Dynamic SPICE-Model of Resource Allocation in Marketing Networks

Authors

  • Movlatkhan T. Agieva Ingush State University
  • Olga I. Gorbaneva South Federal University

DOI:

https://doi.org/10.21638/11701/spbu31.2020.02

Abstract

We consider a dynamic Stackelberg game theoretic model of the coordination of social and private interests (SPICE-model) of resource allocation in marketing networks. The dynamics of controlled system describes an interaction of the members of a target audience (basic agents) that leads to a change of their opinions (cost of buying the goods and services of firms competing on a market). An interaction of the firms (influence agents) is formalized as their differential game in strategic form. The payoff functional of each firm includes two terms: the summary opinion of the basic agents with consideration of their marketing costs (a common interest of all firms), and the income from investments in a private activity. The latter income is described by a linear function. The firms exert their influence not to all basic agents but only to the members of strong subgroups of the influence digraph (opinion leaders). The opinion leaders determine the stable final opinions of all members of the target audience. A coordinating principal determines the firms' marketing budgets and maximizes the summary opinion of the basic agents with consideration of the allocated resources. The Nash equilibrium in the game of influence agents and the Stackelberg equilibrium in a general hierarchical game of the principal with them are found. It is proved that the value of opinion of a basic agent is the same for all influence agents and the principal. It is also proved that the influence agents assign less resources for the marketing efforts than the principal would like.

Keywords:

differential Stackelberg games, marketing, opinion control on networks, resource allocation

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References

Agieva, M.T., A.V. Korolev and G.A. Ougolnitsky (2019). Modeling and Simulation of Impact and Control in Social Networks. In: Modelling and Simulation of Social-Behavioural Phenomena in Creative Societies: First International EURO Mini Conference, MSBC 2019. Vilnius, Lithuania, September 18–20, 2019 Proceedings. Communications in Computer and Information Science (Agarwal, N., L. Sakalauskas and G.-W. Weber, eds), Vol. 1079, pp. 29–40.

Anopchenko, T., O. Gorbaneva, E. Lazareva, A. Murzin and G. Ougolnitsky (2019a). Advanced Solow model as a tool for coordination of interests of spatial economic systems' development (on the materials of the South Russian macro-region). Advances in Systems Science and Applications, 19(4), 1–13.

Anopchenko, T., O. Gorbaneva, E. Lazareva, A. Murzin, G. Ougolnitsky and E. Roshchina (2019b). Dynamic Model of Macroregion Subjects' Interests Coordination. In: Proceedings - 2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency, SUMMA 2019, art. no. 8947516, pp. 141–146.

Chkhartishvili, A., D. Gubanov and D. Novikov (2019). Social Networks: Models of Information Influence, Control, and Confrontation. Springer Publishers.

Gorbaneva, O.I. (2019). Models of social and private interests combining with independent agents. Automation and Remote Control, 80(9), 1745–1753.

Jackson, M. (2008). Social and Economic Networks. Princeton: Princeton University Press.

Long, N.V. (2010). A Survey of Dynamic Games in Economics. World Scientific Publishing Company.

Nisan, N., T. Roughgarden, E. Tardos and V. Vazirani (2007). Algorithmic Game Theory. Cambridge University Press.

Sedakov A.A. and M. Zhen (2019). Opinion dynamics game in a social network with two influence nodes. Applied Mathematics. Computer Science. Control Processes, 15(1), 118–125.

Sukhinov A.I., G.A. Ougolnitsky and A.B. Usov (2020). Methods of Solving the Theoretic Game Models for Coordinating Interests in Regulating the Fishery Industry. Mathematical Models and Computer Simulations, 12(2), 176–184.

Ugol'nitskii G.A. and A.B. Usov (2020). Dynamic Models for Coordinating Private and Public Interests in Economic Corruption. Journal of Computer and Systems Sciences International, 59(1), 39–48.

Zhen, M. (2019). Stackelberg equilibrium in opinion dynamics game in social network with two influence nodes. In: Contributions to Game Theory and Management. Vol. XII. Collected Papers of the Twelfth International Conference "Game Theory and Management" (Petrosyan, L. and N. Zenkevich, eds.), St. Petersburg: Saint Petersburg State University, pp. 29–40.

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Published

2022-02-01

How to Cite

Agieva, M. T., & Gorbaneva, O. I. (2022). Dynamic SPICE-Model of Resource Allocation in Marketing Networks. Contributions to Game Theory and Management, 13. https://doi.org/10.21638/11701/spbu31.2020.02

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Articles