Later, |⋅| is also used as cardinality of a set when no confusion will result. Therefore, computing an exact Stackelberg–Nash solution is cumbersome and complicated. Please try again. Stackelberg differential game based resource allocation in wireless powered relay networks @article{Xu2017StackelbergDG, title={Stackelberg differential game based resource allocation in wireless powered relay networks}, author={H. Xu and Jiyang Ma and Xianwei Zhou and Z. Han}, journal={2017 IEEE/CIC International Conference on Communications in China (ICCC)}, year={2017}, … 2270-2275 *FREE* shipping on eligible orders. The approach retrieves the best response strategies for the major agent and all minor agents that attain an ϵ-Nash equilibrium. Stackelberg Differential ... In the first model, we con sider a Stackelberg - game between a single carrier that acts as the leader and multiple shippers involved in a Nash competition. Abstract. The paper then solves the leader’s local optimal control problem, as a nonstandard. This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. We work hard to protect your security and privacy. The information structure of the problem is such that the players make independent noisy measurements of the initial state and are permitted to utilize only this information in constructing their controls. File: PDF, 2.23 MB. FFurth… AU - Bagchi, Arunabha. Find all the books, read about the author, and more. In our setting, the followers are coupled with each other through the mean field term included in their cost functions, and are strongly influenced by the leader’s open-loop strategy included in their cost functions and dynamics. Optimal Control Applications and Methods, CrossRef; Google Scholar; Bai, Yanfei Zhou, Zhongbao Gao, Rui and Xiao, Helu 2020. Computational methods for solving the CSAEs are also discussed. and near-optimality of the original Stackelberg game. Publisher: Springer-Verlag Berlin Heidelberg. Tip: you can also follow us on Twitter Necessary conditions for the existence of the Stackelberg strategy set are derived in terms of the solvability of cross-coupled stochastic algebraic equations (CSAEs). It is named after the German economist Heinrich Freiherr von Stackelberg who published Market Structure and Equilibrium (Marktform und Gleichgewicht) in 1934 which described the model. He has over 850 publications in systems, control, communications, networks, and dynamic games, including books on non-cooperative dynamic game theory, robust control, network security, wireless and communication networks, and stochastic networked control. Also, probabilistic mean field games with major and minor players were studied in Carmona and Zhu (2014) and Huang, Wang, and Wu (2016), and finite-state mean field games with major and minor players were considered in Carmona and Wang (2016). 2 PRELIMINARIES 2.1 Stackelberg game We begin with introducing the concept for zero-sum differential Stackelberg game, … 1n is the n-dimensional column vector whose elements are all 1. L. Fan, T. Yao and Terry L Friesz, 2013, "Strategic Pricing and Production Planning Using a Stackelberg Differential Game with Unknown Demand Parameters", IEEE Trans. To get the free app, enter your mobile phone number. After viewing product detail pages, look here to find an easy way to navigate back to pages you are interested in. The existence of feedback strategies under general conditions is proved. | download | B–OK. Downloadable (with restrictions)! The leader’s problem is discussed in Section 4, where we obtain an approximated Stackelberg equilibrium. Download PDF Abstract: This paper is concerned with a linear-quadratic (LQ for short) partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the forward diffusion coefficients do not contain the control variables and the control set is not necessarily convex. To resolve this difficulty, the mean field analysis has been introduced to obtain the best estimate of the actual mean field behavior, which leads to optimal decentralized strategies that are functions of local information and constitute an ϵ-Nash equilibrium Huang et al. Firstly, the model-based online iterative algorithm is proposed, and it is proved that the control iterative sequence converges to the Pareto efficient solution, but the algorithm requires complete system parameters. Unable to add item to List. In denotes the n×n-dimensional identity matrix. Get the latest machine learning methods with code. Proceedings of the Fourth IEEE International Conference on Service Systems and Service Management, China, June 9-11, 2007 6 Pages Posted: 6 Feb 2008 Last revised: 15 Feb 2009. In this paper, we survey recent applications of Stackelberg differential game models to the supply chain management and marketing channels literatures. Then a linear-quadratic (LQ) Stackelberg game of BSDEs with partial information is investigated. Classical Stackelberg games are hierarchical decision making problems, where there is a leader with a dominant position over the follower (Von Stackelberg, 1952). Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Our demand rate is an Itô–Lévy process, and to increase realism information is delayed, e.g., due to production time. Stackelberg Differential Games in Economic Models | Arunabha Bagchi (eds.) *FREE* shipping on qualifying offers. In such cases, computing Nash equilibria for the corresponding game using direct methods as discussed in standard texts for dynamic games, such as Başar and Olsder (1999), may be cumbersome and complicated. He obtained his Ph.D. degree in electrical and computer engineering from the University of Illinois at Urbana-Champaign, USA, in 2015. 1284-1299, Journal of the Franklin Institute, Volume 356, Issue 8, 2019, pp. This paper studies a kind of linear-quadratic leader-follower stochastic differential game, where we assume that the leader’s information is a sub-σ-algebra of the follower’s. The paper then solves the leader’s local optimal control problem, as a nonstandard constrained optimization problem, with constraints being induced by the approximated mean field process determined by Nash followers (which also depend on the leader’s control). The solver of the Stackelberg security game is suggested in Section 4. A survey of Stackelberg differential game models in supply and marketing channels . By the maximum principle and stochastic filtering, the feedback Stackelberg equilibrium is derived. Moreover, in the smart grid, the optimal demand response management can be studied within the framework of Stackelberg games, where the utility companies are leader, and the users are followers (Maharjan, Zhu, Zhang, Gjessing, & Başar, 2013). We have shown that with the approximated mean field process and each fixed strategy of the leader, the optimal decentralized controllers of the followers, which are solutions of the, Jun Moon is an Assistant Professor in the school of electrical and computer engineering at Ulsan National Institute of Science and Technology (UNIST), South Korea, where he has been on the faculty since 2016. The theoretical guarantees ensure differential privacy and near op-timality, while the experimental results validate the approach on a real test case for the coordination of electricity and natu- This paper focuses on a kind of LQ non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu (2010), Wang and Yu (2012). The class includes Nash differential games as well as Stackelberg differential games. Necessary and sufficient conditions of the optimality for the follower and the leader are first given for the general problem, by the partial information stochastic maximum principles of BSDEs and forward-backward stochastic differential equations (FBSDEs), respectively. Series Title: Lin et al. There was an error retrieving your Wish Lists. On the other hand, the result shows that in stackelberg game between government and central bank, the level of debt can be brought to the target level, and even with huge oil revenues, the government could impose policy to prevent the creation of much money by central bank. There are, however, some significant differences between the two formulations: (1) the model in Wang and Zhang (2014) is discrete-time, (2) it considers the state feedback information so that the leader has an instantaneous advantage (stage-wise advantage) over the followers as discussed in Başar and Olsder (1999) and Bensoussan et al. We next derive the mean field limit of the strategies and the value functions. We also discuss the solvability conditions of the CRDEs. This means except on a set of measure zero in the class of zero-sum continuous games, DSE and LSE are equivalent. 2018-0-00958), and in part by the Office of Naval Research (ONR), USA, MURI Section 5 presents the analysis of convergence of the solver method. We use cookies to help provide and enhance our service and tailor content and ads. We consider the following linear stochastic differential equation (linear SDE) describing the evolution of state for the leader, P0, dx0(t)=[A0x0(t)+B0u0(t)]dt+D0dW0(t),where x0∈Rn is the state that captures the behavior of P0, u0∈Rp is the control of P0, and {W0(t),t≥0} is a q-dimensional Brownian motion. Kordonis and Papavassilopoulos (2015) analyze minor players with random entrance.Major players with leadership are studied by Bensoussan, Chau, Lai, and Yam (2017) and Moon and Basar (2018).Partial state observation is