Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

Ekaterina Gromova, Anastasiia Zaremba and Shimai Su
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Ekaterina Gromova: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Anastasiia Zaremba: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia
Shimai Su: Faculty of Applied Mathematics and Control Processes, St. Petersburg State University, 199034 St. Petersburg, Russia

Mathematics, 2021, vol. 9, issue 15, 1-14

Abstract: This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n -person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

Keywords: hybrid differential game; cooperative differential game; random time horizon; dynamic programming principle; imputation distribution procedure; time-consistency (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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