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

Jun Moon, M Tamer Basar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

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.

Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control, CDC 2016
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages3578-3583
Number of pages6
ISBN (Electronic)9781509018376
DOIs
StatePublished - Dec 27 2016
Event55th IEEE Conference on Decision and Control, CDC 2016 - Las Vegas, United States
Duration: Dec 12 2016Dec 14 2016

Publication series

Name2016 IEEE 55th Conference on Decision and Control, CDC 2016

Other

Other55th IEEE Conference on Decision and Control, CDC 2016
CountryUnited States
CityLas Vegas
Period12/12/1612/14/16

ASJC Scopus subject areas

  • Artificial Intelligence
  • Decision Sciences (miscellaneous)
  • Control and Optimization

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