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

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 30 اردیبهشت 1404

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.92290.1601

نویسندگان

Marjan Jashnesadeh؛ Zahra Nikooeinejad yazdi^* ؛ Ghasem Barid loghmani

Department of Mathematical Sciences, Yazd University, Yazd, Iran.

چکیده

In this paper, we reconsider the sustainable cooperation among 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 introduced by \cite{Hafezalkotob} in the framework of cooperative differential games on a network, which derives 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 $\tau$-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 is affected by the sensitivity parameters of consumers to companies. Furthermore, we demonstrate that the allocations of the companies in the cooperative game, only for the grand coalition, will be greater than in the non-cooperative one. We find that the greater the coalition, the greater the gains from cooperative advertising. We also demonstrated that for the higher product price, the greater Shapley and $\tau$-values are attributed to the firms.

کلیدواژه‌ها

A new generalized advertising model؛ Cooperative differential game؛ Network؛ Core؛ Shapley value