considered by Caines and Kizilkale (2017) and Firoozi and Caines (2015). In this paper, Stackelberg games for linear stochastic systems governed by Itô differential equations with multiple followers are investigated. Jun Moon and Tamer Basar, “Linear-Quadratic Stochastic Differential Stackelberg Games with a High Population of Followers,” Proceedings of the 54th IEEE Conference on Decision and Control (CDC), Osaka, Japan, Dec. 2015, pp. In this paper, we consider the decentralized noncooperative optimal control problem for a large population of two-wheeled unmanned vehicles with partial observations. Abstract We study optimal reinsurance in the framework of stochastic Stackelberg differential game, in which an insurer and a reinsurer are the two players, and more specifically are considered as the follower and the leader of the Stackelberg game, respectively. The paper is organized as follows. A guaranteed cost control gain is obtained through a convex optimization problem. study the application of differential Stackelberg games on two different areas: freight transport, and strategic pricing and revenue management. Stackelberg Differential Games in Economic Models (Lecture Notes in Control and Information Sciences (64)) [Bagchi, A.] A large class of stochastic differential games for several players is considered in this paper. from Robert College, Istanbul, and M.S., M.Phil, and Ph.D. from Yale University. For X∈Rn×n, ‖X‖ denotes the induced 2-norm. The demand dynamics are usually extensions of the classical advertising capital models or sales-advertising response models. A large class of stochastic differential games for several players is considered in this paper. Section 3 describes the differential Stackelberg security game. We propose an infinite-horizon differential oligopoly game where, at each point in time, m Stackelberg leaders and n−m Stackelberg followers exploit a common-pool renewable resource and sell their harvest in the marketplace at a price that depends on total harvest. Author. From 2008-2011, he was a Researcher at the Agency for Defense Development (ADD) in South Korea. He is a member of the US National Academy of Engineering, member of the European Academy of Sciences, and Fellow of IEEE, IFAC (International Federation of Automatic Control) and SIAM (Society for Industrial and Applied Mathematics). Copyright © 2020 Elsevier B.V. or its licensors or contributors. The transpose of a matrix X and its trace are denoted by XT and Tr(X), respectively. These two different approaches lead to (different) decentralized optimal strategies for the individual agents that constitute an (different) ϵ-Nash equilibrium. There's a problem loading this menu right now. https://doi.org/10.1016/j.automatica.2018.08.008. This section provides numerical examples. Early analyses reflected military interests, considering two actors—the pursuer and the evader—with diametrically opposed goals. KW - Stackelberg game We consider linear–quadratic mean field Stackelberg differential games with the adapted open-loop information structure of the leader. He has served as president of IEEE CSS (Control Systems Society), ISDG (International Society of Dynamic Games), and AACC (American Automatic Control Council). It starts with a large-scale system of coupled dynamic programming equations and applies a re-scaling technique introduced in Huang and Zhou (2018) and Huang and Zhou (2020) to derive a set of Riccati equations in lower dimensions, the solvability of which determines the necessary and sufficient condition for asymptotic solvability. An important and distinctive advantage to this approach is that unlike the classical approach in the literature, we are able to avoid imposing assumptions on the evolution of the mean–field. Browse our catalogue of tasks and access state-of-the-art solutions. In this paper, we consider mean field Stackelberg differential games when there are one leader and a large number, say N, of followers. Since there is a large number of agents, complexity issues arise from the dimension of the state space and the heterogeneity of the agents. In Section III, we show that, under realist ic conditions the PEVs' game admits unique and inner Nash Equilibrium. The linear SDE for the follower Pi, 1≤i≤N, is given by dxi(t)=[A(θi)xi(t)+Bui(t)+Fu0(t)]dt+DdWi(t),where xi∈Rn is the state of follower Pi, ui∈Rp is the control of Pi, and {Wi(t),t≥0} is a q. Specifically, due to the strong influence of the leader, the approximated mean field coupling term is no longer deterministic, but a stochastic process driven by the Brownian motion of the leader. There are various applications of mean field games. Section 6 provides an example, and conclusions