Random Search Methods for the Solution of a Stackelberg Game of Resource Allocation

Authors

  • Grigory I. Belyavsky I. I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences of Southern Federal University
  • Natalya V. Danilova I. I. Vorovich Institute of Mathematics, Mechanics and Computer Sciences of Southern Federal University

Abstract

We consider a dynamic Stackelberg game on a finite time interval. The game is reduced to a problem of infinite-dimensional optimization with two additional constraints. Two finite-dimensional approximations of the problem are defined. They are solved by two numerical algorithms which do not require calculation of the gradient of the payoff function. The first algorithm is an algorithm of simulated annealing with a uniform partition of the interval. The second algorithm uses a piecewise-constant approximation of the solution with a choice of the interval partition. Two illustrative examples connected with a resource allocation problem are considered. The numerical results are given and compared.

Keywords:

random search methods, Stackelberg game, resource allocation

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References

Basar, T., Olsder, G.Y. (1999). Dynamic Non-Cooperative Game Theory. SIAM.

Belyavsky, G.I., Danilova, N.V. Ougolnitsky, G.A. (2016). Evolutionary modeling in sustainable management of active systems. Math. Game Theory Appl., 8(4), 14–29 (in Russian).

Belyavsky, G.I., Danilova, N.V., Ougolnitsky, G.A. (2018a). Evolutionary methods for solving dynamic resource allocation problems. Math. Game Theory Appl., 10(1), 5–22 (in Russian).

Belyavsky, G., Danilova, N., Ougolnitsky, G. (2018b). A Markovian Mechanism of Proportional Resource Allocation in the Incentive Model as a Dynamic Stochastic Inverse Stackelberg Game. Mathematics, 6(8), 131.

Christodoulou, G., Sqouritza, A., Tang, B. (2015). On the Effiency of the Proportional Allocation Mechanism for Divisible Resources. M. Hoefer (Ed.): SAGT. LNCS 9347, 165–177.

Germeier, Yu.B. (1986). Non-antagonistic Games. Reidel Publishing Co., Dordrecht, Boston.

Gorelov, M.A., and Kononenko, A.F. (2015). Dynamic models of conflicts. III. Hierarchical. games. Automation and Remote Control, 76(2), 264–277.

Hazan, E. (2015). Introduction to Online Convex Optimization. Foundations and Trends in Optimization, 2(3–4), 157–325.

Jones, M.T. (2008). Artifcial Intelligence: A Systems Approach. Infinity Science Press, Hingham, MA.

Kononenko, A.F. (1977). On multi-step conflicts with information exchange. USSR Comp. Math. and Math. Phys., 17, 104–113.

Kononenko, A.F. (1980). The structure of the optimal strategy in controlled dynamic systems. USSR Comp. Math. and Math. Phys., 13–24.

Novikov, D. (2013). Theory of Control in Organizations. Nova Science Publishers, New York.

Sutton, R.S., Barto, A. (1998). Reinforcement Learning: An Introduction. MIT Press, Cambridge, MA.

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Published

2022-02-15

How to Cite

Belyavsky, G. I., & Danilova, N. V. (2022). Random Search Methods for the Solution of a Stackelberg Game of Resource Allocation. Contributions to Game Theory and Management, 12. Retrieved from https://gametheory.spbu.ru/article/view/12889

Issue

Vol. 12 (2019)

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.