About one differential game model with dynamic updating

Ovanes L. Petrosyan^ab, Denis S. Tikhomirov^c, Ildus I. Kuchkarov^a, Hongwei Gao<sup>b

a</sup> Saint Petersburg State University
^b Qingdao University
^c National Research University "High School of Economics"

Abstract: Differential game model of limited resource extraction with dynamic updating is studied in the paper. The class of games with dynamic updating is new in the theory of differential games. Cooperative setting of limited resource extraction with dynamic updating is considered. Optimal strategies, cooperative payoff, characteristic function and allocation rule for cooperative payoff between the players are derived in an explicit form. As an optimality principle or cooperative solution Shapley value is used. Results of numerical simulation in the Python environment are demonstrated.

Keywords: differential games, looking forward approach, dynamic updating, continuous updating, cooperative strategies, feedback Nash equilibrium.

UDC: 519.83
BBK: 22.18

Received: 09.12.2018
Revised: 29.03.2019
Accepted: 10.06.2019