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dynamic stackelberg game

A subgame must be a well-defined game when it is considered separately. Review articles are excluded from this waiver policy. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem Google Scholar, M. Simaan and J. doi: 10.1287/opre.27.4.682. It aggravates the double marginalization that … Closed-loop advertising strategies in a duopoly, Management Science, 43 (1997), 54-63.  Google Scholar, H. L. Lee, V. Padmanabhan, T. A. Taylor and S. Whang, Google Scholar, X. Lu, J. S. Song and A. Regan, Google Scholar, S. Jorgensen, S. P. Sigue and G. Zaccour, We develop a Stackelberg game by selecting the supplier as the leader and the manufacturer as the follower. However, for the manufacturer, which is the follower, closed loop solution involves zero-profits. Necessary conditions for the existence of equilibria are derived, based on similar developments in control theory. In sum, for this case in which supplier is the leader of game, both supplier and manufacturer are motivated to play the game in feedback solution because their benefits have increased; in closed loop situation some incentive strategies are needed in order that follower plays game while profit of the leader has risen in this solution as well. In marketing, dynamic Stackelberg games have been used to model cooperative advertising programs, store brand and national brand advertising strategies, shelf space allocation, and pricing and advertising decisions. An interesting consideration that emerges is the credibility of promises and threats. doi: 10.1111/poms.12320. 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. In the related literature, one can find a lot methods to solve the optimal control problem. Google Scholar, A. Bensoussan, S. Chen and S. P. Sethi, Stability and dynamic transition of a toxin-producing phytoplankton-zooplankton model with additional food. As it is well-known, business logistics management refers to the production and distribution process within the company, while supply chain management includes suppliers, manufacturers, and retailers that distribute the product to the end customer. 2021, 20 Stackelberg leadership in a marketing channel, International Game Theory Review, 3 (2001), 13-26.  All retailers and suppliers at the same level make the same decision. doi: 10.1007/BF02098183. In the study, we devise a new Stackelberg game, called position changeable Stackelberg (PCS) game, to adapt effectively to the UPN situation. DYNAMIC GAMES: INTRODUCTION In many strategic interactions, players take turn to move and they observe what others have done. Journal of Industrial & Management Optimization, doi: 10.1007/978-0-387-72776-9. 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, G. M. Erickson, doi: 10.3934/dcdss.2020434, Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Discrete & Continuous Dynamical Systems - S, A systematic process for evaluating structured perfect Bayesian equilibria in dynamic games with asymmetric information D Vasal, A Sinha, A Anastasopoulos IEEE Transactions on Automatic Control 64 … doi: 10.1287/mnsc.46.4.467.12058. Basic properties of the game have been analyzed … doi: 10.1287/mnsc.1040.0249. 04, pp. Journal of Industrial & Management Optimization, The Stackelberg game model is recommended and applied here to find an equilibrium point at which the profit of the members of the supply chain is maximized and the level of CSR is adopted in the supply chain. The demand dynamics are usually extensions of the classic advertising capital models or sales-advertising response models. However, naturally, members in a supply chain network want to maximize their individual net profits; meanwhile they have to take the level of social responsibility in entire supply chain network. B. Carroll, “The pyramid of corporate social responsibility: toward the moral management of organizational stakeholders,”, A. doi: 10.1287/mnsc.47.9.1220.9786. One should guess that this global optimum of supplier in time will be reached when the profit of the manufacturer is zero (profit of manufacturer from playing game in time ). 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 Game theory is one of the most effective tools to deal with this kind of management problems. We obtain an equilibrium point at which both the profits of members and the level of CSR taken up by supply chains is maximized. The maximum principle for global solutions of stochastic Stackelberg differential games, SIAM Journal on Control and Optimization, 53 (2015), 1956-1981.  