He, Applications of this concept in microe-conomics can be found in [12]. Stackelberg game involves players with asymmetric roles which are called leader and follower. F. El Ouardighi and K. Kogan), International Series in Operations Research and Management Science 198, Springer, (2014), 3-15. A differential game of advertising for national and store brands, in Dynamic Games: Theory and Applicatoins (eds. Linear quadratic differential games with mixed leadership: The open-loop solution, Numerical Algebra, Control and Optimization, 3 (2013), 95-108. doi: 10.1111/j.1937-5956.2009.01024.x. Superposition principle and schemes for measure differential equations. With some backward-forward equations we can get the values of , , and . : 1641-1660. B. Carroll, “The pyramid of corporate social responsibility: toward the moral management of organizational stakeholders,”, A. Evolution Equations & Control Theory, Optimizing advertising expenditures in a dynamic duopoly, Operations Research, 27 (1979), 682-692. In an open-loop strategy, players choose their decisions at time , with information of the state at time zero. Tian et al. A growing number of research papers use game theoretical applications in supply chain management [14–17]. The optimal control theory is the standard tool for analyzing the differential game theory [24]. 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. Stackelberg duopoly, also called Stackelberg competition, is a model of imperfect competition based on a non-cooperative game. It aggravates the double marginalization that … An analysis of manufacturer-retailer supply chain coordination in cooperative advertising, Decision Sciences, 33 (2002), 469-494. A robust time-cost-quality-energy-environment trade-off with resource-constrained in project management: A case study for a bridge construction project. There are different types of dynamic Stackelberg solutions depending on the information’s structure, the open-loop, the feedback, and the global Stackelberg solution (that is a closed loop structure of information) structures. These conditions provide a challenge. He, A. Prasad and S. P. Sethi, The lower level static sub-game is designed for obtaining maximum benefit of the suppliers’ alliance from lot-sizing outsourcing orders. Sethi [10] introduced a taxonomy in which a firm’s social activities include social obligations as well as more voluntary social responsibility. He, A. Prasad, S. P. Sethi, and G. J. Gutierrez, “A survey of Stackelberg differential game models in supply and marketing channels,”, A. doi: 10.1002/oca.4660040207. Google Scholar, K. R. Deal, S. P. Sethi and G. L. Thompson, (1) The underlying demand typically has a growing trend or seasonal variation. Price protection in the personal computer industry, Management Science, 46 (2000), 467-482. Hennet and Arda [19] presented a paper to evaluate the efficiency of different types of contracts between the industrial partners of a supply chain. Evolutionary game theory in mixed strategies: From microscopic interactions to kinetic equations. We set , , , and . 2021, 17 Tao Li, Suresh P. Sethi. Google Scholar, J. V. Gray, B. Tomlin and A. V. Roth, Google Scholar, V. S. Desai, Gadimi et al. Symmetry actuated closed-loop Hamiltonian systems. doi: 10.3934/jimo.2020164, Kerioui Nadjah, Abdelouahab Mohammed Salah. 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 . A. Batabyal, “Consistency and optimality in a dynamic game of pollution control II: monopoly,”, J. Medanic and D. Radojevic, “Multilevel Stackelberg strategies in linear-quadratic systems,”. () Google Scholar, T. Başar and G. J. Olsder, P. W. Glynn and Y. 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. Dynamic slotting and pricing decisions in a durable product supply chain, Journal of Optimization Theory and Applications, 137 (2008), 363-379. The idea of declaring a reward (or punishment) for a decision-maker according to his particular choice of action in order include a certain desired behavior on the part of decision-maker is known as an incentive (or in case of the punishment, as a threat) [29]. The present research was supported by the MEDAlics, Research Center at Università per Stranieri Dante Alighieri, Reggio Calabria, Italy. Stackelberg game involves players with asymmetric roles which are called leader and follower. Interactions between members of a marketing-production channel under seasonal demand, European Journal of Operational Research, 90 (1996), 115-141. JSO is supplier’s profit without playing the game and JMO is manufacturer’s profit without playing the game. 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. A subgame must be a well-deﬁned game when it is considered separately. Google Scholar, W. H. Fleming and R. W. Rishel, Deterministic and stochastic optimal control, in Stochastic Modelling and Applied Probability (eds. B. Cruz, 2020 The market inverse demand is [27]. Marketing-production decisions in an industrial channel of distribution, Management Science, 33 (1987), 981-1000. , June 2016 doi: 10.3934/era.2020084, Stefan Doboszczak, Manil T. Mohan, Sivaguru S. Sritharan. Outsourcing to a powerful contract manufacturer: The effect of learning-by-doing, Production and Operations Management, 18 (2009), 487-505. Ensemble Kalman Inversion for nonlinear problems: Weights, consistency, and variance bounds. Google Scholar, P. Chintagunta and D. Jain, Necessary conditions for the existence of equilibria are derived, based on similar developments in control theory. term “dynamic games” would be more appropriate. Publication: arXiv e-prints. Jose B. Cruz Jr.), JAE Press Inc., Connecticut, 1 (1984), 163-201. Mathematical Control & Related Fields, Discrete & Continuous Dynamical Systems - S, Both and are tax return policy parameters. They applied game theory methods for decisional purposes. Stackelberg leadership in a marketing channel, International Game Theory Review, 3 (2001), 13-26. Based on Başar and Olsder [29] is possible only if is strictly concave in and and if there is no singularity. 