TY - GEN

T1 - Discrete-time stochastic Stackelberg dynamic games with a large number of followers

AU - Moon, Jun

AU - Basar, M Tamer

PY - 2016/12/27

Y1 - 2016/12/27

N2 - We consider a class of discrete-time stochastic Stackelberg dynamic games with one leader and the N followers where N is sufficiently large. The leader and the followers are coupled through a mean field term, representing the average behavior of the followers. We characterize a Nash equilibrium at the followers level, and a Stackelberg equilibrium between the leader and the followers group. To circumvent the difficulty that arises in characterizing a Stackelberg-Nash solution due to the presence of a large number of followers, our approach is to imbed the original game in a class of mean-field stochastic dynamic games, where each follower solves a generic stochastic control problem with an approximated mean-field behavior and with an arbitrary control for the leader. We first show that this solution constitutes an -Nash equilibrium for the followers, where can be picked arbitrarily close to zero when N is large. We then turn to the leader's problem, and show that the associated local optimal control problem, constructed via the mean field approximation, admits an (1; 2)-Stackelberg equilibrium, where both 1 and 2 are arbitrarily close to zero as N becomes arbitrarily large. Numerical examples included in the paper illustrate the theoretical results.

AB - We consider a class of discrete-time stochastic Stackelberg dynamic games with one leader and the N followers where N is sufficiently large. The leader and the followers are coupled through a mean field term, representing the average behavior of the followers. We characterize a Nash equilibrium at the followers level, and a Stackelberg equilibrium between the leader and the followers group. To circumvent the difficulty that arises in characterizing a Stackelberg-Nash solution due to the presence of a large number of followers, our approach is to imbed the original game in a class of mean-field stochastic dynamic games, where each follower solves a generic stochastic control problem with an approximated mean-field behavior and with an arbitrary control for the leader. We first show that this solution constitutes an -Nash equilibrium for the followers, where can be picked arbitrarily close to zero when N is large. We then turn to the leader's problem, and show that the associated local optimal control problem, constructed via the mean field approximation, admits an (1; 2)-Stackelberg equilibrium, where both 1 and 2 are arbitrarily close to zero as N becomes arbitrarily large. Numerical examples included in the paper illustrate the theoretical results.

UR - http://www.scopus.com/inward/record.url?scp=85010818159&partnerID=8YFLogxK

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U2 - 10.1109/CDC.2016.7798807

DO - 10.1109/CDC.2016.7798807

M3 - Conference contribution

AN - SCOPUS:85010818159

T3 - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

SP - 3578

EP - 3583

BT - 2016 IEEE 55th Conference on Decision and Control, CDC 2016

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 55th IEEE Conference on Decision and Control, CDC 2016

Y2 - 12 December 2016 through 14 December 2016

ER -