Specifically, all of the social responsibilities taken up by the firm at period can be expressed as the investment . Google Scholar, J. D. C. Little, B. Cruz, 2020  325-339 (2001) No Access A STACKELBERG GAME OF INNOVATION DIFFUSION: PRICING, ADVERTISING AND … Journal of Industrial & Management Optimization, Superposition principle and schemes for measure differential equations. doi: 10.3934/jgm.2020030, Zhiyan Ding, Qin Li, Jianfeng Lu. Therefore, consequently the model has only one supplier, one manufacturer, and one retailer. chastic dynamic Stackelberg games is discussed in detail. Note that it is possible for a single-act game to be dynamic and for a multi-act game to be static. 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. () Comparison of the manufacturer’s profits, playing game and without playing any game in feedback and closed loop solutions. JSO is supplier’s profit without playing the game and JMO is manufacturer’s profit without playing the game. A chance-constrained stochastic model predictive control problem with disturbance feedback. 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.  Channel coordination through a revenue sharing contract in a two-period newsboy problem, European Journal of Operational Research, 198 (2009), 822-829.  Feedback Stackelberg solutions of infinite-horizon stochastic differential games, in Models and Methods in Economics and Management Science (eds. A stage-by-stage decomposition is used to provide sufficient conditions for the existence of an equilibrium solution. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. 2021, 14 Discrete & Continuous Dynamical Systems - S, Google Scholar, W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, in Stochastic Modelling and Applied Probability (eds. In Stackelberg game, under the feedback structure of information assumption that the players use their knowledge of the current state at time in order to formulate their decisions at time . The Stackelberg leadership model is a strategic game in economics in which the leader firm moves first and then the follower firms move sequentially. 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. These conditions provide a challenge. The Theory of the Market Economy translated by Peacock A. T. , William Hodge and Co. , London, 1952. In this paper we give relevant dynamic Stackelberg game models, and review their applications to operations management and marketing channels. Google Scholar, X. 2020  This is because unlike other games, in such dynamic games of asymmetric information, there is coupling of players’ strategies across time. Mathematically, the integrated problem is formulated into a bilevel program. Kinetic & Related Models, 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. In order to deal with this situation, we use Stackelberg game model which is often applied to study dynamic problems. Supply chain efficiency is the highest when only the manufacturer prices statically. Second, we study the problem of computing a Stackelberg equilibrium for this game and exploit problem We propose a Hamiltonian matrix to solve the optimal control problem in obtaining the equilibrium in this game. Table 1 shows the cumulated payoffs of players in feedback and closed loop Stackelberg game. Google Scholar, S. J. Rubio, The present research was supported by the MEDAlics, Research Center at Università per Stranieri Dante Alighieri, Reggio Calabria, Italy. [8] established an effective approach and demonstrated that environmental purchasing is significantly related to both net income and cost of goods sold. Electronic Research Archive, : 75-86. Cachon and Zipkin [18] discuss Nash equilibrium in noncooperative cases in a supply chain with one supplier and multiple retailers. B. Carroll, “A three-dimensional conceptual model of corporate performance,”, S. Frost and M. Burnett, “Case study: the apple iPod in China,”, R. Aydin, C. K. Kwong, and P. Ji, “Coordination of the closed-loop supply chain for product line design with consideration of remanufactured products,”, K. Kogan, Y. Perlman, and S. Hovav, “Equilibrium replenishment in a supply chain with a single distributor and multiple retailers,”, J. Ma and H. Wang, “Complexity analysis of dynamic noncooperative game models for closed-loop supply chain with product recovery,”, D. Yang, J. Jiao, Y. Ji, G. Du, P. Helo, and A. Valente, “Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game,”, G. P. Cachon and P. H. Zipkin, “Competitive and cooperative inventory policies in a two-stage supply chain,”, J.-C. Hennet and Y. Arda, “Supply chain coordination: a game-theory approach,”, Y. Tian, K. Govindan, and Q. Zhu, “A system dynamics model based on evolutionary game theory for green supply chain management diffusion among Chinese manufacturers,”, S. Ghadimi, F. Szidarovszky, R. Farahani, and A. Y. Khiabani, “Coordination of advertising in supply chain management with cooperating manufacturer and retailers,”, X. In that game, generators form an oligopoly and act as Cournot-Nash competitors who non-cooperatively maximize their own pro ts. Stackelberg game involves players with asymmetric roles which are called leader and follower. The optimal control theory is the standard tool for analyzing the differential game theory [24]. doi: 10.1109/PICMET.2008.4599783. Markov perfect equilibrium advertising strategies of Lanchester duopoly model: A technical note, Management Science, 50 (2004), 995-1000.  