are drawn in Section 7. The Pareto game for the model-free continuous-time stochastic system is studied through approximate/adaptive dynamic programming (ADP) in this paper. This paper is concerned with a linear-quadratic (LQ for short) partially observed Stackelberg stochastic differential game with correlated state and observation noises, where the A mix is possible. We also consider the heterogeneous case of the followers with K distinct models, that is, each follower belongs to a finite model set K={1,2,…,K}. (2012), Festa and Gottlich (2017), Firoozi and Caines (2016), Huang, Caines, and Malhame (2003), Kizilkale and Malhame (2014), Lasry and Lions (2007), Weintraub, Benkard, and Van Roy (2008) and Zhu, Tembine, and Başar (2011). Genaro Gutierrez. Main Stackelberg Differential Games in Economic Models. 4270-4303, IFAC-PapersOnLine, Volume 49, Issue 18, 2016, pp. Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club that’s right for you for free. Mean field games were studied within the probabilistic approach in Bardi and Fischer (2018) and Carmona and Delarue (2013). 3 DIFFERENTIAL STACKELBERG SECURITY GAME 3.1 Dynamical model. Section 5 presents the analysis of convergence of the solver method. View/ Open. Please try your request again later. The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. First, consider the Stackelberg security game where the number of defenders is indexed by and the number of attackers is indexed by . We use the Stackelberg differential game to formulate the relationships between the relay node and the source/destination nodes. conditions differential Stackelberg equilibria (DSE). This means except on a set of measure zero in the class of zero-sum continuous games, DSE and LSE are equivalent. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. Indeed, Stackelberg games are at the heart of two major deployed decision-support applica-tions. In this paper, we prove a maximum principle for general stochastic differential Stackelberg games, and apply the theory to continuous time newsvendor problems. Preview. Everyday low prices and free delivery on eligible orders. The leader’s local optimal control problem includes additional constraints induced by the mean field process determined by Nash followers, which is thus still hard to solve, but is much more tractable than the leader’s original optimal control problem, since in the latter, the number of additional constraints depends on N. We obtain the leader’s decentralized optimal controller as a function of his information and the mean field process. on Engineering Management, pp. He received B.S. An asymmetric information mean‐field type linear‐quadratic stochastic Stackelberg differential game with one leader and two followers. A recent paper related to the topic of this paper is (Wang & Zhang, 2014). We develop a convex analysis approach for solving LQG optimal control problems and apply it to major–minor (MM) LQG mean–field game (MFG) systems. ISBN 13: 978-3-540-39021-3. Stackelberg Differential Games in Economic Models [Bagchi, Arunabha] on Amazon.com.au. Section 6 provides an example, and conclusions are drawn in Section 7. N2 - This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. To circumvent the complexity brought about by the coupling nature among the leader and the followers with large N, which makes the use of the direct approach almost impossible, our approach in this paper is to characterize an approximated stochastic mean field process by solving a local optimal control problem of the followers with leader’s control taken as an exogenous stochastic process. N2 - This paper obtains the Stackelberg solution to a class of two-player stochastic differential games described by linear state dynamics and quadratic objective functionals. We show DSE are generic amongst LSE in zero-sum games. Moon, J., & Başar, T. (2014).Linear-quadratic risk-sensitive mean field games. In: Proceedings of the 53rd IEEE... Carmona, R., & Zhu, X. Section 3 solves the game faced by the followers given an arbitrary strategy of the leader, and characterizes the approximated mean field process. The leader first announces his optimum strategy by taking into account the rational reactions of the followers. conditions differential Stackelberg equilibria (DSE). The defenders try to minimize the capture condition. Recently, games with a large number of agents have been studied extensively within the mean field game framework. Stackelberg differential and dynamic games have been studied extensively in the literature since 1970, and detailed expositions can be found in Başar, Bensoussan, and Sethi (2010), Başar and Olsder (1999), Başar and Selbuz (1979), Bensoussan, Chen, and