TY - JOUR
T1 - Semiexplicit Solutions to Some Nonlinear Nonquadratic Mean-Field-Type Games
T2 - A Direct Method
AU - Barreiro-Gomez, Julian
AU - Duncan, Tyrone E.
AU - Pasik-Duncan, Bozenna
AU - Tembine, Hamidou
N1 - Funding Information:
Manuscript received December 31, 2018; revised April 21, 2019; accepted August 19, 2019. Date of publication October 8, 2019; date of current version May 28, 2020. This work was supported in part by the U.S. Air Force Office of Scientific Research under Grant FA9550-17-1-0259, Grant FA9550-17-1-0073, and in part by the National Science Foundation under Grant DMS 1411412. Recommended by Associate Editor Prof. Roland P. Malhame. (Corresponding author: Hamidou Tem-bine.) J. Barreiro-Gomez and H. Tembine are with the Learning and Game Theory Laboratory, Engineering Division, New York University Abu Dhabi, Abu Dhabi 129188, United Arab Emirates (e-mail: jbarreiro@ nyu.edu; tembine@nyu.edu).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/6
Y1 - 2020/6
N2 - 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. Nonlinear 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 nonquadratic mean-field-type games under jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motions and multifractional Brownian motions. We provide semiexplicit solutions to the fully cooperative, noncooperative nonzero-sum, and adversarial game problems.
AB - 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. Nonlinear 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 nonquadratic mean-field-type games under jump-diffusion-regime switching Gauss-Volterra processes which include fractional Brownian motions and multifractional Brownian motions. We provide semiexplicit solutions to the fully cooperative, noncooperative nonzero-sum, and adversarial game problems.
KW - Direct method
KW - mean-field-type games
KW - nonlinear
KW - nonquadratic systems
KW - risk-awareness
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U2 - 10.1109/TAC.2019.2946337
DO - 10.1109/TAC.2019.2946337
M3 - Article
AN - SCOPUS:85082468595
SN - 0018-9286
VL - 65
SP - 2582
EP - 2597
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
IS - 6
M1 - 8862869
ER -