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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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TL;DR: It is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate, and that these robust optimization problems can be formulated into semidefinite programming.
Abstract: In this paper, we study different secrecy rate optimization techniques for a multiple-input–multiple-output (MIMO) secrecy channel, where a multiantenna cooperative jammer is employed to improve secret communication in the presence of a multiantenna eavesdropper. Specifically, we consider two optimization problems, namely, power minimization and secrecy rate maximization. These problems are not jointly convex in terms of the transmit covariance matrices of the legitimate transmitter and the cooperative jammer. To circumvent these nonconvexity issues, we alternatively design the transmit covariance matrix of the legitimate transmitter and the cooperative jammer. For a given transmit covariance matrix at the cooperative jammer, we solve the power minimization and secrecy rate maximization problems based on a Taylor series expansion. Then, we propose two iterative algorithms to solve these approximated problems. In addition, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure , we show that these robust optimization problems can be formulated into semidefinite programming. Moreover, we consider the secrecy rate maximization problem based on game theory, where the jammer introduces charges for its jamming service based on the amount of the interference caused to the eavesdropper. This secrecy rate maximization problem is formulated into a Stackelberg game where the jammer and the transmitter are the leader and the follower of the game, respectively. For the proposed game, Stackelberg equilibrium is analytically derived. Simulation results have been provided to validate the convergence and performance of the proposed algorithms. In addition, it is shown that the proposed robust scheme outperforms the nonrobust scheme in terms of the achieved secrecy rate and the worst-case secrecy rate. Finally, the Stackelberg equilibrium solution has been validated through numerical results.
216 citations
TL;DR: In this article, a Stackelberg game model is used to investigate the optimal decisions of local advertising, used-product collection and pricing in centralized and decentralized closed-loop supply chains.
215 citations
TL;DR: In this paper, the authors model the supply chain problem as a stochastic Stackelberg differential game and obtain the condition when offering co-op advertising is optimal for the manufacturer.
Abstract: Cooperative (co-op) advertising is an important instrument for aligning manufacturer and retailer decisions in supply chains. In this, the manufacturer announces a co-op advertising policy, i.e., a participation rate that specifies the percentage of the retailer's advertising expenditure that it will provide. In addition, it also announces the wholesale price. In response, the retailer chooses its optimal advertising and pricing policies. We model this supply chain problem as a stochastic Stackelberg differential game whose dynamics follows Sethi's stochastic sales-advertising model. We obtain the condition when offering co-op advertising is optimal for the manufacturer. We provide in feedback form the optimal advertising and pricing policies for the manufacturer and the retailer. We contrast the results with the advertising and price decisions of the vertically integrated channel, and suggest a method for coordinating the channel.
213 citations
TL;DR: In this paper, the authors presented two models of an electric power market with arbitrage on a linearized DC network with a affine price function, and showed that these two models yield the same prices, producer outputs, and profits as a model of Cournot competition in a Poolco system, in which a system operator runs a centralized auction and buys all production and then resells it to consumers.
Abstract: Extending a prior arbitrage-free model of Hobbs (2001), this article presents two models of an electric power market with arbitrage on a linearized DC network with a affine price functions The two models represent a decentralized system involving bilateral contracts between producers and consumers in which the system operator's role is limited to providing transmission services The two models differ in how arbitrage is handled In the first model, the producers anticipate the effect of arbitrage upon prices at different locations (Stackelberg assumption), and therefore treat the arbitrage amounts as decision variables in their profit maximization problems In the second model, the firms take the arbitrage quantities as inputs in their problems (Cournot assumption), and the arbitrager solves a separate profit maximization problem that takes the electricity prices and the transmission costs as inputs In each model, we adopt a Nash-Cournot equilibrium as the solution concept for the game among producers We show that the resulting equilibrium problems can be formulated as monotone mixed linear complementarity problems Based on such a formulation, we obtain existence,uniqueness,and various quantitative properties of the equilibrium solutions to the models It is also demonstrated that these two models of a bilateral market yield the same prices, producer outputs, and profits as a model of Cournot competition in a “Poolco” system,in which a system operator runs a centralized auction and buys all production, and then resells it to consumers This result implies that Cournot competition among producers yields the same outcomes for two distinct market designs Finally, we present a numerical example to illustrate the theoretical results
212 citations
TL;DR: It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium solution of the game.
Abstract: This paper studies the solution of joint energy storage (ES) ownership sharing between multiple shared facility controllers (SFCs) and those dwelling in a residential community. The main objective is to enable the residential units (RUs) to decide on the fraction of their ES capacity that they want to share with the SFCs of the community in order to assist them in storing electricity, e.g., for fulfilling the demand of various shared facilities. To this end, a modified auction-based mechanism is designed that captures the interaction between the SFCs and the RUs so as to determine the auction price and the allocation of ES shared by the RUs that governs the proposed joint ES ownership. The fraction of the capacity of the storage that each RU decides to put into the market to share with the SFCs and the auction price are determined by a noncooperative Stackelberg game formulated between the RUs and the auctioneer. It is shown that the proposed auction possesses the incentive compatibility and the individual rationality properties, which are leveraged via the unique Stackelberg equilibrium solution of the game. Numerical experiments are provided to confirm the effectiveness of the proposed scheme.
209 citations