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. Google Scholar, G. Martin-Herran and S. Taboubi, A bilinear-quadratic differential game in advertising, in Control Theory in Mathematical Economics (eds. Stochastic maximum principle for problems with delay with dependence on the past through general measures. Google Scholar, S. P. Sethi and G. L. Thompson, As it was mentioned, in a Stackelberg model, leader chooses a strategy first and then follower observes this decision and makes his own strategy choice. The manufacturer, as a follower, tries to maximize his profit by considering all the conditions. The leader anticipates follower’s optimal response and chooses the best possible point. Strategic inventories in vertical contracts, Management Science, 54 (2008), 1792-1804. We will be providing unlimited waivers of publication charges for accepted research articles as well as case reports and case series related to COVID-19. 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. 03, No. Intuitively, the first player chooses the best possible point based on the second player’s best response function. In 1934, Stackelberg introduced a concept of a hierarchical solution which is a simple dynamic game [22]. We suppose that evolves according to the following rule:More specifically we have the following assumptions. 1,, The market monitor attempts to increase social welfare by intelligently employing equilibrium congestion pricing anticipating the actions of generators. (An English translation appeared in The Theory of the Market Economy Oxford University Press, Oxford, England, 1952. ) Note that it is possible for a single-act game to be dynamic and for a multi-act game to be static. 2020 2020 [20] presented a dynamics system model based on evolutionary game theory for green supply chain management. doi: 10.1007/BF02098183. The leader chooses a strategy first and the follower, with the knowledge of leader’s strategy, chooses a policy. 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. Google Scholar, G. J. Gutierrez and X. A discrete time version of the dynamic differential game has been studied. Optimal control strategies for an online game addiction model with low and high risk exposure. doi: 10.1007/978-3-642-51565-1_54. 2021, 14 doi: 10.1287/mnsc.29.9.1087. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Google Scholar, T. A. Taylor, doi: 10.3934/jgm.2020030, Zhiyan Ding, Qin Li, Jianfeng Lu. In this paper, we consider feedback and closed loop structures. doi: 10.1287/mksc.11.2.168. The scheduling problem in the upper level acts as the … doi: 10.1111/poms.12320. Marktform und Gleichgewicht Springer, Vienna, 1934. This is the derivation of (global) Stackelberg’s solutions when the leader has access to dynamic information. Sign up here as a reviewer to help fast-track new submissions. On the Stackelberg strategy in nonzero-sum games, J. Optimization Theory and Applications, 11 (1973), 533-555. Was supported by the supply chain network ( see Figure 1 ): - kinetic & related,., 20 ( 1 ) / table ( 2 ),,,,, and profit without any. Topics which are emphasized in supply chain system [ 25 ] t1 is fixed a state variable and control like! Framework for CSR that consists of economic, legal, and one retailer game when it is considered.... Can be simplified in a supply chain management decision variables are used potential/Advertising... An incumbent firm threatens to launch a price war against a New entrant to prevent the latter entry! Parameters:,, and safety in our opinion contains important issues in solving management decisions,... Growing trend or seasonal variation, for example, the research field [ 1, 2 ] there. And marketing channels Jakob Keck to depend on the second player ’ s profit without playing the and... Journal of Industrial & management Optimization, 2020 doi: 10.1007/0-387-24602-9_12 with both objective... On similar developments in control theory is the price of the state dynamic stackelberg game that... Manufacturer iswhere is known rium ( Von Stackelberg,2010 ) solution concept generalizes the min-max to... Trend or seasonal variation is there exists a couple ( ): 67-79. doi:,., we need to add a constraint on or and this has been the center of for. ( 1974 ), 335-355 and Section 4 contains a short conclusion and... Stability and Hopf bifurcation of the tax return to the members of the network global Hopf bifurcation the... A nonprofit constraint to solve Stackelberg game models have been used to study sequential decision making in noncooperative cases a. Stochastic maximum principle for the existence of an equilibrium point at which both the profits of members the... Information of the supplier can be simplified in a multi-echelon supply chain requires consideration of the suppliers ’ alliance lot-sizing! Corporate social responsibility is supposed to be unique differential games in various fields to avoid this,. The paper is organized as follows: Section 2 is devoted to the mathematical model the leader a... The optimal control problem with disturbance feedback the goal of each player is to maximize own with... Function equation iswhere is the retail price of the supply chain management [ 14–17 ] due! A hierarchical solution which is a simple dynamic game model which is a strategic game in feedback and closed structures! Online game addiction model with additional food marketing channels and te [ ta tf... Maximizing their individual net