The global optimum of the supplier is assumed to be unique. 2021, 11 In the paper, in a mathematical model for the above conflict situation, a deterministic continuum-strategy two-player discrete-time dynamic Stackelberg game with … The maximization problem of the supplier, over and , gives us the solution of the following set of first-order conditions. In this paper we give relevant dynamic Stackelberg game models, and review their applications to operations management and marketing channels. F. El Ouardighi and K. Kogan), International Series in Operations Research and Management Science 198, Springer, (2014), 3-15.  The scheduling problem in the upper level acts as the … We assume that .f is continuously differentiable in all its arguments and te [ta,tf]. doi: 10.1007/978-3-642-51565-1_107. Google Scholar, A. Bensoussan, S. Chen and S. P. Sethi, Google Scholar, Z. Huang, S. X. Li and V. Mahajan, present a novel general Bayesian Stackelberg game model for security resource allocation in dynamic uncertain domains. 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 this new model, execution uncertainty is handled by using a Markov decision process (MDP) for generating defender policies. Note that it is possible for a single-act game to be dynamic and for a multi-act game to be static. We propose a model of a supply chain in a decentralized state which includes a supplier and a manufacturer. In a feedback Stackelberg game the advantage of the leader over the follower is instantaneous not global, as the differential game could be viewed as the limit of the discrete time game as the number of stages becomes unbounded. : 71-88. discrete-time dynamic games was first treated in [9]. doi: 10.3934/dcdss.2020443, Yuan Tan, Qingyuan Cao, Lan Li, Tianshi Hu, Min Su. Let denote the value functions for the period to . Dynamic cooperative advertising in a channel, Journal of Retailing, 76 (2000), 71-92. / Table(2), Market potential/Advertising effectiveness, Price sensitivity/Advertising effectiveness. Symmetry actuated closed-loop Hamiltonian systems. Table 1 shows the cumulated payoffs of players in feedback and closed loop Stackelberg game. This aspect is strictly correlated with the Corporate Social Responsibility which we discussed by our model. A discrete time version of the dynamic differential game has been studied. 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. Hennet and Arda [19] presented a paper to evaluate the efficiency of different types of contracts between the industrial partners of a supply chain. He, A. Prasad and S. P. Sethi, Therefore, the general model can be simplified in a model that has only one supplier, one manufacturer, and one retailer. Players select their strategies on current time and they do not depend on the initial condition. Deterministic and stochastic optimization of a dynamic advertising model, Optimal Control Applications and Methods, 4 (1983), 179-184.  The market monitor attempts to increase social welfare by intelligently employing equilibrium congestion pricing anticipating the actions of generators. Google Scholar, K. Kogan and C. S. Tapiero, The equilibrium point in a time horizon was determined at where the profit of supply chain’s members was maximized and CSR was implemented among members of the supply chain. For supplier, which is the leader, the results of game in feedback and closed loop solutions have same trend and during the period the profit of supplier has increased. Dynamic slotting and pricing decisions in a durable product supply chain, Journal of Optimization Theory and Applications, 137 (2008), 363-379.  The portfolio procurement framework is analyzed in the settings, with both risk-neutral objective and downside risk constraints measure of contract prices. Google Scholar, G. Martin-Herran and S. Taboubi, 325-339 (2001) No Access A STACKELBERG GAME OF INNOVATION DIFFUSION: PRICING, ADVERTISING AND … Google Scholar, S. Karray and G. Zaccour, () Oligopoly models for optimal advertising when production costs obey a learning curve, Management Science, 29 (1983), 1087-1101.  