Geodesic
Coordination in supply networks with combined topology
Contributions to game theory and management, Tome 15 (2022), pp. 325-338.

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The paper considers the problem of supply chain coordination in supply networks using the revenue-sharing contract. The supply network has a combined topology and consists of three levels of participants: manufacturers, a distributor, and retailers. The authors consider the companies' performance improvement as the motivation of companies to operate in coordinating conditions. Simulation of contract conditions is implemented for different types of supply networks: from a simple case to a more complex one. The contract procedure is modeled as a game between two companies. The game solution is a set of contract parameters, providing Nash equilibrium, achieving the maximum of the supply network profit and Pareto-optimality of the obtained solution. The results show the application of revenue-sharing contracts in such networks has several peculiarities: the role of a coordinator in the supply network should be performed by a distributor; the distributor, by setting unified revenue shares for all retailers and manufacturers, gets a share of the expected profit of the supply network, each retailer gets a share of the supply network profit for its sales channel, and each manufacturer gets a share of the supply network profit for its product.
Keywords: supply network, motivation, performance, coordination, coordinating contract, revenue-sharing contract. 
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Nikolay A. Zenkevich; Natalia K. Nikolchenko; Irina V. Berezinets; Margarita V. Ivanova. Coordination in supply networks with combined topology. Contributions to game theory and management, Tome 15 (2022), pp. 325-338. http://geodesic.mathdoc.fr/item/CGTM_2022_15_a24/

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