A new generalized model of cooperation of advertising companies based on differential games on networks

Iranian Journal of Numerical Analysis and Optimization

مقاله 10، دوره 15، Issue 3 - شماره پیاپی 34، آذر 2025، صفحه 1116-1144   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92290.1601

نویسندگان

M. Jashnesade؛ Z. Nikooeinejad^* ؛ G.B. Loghmani

Department of Applied Mathematics, Faculty of Mathematical Sciences, Yazd University, Yazd, Iran.

چکیده

In this paper, we reconsider the sustainable cooperation of advertising companies problem on a network of companies and consumers. The aim of this paper is to investigate cooperation and profit distribution within networks involving companies and consumers with asymmetric roles and to compare two scenarios based on advertising efficiency. We extend a model in the framework of cooperative differential games on network, which derive analytically the construction of the characteristic function. Unlike previous dynamic marketing models that all firms advertise for homogeneous consumers and they view companies as identical, in the proposed generalized model, we assume that companies and consumers are heterogeneous players in the network. The Shapley value, Core and τ -value are obtained analytically. A numerical simulation of the proposed model for a graph of advertising firms and consumers with different parameters is presented to obtain sensitivity analysis results. The results show that the optimal cooperative advertisement rate of firms are affected by the sensitivity parameters of consumers to companies. Furthermore, we demonstrate that the allocations of the companies in the cooperative game only for grand coalition will be greater than in the non-cooperative one. We find that the greater the coalition, the more gains from cooperative advertising. We also demonstrated that for the higher product price, the greater Shapley and τ -values attributed to the firms.

کلیدواژه‌ها

Differential game؛ Cooperative advertising؛ Shapley value؛ Network

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