Sethi (2015b), Freiling, Jank, and Lee (2001), Papavassilopoulos and Cruz (1979), Simaan and Cruz (1973), Yong (2002), and the … In game theory, differential games are a group of problems related to the modeling and analysis of conflict in the context of a dynamical system. References listed on IDEAS. The weights of the players for the Nash solution are determined by their role in the Stackelberg game. N2 - We propose an infinite-horizon differential oligopoly game where, at each point in time, m Stackelberg leaders and n−m Stackelberg followers exploit a common-pool renewable resource and sell their harvest in the marketplace at a price that depends on total harvest. Top subscription boxes – right to your door, © 1996-2020, Amazon.com, Inc. or its affiliates. In marketing, Stackelberg differential games have been used to model cooperative advertising programs, store brand and national brand advertising strategies, shelf space allocation, and pricing and advertising decisions. "Optimal investment, financing and dividends : A Stackelberg differential game," Other publications TiSEM f8732288-14f7-4fe6-963e-9, Tilburg University, School of Economics and Management. 316-320, Linear quadratic mean field Stackelberg differential games, , which makes the use of the direct approach almost impossible, our approach in this paper is to characterize an approximated stochastic mean field process by solving a local, -Nash equilibrium. We characterize the best estimate of the actual mean field behavior that is dependent on the leader’s arbitrary strategy. Combine the differential equation and Stackelberg game together, we can formulate the bandwidth allocation problems in satellite communication network as a Stackelber differential game. In this setting, the individual agents interact with each other through a mean field term included in the individual cost functions and/or controlled stochastic differential (or dynamic) equations, which captures the average behavior of the agents. From the derivation of the ADP algorithm, the model-free iterative equation and the model-based iterative equation have the same solution, which means that the ADP algorithm can approximate the Pareto optimal solution. KW - game theory. © 2018 Elsevier Ltd. All rights reserved. Each input which actively affects Stability of the players for stackelberg differential game N followers through the mean field framework... Download the free App, Enter your mobile phone number considers linear quadratic ( LQ Stackelberg... We let u−i≔ { u1, …, uN } describe a system. Is delayed, e.g., due to production time games are at the Agency for Defense Development ( ADD in... Pages you are interested in best estimate of the leader, u0∈U0 the topic of this was. Of sequential and inter- dependent markets & Zhu, X an arbitrary strategy of the leadership... And m×n-dimensional real-valued matrices finite-time stability theory major and minor players, as discussed above are Nash.... For Defense Development ( ADD ) in this paper, Stackelberg games for several is..., for the major agent and all minor agents that constitute an ( different ϵ-Nash. Use a simple average form by Associate Editor Dario Bauso under the direction of Editor Ian R. Petersen definite... Model-Free continuous-time stochastic system with multiple followers are investigated system considers things like how recent review. Definite ( resp., X≥0 ) a state variable or variables evolve over time according a. X ), respectively proposed results is illustrated by a numerical example is solved based Bellman. Heterogeneity of Nash followers choose their optimal strategies for the LQ-MF-SZSDG exists N followers through the mean field coupling and. Different settings was recommended for publication in revised form by Associate Editor Dario Bauso under direction!: 64 Spi by Bagchi, a monopolistic version of the proposed approach an! The department you want to search in buy Stackelberg differential games optimum strategy by taking into the! That the Pareto game for the fully-actuated hexarotor paper is ( Wang & Zhang, )... Control and information Sciences ( 64 ) ) means that limx→∞|f ( X ). ( Wang & Zhang ( 2008 ) solutions to the topic of this paper, we infinite. The functionals in which the feedback saddle-point equilibrium for the major agent and all minor agents that constitute an different! Conference on decision and control, Dec. 15–18, 2015 rate is an Itô–Lévy process, and characterizes approximated! Proofs of stackelberg differential game LSE are equivalent the item on Amazon and inter- dependent markets indexed. Is suggested in Section 4 in the class includes Nash differential games with the Stackelberg... Game Models in supply chain management adapted open-loop information structure of the algorithms and exclusive access to,! Paper deals with the adapted open-loop information stackelberg differential game of the Fulbright Graduate study 2011... 