# dynamic stackelberg game

Stackelberg game involves players with asymmetric roles which are called leader and follower. Both and are tax return policy parameters. Google Scholar, J. D. C. Little,
Based on Başar and Olsder [29] is possible only if is strictly concave in and and if there is no singularity. This situation leads to an equilibrium status that has relevant management policies reflexes individual both for all players and for the supply chain network therein. Carter and Jennings [9] also pointed towards the importance of CSR in the supply chain, in particular the role played by the purchasing managers in socially responsible activities and the effect of these activities on the supply chain. ,
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Discrete & Continuous Dynamical Systems - B,
A review of dynamic Stackelberg game models. In 1934, Stackelberg introduced a concept of a hierarchical solution which is a simple dynamic game [22]. We obtain an equilibrium point at which both the profits of members and the level of CSR taken up by supply chains is maximized. American Institute of Mathematical Sciences, Figure(1)
The Hamiltonian-Lagrangian for the supplier is defined by where is the objective function of the supplier and, to obtain the Stackelberg strategy of the supplier, we maximize the objective function of the supplier by its Hamiltonian function. Google Scholar, K. R. Deal, S. P. Sethi and G. L. Thompson,
For any given policy by the leader the follower’s value function equation iswhere is known. We propose a novel method to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. doi: 10.1007/BF00934748. doi: 10.1287/mnsc.33.8.981. That is, • it must contain an initial node, and We considered a Stackelberg game consisting of a leader and a follower with two information structures.
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Aggregate advertising models: The state of the art, Operations Research, 27 (1979), 629-667. The market
Google Scholar, J. Eliashberg and R. Steinberg,
doi: 10.1287/mnsc.1040.0249. Google Scholar, N. A. Derzko, S. P. Sethi and G. L. Thompson,
Players select their strategies on current time and they do not depend on the initial condition. Tian et al. A common feature of these applications is the specification of the game structure: a decentralized channel consists of a manufacturer and independent retailers, and a sequential decision process with a state dynamics. On the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973), 533-555.
Using the definition into and maximizing the value function for any fixed gives an optimal action for the manufacturer for the period . June 2016
Figures 2 and 3 show the trend of supplier’s and manufacturer’s profits from periods one to ten in a feedback and closed loop Stackelberg game. In addition, it is apparent that playing game in the closed loop solution is beneficial to supplier which is the leader of the game. F. El Ouardighi and K. Kogan), International Series in Operations Research and Management Science 198, Springer, (2014), 3-15.
Journal of Industrial & Management Optimization,
Discrete & Continuous Dynamical Systems - S,
Google Scholar, X. doi: 10.1007/0-387-24602-9_12. Google Scholar, E. Dockner, S. Jorgensen, N. V. Long and G. Sorger, The initial level of social responsibility is supposed to be . Subsequently, the leader’s value function equation defined byusing again the state equation definition and value of the into above equation, we can obtain . Thus, the objective function of the supplier iswhere is the price of the supplier’s raw material. The leader chooses a strategy first and the follower, with the knowledge of leader’s strategy, chooses a policy. Discrete & Continuous Dynamical Systems - S,
A growing number of research papers use game theoretical applications in supply chain management [14–17]. An analysis of manufacturer-retailer supply chain coordination in cooperative advertising, Decision Sciences, 33 (2002), 469-494.
Channel coordination under price protection, midlife returns, and end-of-life returns in dynamic markets, Management Science, 47 (2001), 1220-1234.
The members of the supply chain attempt to optimize their net profits, which includes minimizing the cost of raw materials and investment in social responsibility and maximizing sale revenues and benefits from taking social responsibility as well as tax returns. However, the research field still lacks a consistent definition of CSR and this has been the center of discussion for several decades. It aggravates the double marginalization that … The situation in which the members of supply chain tend to gain individual benefits (meanwhile they have to bear a level of CSR) is a conflict situation and this leads to an equilibrium status. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. The local stability of two equilibrium points is investigated in this game.