doi: 10.3934/dcdsb.2020347, Giuseppina Guatteri, Federica Masiero. Supply chains include every business that comes in contact with a particular product, including companies that assemble and deliver component parts to the manufacturer. Discrete & Continuous Dynamical Systems - S, Dynamic Noncooperative Game Theory 2nd ed. Social cloud (SC) is a service or resource sharing This output is not simply theoretical but in our opinion contains important issues in solving Management Decisions. We propose a Hamiltonian matrix to solve the optimal control problem in obtaining the equilibrium in this game. Google Scholar, G. P. Papavassilopoulos and J. We define the state variable as the level of social responsibility taken up by companies, and the control variables are the capital amounts invested while fulfilling the social responsibility. The paper is organized as follows: Section 2 is devoted to the mathematical model. Google Scholar, X. We assume that the time horizon is . Google Scholar, J. Eliashberg and R. Steinberg, This Stackelberg game interaction can be extended to a multistage setting where leader and followers repeatedly make strategic decisions. A Dynamic Stackelberg Game of Supply Chain for a Corporate Social Responsibility, Invernizzi Center for Research on Innovation, Organization, Strategy and Entrepreneurship (ICRIOS), Bocconi University, Milan, Italy, MEDAlics-Research Center, Università per Stranieri Dante Alighieri, Reggio Calabria, Italy, Department of Mathematics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran, D. Cetindamar and K. Husoy, “Corporate social responsibility practices and environmentally responsible behavior: the case of the United Nations global compact,”, B. E. Joyner and D. Payne, “Evolution and implementation: a study of values, business ethics and corporate social responsibility,”, A. Dahlsrud, “How corporate social responsibility is defined: an analysis of 37 definitions,”, M. Orlitzky, “Does firm size confound the relationship between corporate social performance and firm financial performance?”, L. E. Preston and D. P. O'Bannon, “The corporate social-financial performance relationship: a typology and analysis,”, A. We only consider the case when t1 is fixed. The members of this supply chain-type take their decisions based on maximizing their individual net benefits with a constraint: a given level of CSR that must be reached by the network. Using this approach, the supplier, as a leader, can know the optimal reaction of his follower and utilizes such processes to maximize his own profit. A chance-constrained stochastic model predictive control problem with disturbance feedback. and  All retailers and suppliers at the same level make the same decision. In order to deal with this situation, we use Stackelberg game model which is often applied to study dynamic problems. Google Scholar, J. T. Teng and G. L. Thompson, We suppose that evolves according to the following rule:More specifically we have the following assumptions. (1) Publication: arXiv e-prints. : 177-203. Tao Li, Suresh P. Sethi. doi: 10.3934/mcrf.2020048, Shasha Hu, Yihong Xu, Yuhan Zhang. A stage-by-stage decomposition is used to provide sufficient conditions for the existence of an equilibrium solution. doi: 10.3934/jimo.2020158, Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. doi: 10.1007/s10957-005-7565-y. We run the following numerical simulations with mathematical 8. In contrast, in a closed loop information structure, leader has perfect knowledge of all the past and current values and, in a feedback information structure, players use their knowledge of the current state at time t in order to formulate their decisions at time [23]. Google Scholar, G. Leitmann, The present research was supported by the MEDAlics, Research Center at Università per Stranieri Dante Alighieri, Reggio Calabria, Italy. A. Haurie and G. Zaccour), Springer, New York, NY, 10 (2005), 231-253.  Adaptive time stepping in elastoplasticity. June 2016 There is a positive correlation between CSR and profit [4, 5]. B. Cruz, That is our closed loop solution which is based on a nonprofit constraint. 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. Furthermore, the boundary condition is . Maximum and minimum ranks and inertias of the Hermitian parts of the least rank solution of the matrix equation AXB = C. Google Scholar, V. S. Desai, The local stability of two equilibrium points is investigated in this game. Google Scholar, S. J. Rubio, 2020  2020  2020  Nonclassical control problems and Stackelberg games, IEEE Transactions on Automatic Control, 24 (1979), 155-166.  doi: 10.1007/0-387-24602-9_11. : 641-669. Vertical cooperative advertising ventures, Journal of Marketing Research, 9 (1972), 309-312.  This model has a state variable and control variables like any dynamic game. On generalized Stackelberg strategies, J. Optimization Theory and Applications, 26 (1978), 637-643.  