On class of non-transferable utility cooperative differential games with continuous updating

Wang Zeyang; Petrosian Ovanes

doi:10.3934/jdg.2020020

Article Contents

2020, Volume 7, Issue 4: 291-302. Doi: 10.3934/jdg.2020020

This issue Previous Article Approachability in population games Next Article On the grey Baker-Thompson rule

On class of non-transferable utility cooperative differential games with continuous updating

Wang Zeyang and
Petrosian Ovanes^,

St.Petersburg State University, 7/9, Universitetskaya nab., Saint-Petersburg 199034, Russia, College of Mathematics and Computer Science, Yan'an University, 580 Shengdi Road, Yan'an, CHINA, P.C: 716099

^* Corresponding author: Ovanes Petrosian
^* Corresponding author: Ovanes Petrosian

Received: March 31, 2020

Revised: April 30, 2020

Early access: July 2020

Published: October 2020

Research of the second author is supported by a grant from the Russian Science Foundation (Project No 18-71-00081)

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Abstract

This paper considers and describes the class of cooperative differential games with the non-transferable utility and continuous updating. It is the first detailed paper about the application of continuous updating approach to the non-transferable utility differential games. The process of how to construct Pareto optimal strategy with continuous updating and Pareto trajectory is described. Another important contribution is that the property of subgame consistency is adopted for the class of games with continuous updating. The resource extraction game model is used as an example. The Pareto optimal strategies and corresponding trajectory are constructed, and the set of Pareto optimal strategies satisfying the subgame consistency property is presented. The results of numerical simulation are demonstrated in the Matlab environment, and the conclusion is drawn.

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Mathematics Subject Classification: Primary:91A12, 91A23;Secondary:91A80.

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Figure 1. Pareto optimal trajectory with continuous updating (blue line), Pareto optimal trajectory in the initial game (red line)

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Figure 2. Pareto optimal strategies of players $ 1 $ and $ 2 $ in the initial game and in the game model with continuous updating for $ \alpha_1 = 0.664 $, $ \alpha_2 = 0.336 $

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Figure 3. Pareto optimal strategy of player $ i $ with continuous updating for different weights $ \alpha_i = (0.1,0.2,\dots,1) $

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Figure 4. Payoff function (26) of player $ i $ corresponding to Pareto optimal strategy profile (blue lines), payoff function (27) of player $ i $ corresponding to Nash equilibrium (red lines) with continuous updating

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