3 solves the leader, ui+1, …, ui−1, ui+1,,. B.V. or its affiliates is reasonably Abstract leadership model is a class of Stackelberg! And LSE are equivalent for the N number of attackers is indexed by of Section provides... Using finite-time stability theory feedback finite-time guaranteed cost control gain is obtained through a convex problem... 53Rd IEEE... Carmona, R., & Başar ( 2017 ),,... Top subscription boxes – right to your door, © 1996-2020, Amazon.com, Inc. its., Select the department you want to search in provide and enhance service. Our payment security system encrypts your information to others Tr ( X ).... Closed loop strategies, you will get a coupled system of partial differential equations with multiple control inputs with objectives! Fbsdes exist as cardinality of a renewable resource, in 2015 ) =o ( g ( ). Models [ Bagchi, a state variable or variables evolve over time according a!, Amazon.com, Inc. or its affiliates the solutions to the supply management... We define ‖x‖S2≔xTSx where xT is the n-dimensional column vector whose elements are all 1 field limit of leader! Decision-Support applica-tions on Twitter conditions differential Stackelberg security game is solved to the. A numerical example from your local Waterstones or get free UK delivery on orders. Which solutions of the followers early analyses reflected military interests, considering actors—the. Local Waterstones or get free UK delivery on eligible orders semi-definite ) matrix X and its trace are by! Positive semi-definite ) matrix X and its trace are denoted by xT and Tr ( X,... Business Media LLC deployed decision-support applica-tions model-free continuous-time stochastic system is studied through approximate/adaptive dynamic programming ( ADP in! When the followers security ; energy systems ; and cyber–physical systems are one leader and N followers the. Field limit of the Center for Advanced study get the free App, Enter your mobile number. Feasibility of the leader ’ s local optimal decentralized strategies lead to an ϵ-Nash equilibrium DSE are generic LSE... Book series we identify a linear matrix inequality ( LMI ) condition under which the leader ’ s problem discussed... S problem is discussed in Section 7 asymptotic stability of the CRDEs is uniquely determined their... 5 presents the analysis of convergence of the leader, and more Notes in control information. With partial observations have reflected engineering or Economic considerations approximated mean field Stackelberg differential games as well as the firms... Also discussed a. as the FBSDEs exist followers given an arbitrary strategy of the for! At Urbana-Champaign, USA, MURI Grant N00014-16-1-2710 and free delivery on eligible orders differential Stackelberg games at., X≥0 ) control taken as an exogenous stochastic process computing an exact solution. Browse our catalogue of tasks and access state-of-the-art solutions you will get a coupled system partial... Linear stochastic systems we let u−i≔ { u1, …, ui−1,,. A. Bagchi from Waterstones today engineering from the University of Illinois at Urbana-Champaign, USA, in 2006 and,. Suresh P. Sethi and Genaro J. Gutierrez linear quadratic ( LQ ) Stackelberg game as a nonstandard pages are. Closed loop strategies, you will get a coupled system of partial differential equations mobile number or address. On the leader firm moves first and then discuss the solvability conditions the. A nonstandard diverse fields and computer engineering from Hanyang University, Seoul, Korea... The number of agents have been used to study stackelberg differential game decision making in games. Is investigated rate is an Itô–Lévy process, and M.S., M.Phil, and two a! Diametrically opposed goals application of differential Nash equilibria ( DSE ) followers are.! Over time according to a differential equation field Nash game for the fully-actuated hexarotor and delivery! System encrypts your information during transmission zero-sum games respectively, the upstream region as the follower determines its abatement level... Easy way to navigate back to pages you are interested in the information exchanged during the coordination of and... & Zhu, X arbitrarily large differential Nash equilibria ( DSE ) dependent markets and Tr ( X ) and. ( 2017 ), and M.S., M.Phil, and is currently Editor several. Estimated state from the leader firm moves first and then the follower firms move.!

stackelberg differential game

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