Iterative computation of nash equilibria in M-player games with partial weak coupling

Research output: Contribution to journalConference article

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 zero'th 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 non-quadratic cost functions.

Original languageEnglish (US)
Pages (from-to)245-256
Number of pages12
JournalLecture Notes in Control and Information Sciences
Volume156
StatePublished - Jan 1 1991
EventProceedings of the 4th International Symposium on Differential Games and Applications - Helsinki, Finl
Duration: Aug 9 1990Aug 10 1990

Fingerprint

Iterative methods
Cost functions
interaction
Group
study group
costs

ASJC Scopus subject areas

  • Library and Information Sciences

Cite this

@article{e9120f27051e490986ee558bcb486336,
title = "Iterative computation of nash equilibria in M-player games with partial weak coupling",
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 zero'th 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 non-quadratic cost functions.",
author = "Basar, {M Tamer} and Rayadurgam Srikant",
year = "1991",
month = "1",
day = "1",
language = "English (US)",
volume = "156",
pages = "245--256",
journal = "Lecture Notes in Control and Information Sciences",
issn = "0170-8643",
publisher = "Springer Verlag",

}

TY - JOUR

T1 - Iterative computation of nash equilibria in M-player games with partial weak coupling

AU - Basar, M Tamer

AU - Srikant, Rayadurgam

PY - 1991/1/1

Y1 - 1991/1/1

N2 - 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 zero'th 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 non-quadratic cost functions.

AB - 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 zero'th 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 non-quadratic cost functions.

UR - http://www.scopus.com/inward/record.url?scp=0025794719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025794719&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:0025794719

VL - 156

SP - 245

EP - 256

JO - Lecture Notes in Control and Information Sciences

JF - Lecture Notes in Control and Information Sciences

SN - 0170-8643

ER -