Geodesic
Competitive and cooperative behavior in distribution networks
Contributions to game theory and management, Tome 11 (2018), pp. 73-102.

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This paper considers the problem of cooperation in supply networks. The model is based on distribution network, which includes several manufactures, single distributor and multi retailers, operated and competed in consumer markets that are functioning according to the Cournot model with the linear demand. All participants in a chain are trying to maximize their profit. A multi-stage hierarchic game was carried out. At the first step, we construct the competitive solution for such supply network as the perfect Nash equilibrium in the multi-step hierarchical game in the closed form. At the second step, we construct the cooperative solution for the network, where winnings of all participants in the found perfect Nash equilibrium are considered as the status quo point. Cooperative decision we calculate in the form of the weighted Nash bargaining solution, which comes down to the solution of a separable nonlinear programming problem. Numerical example for the network shows that cooperative decision is more profitable than competitive decision for all participants.
Keywords: distribution network, competitive and cooperative decisions, multi-stage hierarchical game, perfect Nash equilibrium, weighted Nash bargaining solution. 
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Yulia Lonyagina; Natalia Nikolchenko; Nikolay Zenkevich. Competitive and cooperative behavior in distribution networks. Contributions to game theory and management, Tome 11 (2018), pp. 73-102. http://geodesic.mathdoc.fr/item/CGTM_2018_11_a6/

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