Sequential decomposition and policy iteration schemes for M-player games with partial weak coupling

Research output: Contribution to journalArticle

Abstract

We formulate two general classes of M-player deterministic and stochastic nonzero-sum games where the players can be placed into two groups such that there are strong interactions within each group and a weak interaction between the two groups. This weak interaction is characterized in terms of a small parameter ε which, when set equal to zero, leads to two independent nonzero-sum games. Under the Nash equilibrium solution concept both within and in between the groups, we study the merits of an iterative method for the construction of the equilibrium by solving simpler problems at each stage of the iteration. In this iterative scheme, the zeroth order solution is the Nash equilibrium of the two independent games obtained by setting ε = 0, whereas the higher-order solutions are Nash equilibria of quadratic games, even though the original problem may have nonquadratic cost functions.

Original languageEnglish (US)
Pages (from-to)95-105
Number of pages11
JournalAutomatica
Volume28
Issue number1
DOIs
StatePublished - Jan 1992

Keywords

  • Nash equilibria
  • Noncooperative nonzero-sum games
  • iterative computation
  • weak coupling

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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