A Time-consistent Solution Formula for Linear-Quadratic Discrete-time Dynamic Games with Nontransferable Payoffs

Authors

  • Anna Tur Saint Petersburg State University

Abstract

The solution formula for the payoff distribution procedure of a bargaining problem in a cooperative differential game with nontransferable payoffs that lead to a time consistent outcome is proposed by Leon A. Petrosyan and D.W.K. Yeung (2014). In this paper we study this formula for linear-quadratic discrete-time dynamic games with nontransferable payoffs. Pareto-optimal solution is studied as optimality principle. The time consistency and irrational behavior proof condition of this solution are investigated. As an example the government debt stabilization game is considered.

Keywords:

linear-quadratic games, discrete-time games, games with nontransferable payoffs, Pareto-optimal solution, time consistency, PDP, irrational behavior proof condition

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References

Aarle, B. van, Bovenberg, L. and Raith, M. (1995). Monetary and fiscal policy interaction and government debt stabilization. Journal of Economics, 62(2), 111–140.

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Belitskaia, A. V. The D.W.K. Yeung Condition for Cooperative Differential Games with Nontransferable Payoffs. Graduate School of Management, Contributions to game theory and management, 5, 45–50.

Engwerda, J. C. (2005). LQ Dynamic Optimization and Differential Games. Chichester: John Wiley Sons, 497 p.

Petrosyan L. A. (1993). Differential Games of Pursuit. World Scientific, Singapore.

Petrosyan L. A. (1997). Agreeable Solutions in Differential Games. International Journal of Mathematics, Game Theory and Algebra, 7, 165–177.

Petrosyan, L. A. and N. N. Danilov (1982). Cooperative differential games and their applications. (Izd. Tomskogo University, Tomsk).

Rincon-Zapatero, J. P., Martin-Herran, G., Martinez, J. (2000). Identification of Efficient Subgame-Perfect Nash Equilibria in a Class of Differential Games. Journal of Optimization Theory and Applications, 104(1), 235–242.

Yeung, D. W. K. (2006). An Irrational-Behavior-Proof Condition in Cooperative Differential Games. IGTR, 8(1), 739–744.

Yeung, D. W. K. and L. A. Petrosyan (2014). A Time-consistent Solution Formula for Bargaining Problem in Differential Games. Int. Game Theory Rev., 16(4), 1450016.

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Published

2022-05-02

How to Cite

Tur, A. (2022). A Time-consistent Solution Formula for Linear-Quadratic Discrete-time Dynamic Games with Nontransferable Payoffs. Contributions to Game Theory and Management, 8. Retrieved from https://gametheory.spbu.ru/article/view/13466

Issue

Vol. 8 (2015)

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.

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