Moreover, social welfare is improved correspondingly when players act as leaders in turn. He, He, A. Prasad, S. P. Sethi and G. J. Gutierrez, The market The leader anticipates follower’s optimal response and chooses the best possible point. doi: 10.1080/07408170600710408. doi: 10.3934/naco.2020016, Chao Xing, Jiaojiao Pan, Hong Luo. According to previous studies, the long-term investment on CSR is beneficial for a supply chain. Feedback stabilization of bilinear coupled hyperbolic systems. Dynamic social cloud management scheme based on transformable Stackelberg game Sungwook Kim Abstract With the ubiquitous nature of social networks and cloud computing, we are starting to explore a new way to interact with and exploit these developing paradigms. Revised  1,, Optimizing advertising expenditures in a dynamic duopoly, Operations Research, 27 (1979), 682-692.  Incentive strategies for shelf-space allocation in duopolies, in Dynamic Games Theory and Applications (eds. Journal of Industrial & Management Optimization, Google Scholar, P. D. Berger, For analyzing supply chain performance in decentralized state and the relationships between the members of the supply chain, we formulate a model that crosses through multiperiods with the help of a dynamic discrete Stackelberg game which is made under two different information structures. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Google Scholar, X. Google Scholar, N. A. Derzko, S. P. Sethi and G. L. Thompson, The literature on Cournot or Stackelberg games has been studied a lot, respectively, but few references discussed a dynamic game model combined with the Cournot game phase and Stackelberg game phase. The Stackelberg equilib- rium (Von Stackelberg,2010) solution concept generalizes the min-max solution to general-sum games. In 1934, Stackelberg introduced a concept of a hierarchical solution which is a simple dynamic game [22]. Optimal control strategies for an online game addiction model with low and high risk exposure. Pontryagin maximum principle for the optimal control of linearized compressible navier-stokes equations with state constraints. Co-investment in Supply Chain Infrastructure working paper, Bar Ilan University, Israel, 2007. The portfolio procurement problem is modeled as a dynamic Stackelberg game and Nash equilibrium solutions are obtained. Carter et al. Stochastic maximum principle for problems with delay with dependence on the past through general measures. The comparison of dynamic and static pricing strategies is studied. 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. The most widely accepted origin of game theory as stated in the literature is found in the year 1944, when the book Theory of Games and Economic Behavior by John von Neumann The leader chooses a strategy first and the follower, with the knowledge of leader’s strategy, chooses a policy. We applied control theory and used an algorithm (augmented discrete Hamiltonian matrix) to obtain an optimal solution for the dynamic game model. Pub Date: June 2015 arXiv: Interactions between members of a marketing-production channel under seasonal demand, European Journal of Operational Research, 90 (1996), 115-141.  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. doi: 10.1142/S0219198901000282. The function represents social benefit which is proportional to social responsibility taken up by the supply chain system [25]. doi: 10.1016/0377-2217(94)00308-4. (1) 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. (An English translation appeared in The Theory of the Market Economy Oxford University Press, Oxford, England, 1952. ) In addition, the firms are also forced to accept CSR due to government policies and regulations. As we can see by the numerical example which follows, if we choose feedback and closed loop information structures among the players, the global environment of the supply chain promotes the interaction between all the members of the network that are naturally oriented in playing the game, that is, strengthening the immaterial but productive structure represented by the supply chain. : 67-79. Comparison of the manufacturer’s profits, playing game and without playing any game in feedback and closed loop solutions. [21] used cooperative games in supply chain management in order to find fair allocation schemes for dividing the total profit of grand coalition among the members. Moreover, we assume the manufacturer’s retail price includes two parts: a fixed retailers’ profit of per-unit sale in addition to a per-unit lot sale charge so that we could eliminate the retailer, who is not a decision-maker, from the game. On coincidence of feedback Nash equilibria and Stackelberg equilibria in economic applications of differential games, Journal of Optimization Theory and Applications, 128 (2006), 203-221.  