Dynamic Games with Incomplete Knowledge in Metric Spaces

Authors

  • Igor Konnov Kazan Federal University

DOI:

https://doi.org/10.21638/11701/spbu31.2022.09

Abstract

We describe a model of a discrete time dynamic system with active elements (players) and states in a metric space. Each state is associated with the common utility value and player shares. Coalitions of players can change the system state, but each move requires their expenses. The players may have only restricted and local knowledge about the system. We define the concept of an equilibrium state in this dynamic game and present iterative algorithms that create feasible trajectories tending to equilibrium states under rather general conditions.

Keywords:

dynamic games, discrete time, incomplete knowledge, utility shares distributions, equilibrium states, solution trajectories

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References

Alpcan T., Boche, H., Honig, M. and H. V. Poor (eds.) (2014). Mechanisms and Games for Dynamic Spectrum Allocation. Cambridge University Press, New York

Kelly, F. P., Maulloo, A. and Tan, D. (1998). Rate control for communication networks: shadow prices, proportional fairness and stability. J. Oper. Res. Soc. 49, 237–252

Konnov, I. V. (2019). Equilibrium formulations of relative optimization problems. Mathem. Meth. Oper. Res. 90, 137–152

Konnov, I. V. (2021). A general class of relative optimization problems. Mathem. Meth. Oper. Res. 93, 501–520

Mazalov, V. V. (2010). Mathematical Game Theory and Applications. Lan', St. Petersburg

Okuguchi, K. and Szidarovszky, F. (1990). The Theory of Oligopoly with Multi-product Firms. Springer-Verlag, Berlin

Peters, H. (2015). Game Theory. Springer-Verlag, Berlin

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Published

2023-01-26

How to Cite

Konnov, I. (2023). Dynamic Games with Incomplete Knowledge in Metric Spaces. Contributions to Game Theory and Management, 15, 109–120. https://doi.org/10.21638/11701/spbu31.2022.09

Issue

Vol. 15 (2022)

Section

Articles

License

Articles of "Contributions to Game Theory and Management" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.