Mean Field Games With Parametrized Followers

Bensoussan, Alain; Cass, Tony; Chau, Man Ho Michael; Yam, Philip

doi:10.1109/tac.2019.2910945

Cited by 8 publications

(3 citation statements)

References 15 publications

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“…This would offer further insight into the role and value of distributors in an increasingly globalized world, where the transport costs to various markets can differ significantly. This idea could be taken further by considering the problem within a mean-field Stackelberg game framework, as systematically studied in Bensoussan et al (2013Bensoussan et al ( , 2015aBensoussan et al ( , 2020. Along this same vein, we might also consider a manufacturer that produces competing products, say for example smartphones, that the competing brands have contracted with the manufacturer to produce.…”

Section: Discussionmentioning

confidence: 99%

“…This idea could be taken further by considering the problem within a mean‐field Stackelberg game framework, as systematically studied in Bensoussan et al. (2013, 2015a, 2020). Along this same vein, we might also consider a manufacturer that produces competing products, say for example smartphones, that the competing brands have contracted with the manufacturer to produce.…”

Section: Discussionmentioning

confidence: 99%

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Cooperative Advertising in a Dynamic Three‐Echelon Supply Chain

Kennedy

Sethi

Siu

et al. 2021

Production and Operations Management

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We propose a model to assess the value of a distributor in a dynamic stochastic cooperative advertising supply chain in which a manufacturer wholesales its product to a distributor who in turn sells it to a retailer. Moreover and importantly, the distributor also intermediates the pricing and advertising decisions between the manufacturer and the retailer. For the resulting three‐player hierarchical game formulation of the supply chain, we characterize the feedback Stackelberg equilibrium in terms of a system of coupled algebraic equations and show it to admit a unique solution. We find that the value added by the distributor to the supply chain depends critically on the nature of the demand function for the product, a result that has practical implications for the kinds of product where having a distributor is most desirable. Second, our model indicates that the presence of the distributor can enhance the margins of both the retailer and the manufacturer relative to the case of no distributor, and provide explicit conditions for this to occur. Third, we present numerical analysis that indicates that if the distributor generates sufficiently large transportation cost savings, then the three‐echelon supply chain can lead in the long run to higher market awareness, lower advertising expenditure, and higher value extracted, relative to the two‐echelon model. Finally, in addition to retailer advertising that is subsidized by the manufacturer, we also provide the manufacturer an option to do national advertising and show its viability.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Cooperative Advertising in a Dynamic Three‐Echelon Supply Chain

Kennedy

Sethi

Siu

et al. 2021

Production and Operations Management

Self Cite

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“…On the other hand, the mean field term (see the definition (11)) also serves as a feedback mechanism that influences leaders' decisions, whose importance in maintaining the stability of a financial system is highlighted in Cooper [21]. Under a single-leader game, Bensoussan et al [7,8] considered a model where followers are subject to delayed effects from the state dynamics of themselves and the leader; Fu and Horst [26] studied a mean field type leader-follower control problem and its associated McKean-Vlasov forward-backward stochastic differential equations (FBSDEs).…”

Section: Introductionmentioning

confidence: 99%

Office automation at the Department of Management Studies, the University of Hong Kong : a feasibility study

Chu¹,

朱家心²

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This article studies linear-quadratic Stackelberg games between two dominating players (or equivalently, leaders) and a large group of followers, each of them interacting under a mean field game (MFG) framework. Unlike the conventional major-minor player game, the mean field term herein is endogenously determined by the two leaders simultaneously. These homogeneous followers are not cooperative, whereas the two leaders can either compete or cooperate with each other, which are respectively formulated as a Nash and a Pareto game. The complete solutions of the leader-follower game can be expressed in terms of the solutions of some non-symmetric Riccati equations. Conceivably, the two modes of interactions between leaders each has their own merits and neither is always more favourable to the community, i.e., to the followers. While a comparative statics of the effect of different modes of governance on the society is relatively rare in the literature, we attempt to provide some preliminary quantitative analysis on this topic. In particular, under a broad class of practically relevant models, we provide sufficient conditions to decide whether cooperation or competition between leaders is more favourable to the followers via a comprehensive study. Intutively, the relative merits of the two games depend on whether the interests between the two leaders and the followers align with each other. Numerical examples supporting the findings are also provided.

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