doi: 10.1016/S0377-2217(02)00641-0. The accumulation of the level of social responsibility taken up by the firms is given by . doi: 10.3934/krm.2020051, Youming Guo, Tingting Li. , We assume that the time horizon is . () Google Scholar, T. Li, S. P. Sethi and X. The members of a supply chain play games with each other to maximize their own profits; thus, the model used was a long-term coinvestment game model. We are committed to sharing findings related to COVID-19 as quickly as possible. We obtain an equilibrium point at which both the profits of members and the level of CSR taken up by supply chains are maximized. The members of a supply chain take their decisions based on maximizing their individual net benefits. That is our closed loop solution which is based on a nonprofit constraint. Linear quadratic differential games with mixed leadership: The open-loop solution, Numerical Algebra, Control and Optimization, 3 (2013), 95-108.  Google Scholar, G. Martin-Herran and S. Taboubi, International Game Theory Review Vol. Incentives for retailer promotion in a marketing channel, Annals of the International Society of dynamic Games, 8 (2006), 365-378.  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. Google Scholar, F. M. Bass, A subgame must be a well-defined game when it is considered separately. 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. P.-T. Liu and J. G. Sutinen), Marcel Dekker, Inc., New York, NY., 47 (1979), 91-109. 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. Management policies and numerical examples are illustrated in Section 3 and Section 4 contains a short conclusion. doi: 10.1002/oca.4660040207. Recently, based on many interesting social phenomena, Nie proposed a dynamic Stackelberg game with alternating leaders and analysed the properties of the game [2–4]. The manufacturer, as a follower, tries to maximize his profit by considering all the conditions. Moreover, in feedback solution the profit of manufacturer has risen over time. Google Scholar, S. Jorgensen, S. P. Sigue and G. Zaccour, Rebate, returns and price protection policies in channel coordination, IIE Transactions, 39 (2007), 111-124.  Discrete & Continuous Dynamical Systems - S, 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. Furthermore, the boundary condition is . We obtain an equilibrium point at which both the profits of members and the level of CSR taken up by supply chains is maximized. 03, No. He, A. Prasad, S. P. Sethi and G. J. Gutierrez, And Carroll [11, 12] developed a framework for CSR that consists of economic, legal, and ethical responsibilities. Simultaneous price production in channels, Marketing Science, 7 (1974), 335-355. Based on Başar and Olsder [29] is possible only if is strictly concave in and and if there is no singularity. We propose a model of a supply chain in a decentralized state which includes a supplier and a manufacturer. Google Scholar, K. Kogan and C. S. Tapiero, doi: 10.1007/978-0-387-72776-9. Retail promotions with negative brand image effects: Is cooperation possible?, European Journal of Operational Research, 150 (2003), 395-405.  Furthermore, a sustainable supply chain requires consideration of the social aspects of the business [7]. Journal of Industrial & Management Optimization, In particular, we formulate a model that crosses through multi-periods with the help of a dynamic discrete Stackelberg game. In this paper, we establish a dynamic game to allocate CSR (Corporate Social Responsibility) to the members of a supply chain. doi: 10.1007/BF00935665. Evolution Equations & Control Theory, The local stability of two equilibrium points is investigated in this game. In this section, the structure of information is considered closed loop model of Başar and Olsder [29]. Dynamic cooperative advertising in a channel, Journal of Retailing, 76 (2000), 71-92. doi: 10.3934/dcdss.2020323, Copyright © 2020 American Institute of Mathematical Sciences, Primary:91A25, 91A15, 91A23;Secondary:91A1. Dynamic Stackelberg game models have been used to study sequential decision making in noncooperative games in various fields. 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. Supply chains include every business that comes in contact with a particular product, including companies that assemble and deliver component parts to the manufacturer. 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. In this paper, we consider feedback and closed loop structures. Jose B. Cruz Jr.), JAE Press Inc., Connecticut, 1 (1984), 163-201. Incentive strategies for shelf-space allocation in duopolies, in Dynamic Games Theory and Applications (eds. American Institute of Mathematical Sciences, Figure(1) ... than the Stackelberg strategy but it is still more difficult to compute compared , SIAM, Philadelphia, PA, 1999. In the related literature, one can find a lot methods to solve the optimal control problem. Moreover, social welfare is improved correspondingly when players act as leaders in turn. / Table(2), Market potential/Advertising effectiveness, Price sensitivity/Advertising effectiveness. We draw the results of the model, in feedback and closed loop Stackelberg dynamic game. Imperfect Information Dynamic Stackelberg Game Based Resource Allocation Using Hidden Markov for Cloud Computing Abstract: Existing static grid resource scheduling algorithms, which are limited to minimizing the makespan, cannot meet the … : 67-79. It aggravates the double marginalization that … Addiction model with low and high risk exposure iswhere is the highest when only the manufacturer as the chooses... 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This Section, the objective functions are made to depend on the condition... Papers use game theoretical dynamic stackelberg game in supply chain networks under CSR conditions with one leader and follower article. Youming Guo, Tingting Li ] discuss Nash equilibrium in this New model, uncertainty! Is to maximize his profit by considering all the conditions an augmented discrete Hamiltonian matrix ) to obtain optimal!
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