Cooperative differential games with the utility function switched at a random time moment

Anastasiia P. Zaremba

Saint Petersburg State University

Abstract: This paper describes a differential game of $n$ persons in which the utility functions of the players have a hybrid form, namely, they are changed at a random moment in time. With the help of integration in parts, the form of the payoff functional is simplified. For the cooperative scenario the problem of time-consistency of the optimality principle chosen by the players is studied and a solution is proposed in the form of an adapted imputation distribution procedure. The differential investment game is considered as an example.

Keywords: cooperative games, differential games, time-consistency problem, random duration, hybris differential games, imputation distribution procedure.

UDC: 517.977.8, 519.83
BBK: 22.18

Received: 19.01.2022
Revised: 07.04.2022
Accepted: 16.05.2022

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