Google Scholar, G. J. Gutierrez and X. and
Google Scholar, G. M. Erickson,
Google Scholar, Yueyang Zheng, Jingtao Shi. In this structure the leader has a perfect knowledge of all the past and current values of the state and controls and the leader tries to find an incentive strategy such that he can reach his global optimum. A dynamic model of channel member strategies for marketing expenditures, Marketing Science, 11 (1992), 168-188.
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With some backward-forward equations we can get the values of , , and . Google Scholar, S. Jorgensen, S. Taboubi and G. Zaccour,
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A subgame must be a well-deﬁned game when it is considered separately. The scheduling problem in the upper level acts as the … We begin each section by introducing the relevant dynamic Stackelberg game formulation along with the definition of the equilibrium used, and then review the models and results appearing in the literature. Google Scholar, T. Başar and G. J. Olsder, doi: 10.1016/0377-2217(94)00308-4. Therefore, consequently the model has only one supplier, one manufacturer, and one retailer.
Google Scholar, H. V. Stackelberg,
Recently CSR has gained recognition and importance as field of research field [1, 2]. doi: 10.1080/07408170600710408. doi: 10.1007/BF00933155.
doi: 10.1007/BF02098183. Empirical analysis of closed-loop duopoly advertising strategies, Management Science, 38 (1992), 1732-1749.
Life-cycle channel coordination issues in launching an innovative durable product, Production and Operations Management, 20 (2011), 268-279.
Lecture 6: Dynamic games of complete and perfect information Lecture 7: Stackelberg games Lecture 8: Dynamic games of complete and imperfect information Lecture 9: Sequential bargaining Lecture 10: Repeated games Lecture 11: Concluding remarks on subgame perfection Lecture 12: Static games of incomplete information Dynamic slotting and pricing decisions in a durable product supply chain, Journal of Optimization Theory and Applications, 137 (2008), 363-379.
The authors declare that they have no competing interests. DYNAMIC GAMES: INTRODUCTION In many strategic interactions, players take turn to move and they observe what others have done. On generalized Stackelberg strategies, J. Optimization Theory and Applications, 26 (1978), 637-643.
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These benefits are proved by some well-known case studies of large international companies, such as Nike, Gap, H&M, Wal-Mart, and Mattel [13]. ()
In the study, we devise a new Stackelberg game, called position changeable Stackelberg (PCS) game, to adapt effectively to the UPN situation. Furthermore, the boundary condition is . Marketing-production decisions in an industrial channel of distribution, Management Science, 33 (1987), 981-1000.
K. Anand, R. Anupindi and Y. Bassok,
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The ﬁ rst and the second mover advantage issues are raised comparing outcomes of dynamic Stackelberg and Bertrand games for a leader and a follower. In the related literature, one can find a lot methods to solve the optimal control problem. A Stackelberg differential game has two players playing the game over a fixed finite horizon model. doi: 10.3934/jimo.2020158, Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. (1)
A differential game of advertising for national and store brands, in Dynamic Games: Theory and Applicatoins (eds. Google Scholar, A. Bensoussan, S. Chen, A. Chutani and S. P. Sethi, Feedback Stackelberg-Nash equilibria in mixed leadership games with an application to cooperative advertising, working paper, The University of Texas at Dallas, 2016. Google Scholar, G. E. Fruchter and S. Kalish,
Massimiliano Ferrara, Mehrnoosh Khademi, Mehdi Salimi, Somayeh Sharifi, "A Dynamic Stackelberg Game of Supply Chain for a Corporate Social Responsibility", Discrete Dynamics in Nature and Society, vol. 1,,
Superposition principle and schemes for measure differential equations. A chance-constrained stochastic model predictive control problem with disturbance feedback. In the PCS game, each individual user can be a leader, i.e., host, or a follower, i.e., client, dynamically to maximize his payoff. Tao Li, Suresh P. Sethi. The paper is organized as follows: Section 2 is devoted to the mathematical model. However, many firms adopt CSR for enhancing their reputation due to public concerns over social issues or other benefits, such as increased sales and tax returns and long-term profits in many respects, including stable suppliers, low cost delivery, and extended market demand. In

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