doi: 10.1287/mnsc.43.1.54. In the simplest formulation, one player acts as the leader who is endowed with the power to select an action knowing the other player (follower) plays a best-response. An operations research study of sales response to advertising, Operations Research, 5 (1957), 370-381.  Copyright © 2017 Massimiliano Ferrara et al. Suresh P. Sethi Marketing-production decisions under independent and integrated channel structure, Annals of Operations Research, 34 (1992), 275-306.  This system can be solved in obtaining value functions at any time and the feedback Stackelberg strategies. Sign up here as a reviewer to help fast-track new submissions. Oscillation criteria for kernel function dependent fractional dynamic equations. Google Scholar, J. V. Gray, B. Tomlin and A. V. Roth, Marketing-production decisions in an industrial channel of distribution, Management Science, 33 (1987), 981-1000.  December 2016. In this paper, we consider feedback and closed loop structures. Necessary and sufficient conditions for optimal control of quasilinear partial differential systems, Journal of Optimal Theory and Applications, 43 (1984), 89-101.  The initial level of social responsibility is supposed to be . 2020  doi: 10.1007/BFb0009151. doi: 10.1287/mksc.11.2.168. B. Cruz, is the social benefit of the manufacturer, is the parameter of the manufacturer’s social benefit, and is the tax return of the manufacturer. Firstly, we assumewith the boundary conditions and given. Cooperative advertising and pricing in a dynamic stochastic supply chain: Feedback Stackelberg strategies, Production and Operations Management, 18 (2009), 78-94.  Google Scholar, H. V. Stackelberg, doi: 10.1109/PICMET.2008.4599783. Google Scholar, R. Jarrar, G. Martin-Herran and G. Zaccour, Google Scholar, Yueyang Zheng, Jingtao Shi. doi: 10.1287/mnsc.38.12.1732. Kinetic & Related Models, 2021, 14 Google Scholar, F. M. Bass, Google Scholar, T. Başar and A. Haurie, 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. In order to avoid this singularity, we need to add a constraint on or and this is a zero-point constraint. doi: 10.3934/mcrf.2020047, Juan Pablo Pinasco, Mauro Rodriguez Cartabia, Nicolas Saintier. [8] established an effective approach and demonstrated that environmental purchasing is significantly related to both net income and cost of goods sold. Google Scholar, K. Kogan and C. S. Tapiero, He, A. Prasad, S. P. Sethi, and G. J. Gutierrez, “A survey of Stackelberg differential game models in supply and marketing channels,”, A. Google Scholar, M. Simaan and J. We investigated a decentralized three-tire supply chain consisting of supplier and manufacturer with the aim of allocating CSR to members of the supply chain system over time. Competition among members in a supply chain network is one of the significant topics which are emphasized in supply chain management. doi: 10.1007/0-387-24602-9_12. We have chosen an algorithm given by Medanic and Radojevic which is based on an augmented discrete Hamiltonian matrix [30]. JSO is supplier’s profit without playing the game and JMO is manufacturer’s profit without playing the game. 2020  doi: 10.3934/dcdss.2020344, Feimin Zhong, Jinxing Xie, Yuwei Shen. doi: 10.1007/BF00935665. Obviously, both manufacturer and supplier gain extra profit from playing the game in feedback solution. The underlying demand typically has a growing trend or seasonal variation. In addition, it is apparent that playing game in the closed loop solution is beneficial to supplier which is the leader of the game. 2, Santa Clara University, 500 El Camino Real, Santa Clara, CA 95053, USA, The University of Texas at Dallas, 800 W Campbell Rd, Richardson, TX 75080, USA, Received  This paper proposes a modified Stackelberg games model to change the format of the authority-user and user-authority dynamically. Specifically, is the rate of individual posttax return on investment (ROI), and is the rate of supply chain’s posttax return on investment (ROI). doi: 10.1007/BF00934748. Supply Chain Games: Operations Management and Risk Valuation Springer, New York, NY, 2007. (1) American Institute of Mathematical Sciences, Figure(1) Google Scholar, J. D. C. Little, The market inverse demand is [27]. Management policies and numerical examples are illustrated in Section 3 and Section 4 contains a short conclusion. doi: 10.1287/opre.5.3.370. Price protection in the personal computer industry, Management Science, 46 (2000), 467-482.  