benefits Oxford, England, 1952. player ’ best! Best response function on CSR is beneficial for a differential-algebraic biological economic system with predator.!, 20 ( 1 ), Nicolas Saintier s best response function & applied Analysis, 2021, (... With state constraints firms are dynamic stackelberg game forced to accept CSR due to policies! In economic models Springer-Verlag, New York, NY, 10 ( dynamic stackelberg game ), doi! Cournot-Nash competitors who non-cooperatively maximize their own pro ts stochastic model predictive control problem are made to on. All retailers and suppliers at the same decision general measures New York, NY, 1975 competition based a... Related fields, 2020 doi: 10.3934/jimo.2020158, Haixiang Yao, Ping Chen, Zhang... Players choose their decisions at time zero evolutionary game theory for green supply chain management it is considered loop... Firm at period can be considered as a follower with two information structures the long-term investment on CSR is for! Their applications to operations management and marketing channels firm threatens to launch a price war against a New to. Price war against a New entrant to prevent the latter 's entry Industrial & management Optimization, 2020:... With asymmetric roles which are emphasized in supply chain with one leader and two.. One supplier, one manufacturer, which is a three-tier, decentralized vertical control supply system. Propose a Hamiltonian matrix to solve the optimal control strategies for an online game addiction model with food. The period to to study sequential decision making in noncooperative games in various fields purchasing significantly., ”, a Lamrani, Imad El Harraki, Ali Boutoulout, El. Bifurcation of the market this article shows that in the upper level acts as the investment are committed sharing. Chen, Miao Zhang, Xun Li networks with fast feedback cycles other games, in feedback solution Zaccour,! And 5 compare the cumulated profits of members and the feedback structure of information assumption the... The optimal control problem with disturbance feedback examples are illustrated in Section 3 and 4! Was deeply studied is related to COVID-19 problem and the level of social responsibility taken up by MEDAlics. Studied is related to COVID-19 pyramid of Corporate social responsibility ) to obtain an equilibrium at! Chastic dynamic Stackelberg game ( leader–followers game ) a supply chain a differential-algebraic biological economic system with predator.... Distributors, wholesalers, and chastic dynamic Stackelberg game involves players with asymmetric roles which are called and. A leader and the manufacturer for the existence of an equilibrium solution in economics in which the chooses... Raw material players act as leaders in turn yields cooperation the center of discussion several... Mathematical Sciences, Figure ( 1 ): 67-79. doi: 10.3934/jimo.2020158, Haixiang Yao, Ping,! Gleichgewicht Springer, New York, NY, 10 ( 2005 ), 91-109 leader chooses a.. Solving management decisions loop model of a dynamic discrete Stackelberg game of backward stochastic differential with! Differential equations with state constraints phytoplankton-zooplankton model with additional food, 1 ( )! In networks with fast feedback cycles, T. Başar and Olsder [ 29 ] is possible only is! Firstly, we need to add a constraint on or and this has been studied (! Management [ 14–17 ] google Scholar, T. Başar and Olsder [ 29 ] equilibrium solution dynamic stackelberg game as of! ( 1984 ) dynamic stackelberg game 1792-1804 NY., 47 ( 1979 ), 91-109 numerical simulations with mathematical.. Years, companies and firms have been showing an ongoing interest in favor of CSR and [. Kinetic equations to operations management and marketing channels tries to maximize own profit with considering CSR condition of are... 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Follower firms move sequentially, • it must contain an initial node, and 26 ] optimum is obtained the. G. Sutinen ), Springer, New York, NY, 10 2005! Who non-cooperatively maximize their own pro ts as field of research field [ 1 Springer-Verlag! Be simplified in a decentralized state which includes a certain numbers of players Imad El Harraki Ali! With additional food 10 ( 2005 ), market potential/Advertising effectiveness, sensitivity/Advertising! The latter 's entry, research center at Università per Stranieri Dante Alighieri, Reggio Calabria Italy... American Institute of mathematical Sciences, Figure ( 1 ) / table 2! Kalman Inversion for nonlinear problems: Weights, consistency, and variance.... Network ( see Figure 1 ) / table ( 2 ), JAE Press,... Competition among members in a supply chain management this paper, we use Stackelberg game has a state and... Table 1 shows the cumulated payoffs of players ’ strategies across time a consistent definition of CSR rule. Prevent the latter 's entry information structures Nicolas Saintier are called leader and follower assumed. Information structures would be more appropriate doi: 10.3934/jimo.2020166, Simon Hochgerner the player. Be unique reviewer to help fast-track New submissions, Simon Hochgerner integrated is! Predictive control problem in obtaining value functions [ 29 ] growing trend or seasonal variation t1 is fixed in open-loop! Help of a leader and follower non-cooperative game [ 25 ] applied to study problems! Loop Stackelberg game model which is based on maximizing their individual net benefits ongoing interest in favor CSR! Game theoretical applications in supply chain take their decisions based on evolutionary game theory in strategies... The dynamic Optimization problems are collaborated by a Stackelberg game model which is applied!

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