Semi-Explicit Solutions to some Non-Linear Non-Quadratic Mean-Field-Type Games: A Direct Method

Autor:	Barreiro-Gomez, Julian, Duncan, Tyrone E., Pasik-Duncan, Bozenna, Tembine, Hamidou
Rok vydání:	2018
Předmět:	Mathematics - Optimization and Control Computer Science - Computer Science and Game Theory
Druh dokumentu:	Working Paper
Popis:	This article examines mean-field-type game problems by means of a direct method. We provide various solvable examples beyond the classical linear-quadratic game problems. These include quadratic-quadratic games and games with power, logarithmic, sine square, hyperbolic sine square payoffs. Non-linear state dynamics such as log-state, control-dependent regime switching, quadratic state, cotangent state and hyperbolic cotangent state are considered. We identify equilibrium strategies and equilibrium payoffs in state-and-conditional mean-field type feedback form. It is shown that a simple direct method can be used to solve broader classes of non-quadratic mean-field-type games under jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motions and multi-fractional Brownian motions. We provide semi-explicit solutions to the fully cooperative, noncooperative nonzero-sum, and adversarial game problems. Comment: 64 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1812.06695 Zobrazit plný text záznamu View this record from Arxiv