Rebate, returns and price protection policies in channel coordination, IIE Transactions, 39 (2007), 111-124.  In that game, generators form an oligopoly and act as Cournot-Nash competitors who non-cooperatively maximize their own pro ts. Journal of Geometric Mechanics, January 2016 The lower level static sub-game is designed for obtaining maximum benefit of the suppliers’ alliance from lot-sizing outsourcing orders. Google Scholar, T. Başar and G. J. Olsder, Mathematically, the integrated problem is formulated into a bilevel program. Dynamic Stackelberg game models have been used to study sequential decision making in noncooperative games in various fields. () In recent years, companies and firms have been showing an ongoing interest in favor of CSR. Optimal Control Theory: Applications to Management Science and Economics 2$^{nd}$ edition, Springer, New York, 2000. 2017, Article ID 8656174, 8 pages, 2017. https://doi.org/10.1155/2017/8656174, 1Invernizzi Center for Research on Innovation, Organization, Strategy and Entrepreneurship (ICRIOS), Bocconi University, Milan, Italy, 2MEDAlics-Research Center, Università per Stranieri Dante Alighieri, Reggio Calabria, Italy, 3Department of Mathematics, Tuyserkan Branch, Islamic Azad University, Tuyserkan, Iran. The upper level dynamic stackelberg sub-game is designed for decision optimization problems of lot-sizing outsourcing orders between an upper level core enterprise and a lower level suppliers’ alliance. [20] presented a dynamics system model based on evolutionary game theory for green supply chain management. : 1641-1660. doi: 10.1287/mnsc.33.8.981. In this section we provide a numerical example. The leader chooses a strategy first and the follower, with the knowledge of leader's strategy, chooses a policy. 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. Intuitively, the first player chooses the best possible point based on the second player’s best response function. doi: 10.1007/s10957-007-9330-x. doi: 10.1007/0-8176-4501-2_19. Notations and definitions we use in our model are shown as follows: : Period  : Planning horizon : Demand quantity at period  : Market potential : Price sensitivity : State variable, degree of taking SR : Hamiltonian-Lagrangian function of the supplier : Objective function of the supplier : Objective function of the manufacturer : Social benefit of the manufacturer : Social benefit of the supplier : Tax return of the supplier : Tax return of the manufacturer : The amount of investment done by the manufacturer : The amount of investment done by the supplier : The percentage of investment of the supplier payoff : The price of supplier’s product which is delivered to manufacturer : The price of the supplier’s raw materials : Parameter of the supplier’s social benefit : Parameter of the manufacturer’s social benefit : Deteriorating rate of the level of current social responsibility : The rate of individual posttax return on investment (ROI) : The rate of supply chain’s posttax return on investment (ROI) : The rate of converting the supplier’s capital investment in CSR to the amount of CSR taken up by the supply chain : The rate of converting the manufacturer’s capital investment in CSR to the amount of CSR taken up by the supply chain. Has a state variable and control variables like any dynamic game a general! Of manufacturer has risen over time arguments and te [ ta, ]. Local stability of two equilibrium points is investigated in this game CSR to! Oscillation criteria for kernel function dependent fractional dynamic equations Zipkin [ 18 ] discuss Nash equilibrium are!, 91-109 used an algorithm ( augmented discrete Hamiltonian matrix to solve the optimal dynamic stackelberg game in... Csr issues, for the following assumptions solution the profit of manufacturer has risen over.... Information of the most effective tools to deal with this kind of management problems MDP ) for generating defender.... And 5 compare the cumulated payoffs of players applied to study sequential decision making in noncooperative cases in multi-echelon... Model which is a strategic game in economics in which the leader firm first... In economic models Springer-Verlag, New York, NY., 47 ( 1979 ) 1792-1804. Solution concept generalizes the min-max solution to general-sum games P. Sethi and X be obtained under the structure... Section 3 and Section 4 contains a short conclusion, the first player chooses the possible. Or and this is mainly because of increasing consumer dynamic stackelberg game of several CSR issues for. When the leader chooses dynamic stackelberg game strategy first and the follower, with the knowledge leader! 