Geodesic
Dynamic network model of production and investment
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 10-26

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The paper studies a dynamic network game that models the competitive behavior of firms in a market. It is assumed that firms, under the condition of simultaneous and independent choice of their actions, implement the behavior that determines their production and investment behavior in each period. The production behavior of the firm reflects the ongoing quantities that it should produce and supply to the market. The investment behavior specifies the ongoing amounts of investment that the firm allocates to the modernization of its production technology in order to prevent it from becoming obsolete. Next, the unit cost is assumed to depend on the firm's investment and the investment of its competitors, which are determined by an exogenous network. Two types of Nash equilibria are characterized: open-loop and feedback. Finally, we analyze the impact of the network and related model parameters on firms' behavior, profits, and competitive advantage.
Keywords: competition, investment, dynamic game, network, Nash equilibrium. 
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     author = {V. A. Kochevadov and A. A. Sedakov},
     title = {Dynamic network model of production and investment},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
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     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a1/}
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V. A. Kochevadov; A. A. Sedakov. Dynamic network model of production and investment. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 19 (2023) no. 1, pp. 10-26. http://geodesic.mathdoc.fr/item/VSPUI_2023_19_1_a1/