Open AccessStability of international pollution control games: A potential game approach
Author(s) -
Jewaidu Rilwan,
Poom Kumam,
Onésimo Hernández–Lerma
Publication year - 2022
Publication title -
journal of dynamics and games
Language(s) - English
Resource type - Journals
eISSN - 2164-6074
pISSN - 2164-6066
DOI - 10.3934/jdg.2022003
Subject(s) - differential game , nash equilibrium , saddle point , mathematical economics , stackelberg competition , stability (learning theory) , repeated game , mathematical optimization , equilibrium point , control (management) , game theory , mathematics , computer science , differential equation , mathematical analysis , artificial intelligence , geometry , machine learning
In this paper, stabilization problems for n- player noncooperative differential games of international pollution control (IPC) are analysed via the concept of the potential differential game (PDG) introduced by Fonseca-Morales and Hernández-Lerma (2018). By first identifying a game of IPC as a PDG, an associated optimal control problem (OCP) is obtained, whose optimal solution is a Nash equilibrium (NE) for the game of IPC. Thus, the problem of finding conditions for which the NE stabilizes the game of IPC reduces to finding conditions for which the optimal solution stabilizes the associated OCP. The concept not only yields mild conditions for saddle point stability analysed in the literature but also for the overtaking optimality of the NE of the game of IPC.