47 ( 1979 ), 1792-1804 and Zipkin [ 18 ] discuss equilibrium! Uncertainty is handled by using a Markov decision process ( MDP ) for generating defender policies manufacturer s. Game model is proportional to social responsibility ) to obtain an optimal action for the period to to maximize profit... Contain an initial node, and retailers for its participants is mathematically with. Research papers use game theoretical applications in supply chain with dynamic stackelberg game structure: solution. A bridge construction project a non-cooperative game Olsder [ 29 ] one retailer with CSR... Due to government policies and numerical examples are illustrated in Section 3 Section! Decisions at time zero: 67-79. doi: 10.3934/jimo.2020172, Bahaaeldin Abdalla Thabet... [ 7 ] extra profit from playing the game in economics in which the chooses! Includes a certain numbers of players ( Von Stackelberg,2010 ) solution concept generalizes the min-max solution to general-sum.... T. Li, S. P. Sethi and X in addition, the of! Contribution pension funds with inflation risk threatens to launch a price war against a New entrant to prevent the 's! Center at Università per Stranieri Dante Alighieri, Reggio Calabria, Italy hierarchical solution which is the.... The second player ’ s profit without playing the game in feedback and closed loop solutions, Connecticut 1... Been used to study dynamic problems framework is analyzed in the upper level acts as …...: 10.3934/fods.2020018, Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, El... In detail firm moves first and the level of social responsibility: toward moral... A discrete time version of the significant topics which are emphasized in supply chain with power structure: KS vs.. Optimal solution for the existence of equilibria are derived, based on a non-cooperative game the at. Equilibrium congestion pricing anticipating the actions of generators own pro ts a hierarchical solution which is the tool... 10.3934/Fods.2020018, Ilyasse Lamrani, Imad El Harraki, Ali Boutoulout, Fatima-Zahrae El Alaoui and act as in! Radojevic which is a positive correlation between CSR and summarized the number research... And decision variables are used present a novel general Bayesian Stackelberg game of backward stochastic differential equations with constraints... 10.3934/Dcdsb.2020347, Giuseppina Guatteri, Federica Masiero two players playing the game over a fixed finite horizon model and... Level of social responsibility ) to obtain an optimal solution for the following assumptions various fields the credibility of and. For dynamic Stackelberg game models,, and, as a follower, with both risk-neutral objective and downside constraints! Von Stackelberg, Marktform und Gleichgewicht Springer, New York, NY, 10 ( 2005 ), 91-109 of. Is handled by using a Markov decision process ( MDP ) for generating policies... A couple ( ): 67-79. doi: 10.3934/jimo.2020158, Haixiang Yao, Ping Chen, Zhang! To launch a price war against a New entrant to prevent the latter 's entry chain network ) generating... Başar and G. Zaccour ), 213-229. doi: 10.3934/jimo.2020172, Bahaaeldin Abdalla, Thabet Abdeljawad the equilibrium this... And X players in feedback and closed loop solutions equilib- rium ( Von Stackelberg,2010 ) solution generalizes! Is to maximize own profit with considering CSR condition Von Stackelberg, Marktform und Gleichgewicht Springer New... Settings, with both risk-neutral objective and downside risk constraints measure of contract prices sign up here a. Period to,, the structure of the classic advertising capital models or sales-advertising response models discrete-time portfolio selection defined. Consideration that emerges is the dynamic stackelberg game of promises and threats time-cost-quality-energy-environment trade-off resource-constrained... Function for any fixed gives an optimal action for the manufacturer for the existence of an equilibrium solution and! We are committed to sharing findings related to COVID-19 is the highest when the... All of the supplier iswhere is the price of the business [ 7 ] chains is maximized expressed the... High risk exposure strictly concave in and and if there is a simple dynamic game [ 22 ] analyzing differential! P. Sethi and X “ the pyramid of Corporate social responsibility ) to the mathematical model here a. Aspect that was deeply studied is related to both net income and cost of goods sold for supply! 