions, the other chain may unilaterally improve its profitability by deviating from the equilibrium. Our results lead to several predictions supported by empirical findings, such as that in competitive industries chains will work “close to” the MS contract.

42 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023551
20221,041
2021563
2020557
2019582
2018487