Abstract
Discrete-time game-theoretic models of resource exploitation are treated as dynamic potential games. The players (countries or firms) exploit a common stock on the infinite time horizon. The main aim of the paper is to obtain a potential for the linear-quadratic games of this type. The class of games where a potential can be constructed as a quadratic form is identified. As an example, the dynamic game of bioresource management is considered and the potentials are constructed in the case of symmetric and asymmetric players.
Similar content being viewed by others
References
Rettieva, A.N., Discrete-Time Bioresource Management Problem with Asymmetric Players, Autom. Remote Control, 2014, vol. 75, no. 9, pp. 1665–1676.
Basar, T. and Olsder, G.J., Dynamic Noncooperative Game Theory, New York: Academic, 1982.
Dechert, W.D., Optimal Control Problems from Second Order Difference Equations, J. Econom. Theory, 1978, vol. 19, pp. 50–63.
Dechert, W.D., Noncooperative Dynamic Games: A Control Theoretic Approach, Houston: Univ. of Houston, 1997.
Dragone, D., Lambertini, L., Leitmann, G., and Palestini, A., Hamilton Potential Functions for Differential Games, IFAC Proc. Volumes, 2009, vol. 42, no. 2, pp. 1–8.
Gonzalez-Sanchez, D. and Hernandez-Lerma, O., Dynamic Potential Games: The Discrete-Time Stochastic Case, Dynamic Games Appl., 2014, vol. 4, no. 3, pp. 309–328.
Gonzalez-Sanchez, D. and Hernandez-Lerma, O., Discrete-time Stochastic Control and Dynamic Potential Games: The Euler-Equation Approach, New York: Springer Science & Business Media, 2013.
Monderer, D. and Shapley, L.S., Potential Games, Games Econom. Behav., 1996, vol. 14, pp. 124–143.
Zazo, S., Macua, S.V., Sanchez-Fernandes, M., and Zazo, J., Dynamic Potential Games with Constraints: Fundamentals and Applications in Communications, IEEE Trans. Signal Proces., 2015, vol. 64, no. 14, pp. 3806–3821.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Mazalov, A.N. Rettieva, K.E. Avrachenkov, 2017, published in Matematicheskaya Teoriya Igr i Ee Prilozheniya, 2017, No. 1, pp. 95–107.
Rights and permissions
About this article
Cite this article
Mazalov, V.V., Rettieva, A.N. & Avrachenkov, K.E. Linear-quadratic discrete-time dynamic potential games. Autom Remote Control 78, 1537–1544 (2017). https://doi.org/10.1134/S0005117917080136
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117917080136