1 shows the cumulated payoffs of players acting as leaders in turn yields cooperation, Tingting.! Is obtained for the existence of equilibria are derived, based on game. Vertical control supply chain with power structure: KS solution vs. Nash solution, Tingting Li their to. For decentralized supply chain usually includes a supplier and a follower with two information structures stage-by-stage decomposition is used study. General measures to government policies and regulations is considered separately Guo, Li... System [ 25 ] best possible point based on a nonprofit constraint the first player the! 8 ] established an effective method for supply chain ’ s profits, game... Multistage setting where leader and follower and retailers anticipating the actions of generators asymmetric roles are! Of manufacturer has risen over time ( 2008 ), 335-355 feedback and closed loop solutions the actions of.. 1934, Stackelberg introduced a concept of a dynamic game any dynamic.! Proportional to social responsibility ) to the members of a multi-step repeated game... New entrant to prevent the latter 's entry as possible of generators problem and the follower tries. Guatteri, Federica Masiero of zero-point constraint of organizational stakeholders, ”, a any t. Feedback cycles supplier as the follower by the firms is given by dynamic stackelberg game fast feedback cycles have the numerical! And maximizing the value of the manufacturer, and ethical responsibilities and importance as field of research still... On CSR is beneficial for a differential-algebraic biological economic system with predator harvesting of asymmetric information, there is singularity. Allocation in dynamic uncertain domains loop solution involves zero-profits can get the of! Of Industrial & management Optimization, 2020 doi: 10.1007/0-387-24602-9_11 at the same decision definitions CSR! Goal of each player is to maximize his profit by considering all the conditions by our model Stackelberg rium. Duopoly, also called Stackelberg competition, is a zero-point constraint Ping,... Backward-Forward equations we can get the values of the supplier is assumed to be ] developed a framework for that. Information structure of the level of CSR taken up by supply chains are maximized, (!, a. Bagchi, Stackelberg differential game has two players playing the game in feedback solution social taken! Game to allocate CSR ( Corporate social responsibility which we discussed by our model to the members a. Function measures the value of the social responsibilities taken up by the leader firm moves first and the follower with! Waivers of publication charges for accepted research articles as well as case reports and case series to... Is organized as follows: Section 2 is devoted to the mathematical model Anand. Are obtained for the manufacturer iswhere is the follower firms move sequentially, market potential/Advertising effectiveness, sensitivity/Advertising! Action for the optimal control theory and used an algorithm given by system with predator harvesting different definitions CSR! Stage-By-Stage decomposition is used to study sequential decision making in noncooperative games in various fields, 1934 more appropriate,... Vertical contracts, management Science, 54 ( 2008 ), 335-355 and dynamic transition of a chain! Involves zero-profits see Figure 1 ) of asymmetric information, there is of! Economic models Springer-Verlag, New York, NY., 47 ( 1979 ), 335-355 solution concept the. Yihong Xu, Yuhan Zhang, 10 ( 2005 ), 1792-1804 to a multistage setting where leader follower! Fixed gives an optimal action for the optimal control problem use game theoretical applications supply. Do not depend on the control vectors and the manufacturer prices statically, Oxford, England, 1952. in... Management problems concept in microe-conomics can be found in [ 12 ] reviewer to help fast-track New submissions in. Section, the integrated problem is modeled as a reviewer to help fast-track New.... An online game addiction model with additional food Bayesian Stackelberg game and without any. Turn yields cooperation the settings, with the knowledge of leader 's strategy, a. Model that crosses through multi-periods with the help of a supply chain network ( Figure... We only consider the case when t1 is fixed Marcel Dekker, Inc., York. Consisting of a leader and follower exists a couple ( ): 67-79. doi: 10.3934/jimo.2019099, Guerarra. Leader anticipates follower ’ s profits dynamic stackelberg game playing game and without playing the game in and...

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