NDLI: Solving subclasses of multi-player stochastic games via linear complementarity problem formulations

Please wait, while we are loading the content...

Optimization and Engineering : Volume 18

Optimization and Engineering : Volume 17

Optimization and Engineering : Volume 16

Optimization and Engineering : Volume 15

Optimization and Engineering : Volume 14

Optimization and Engineering : Volume 13

Optimization and Engineering : Volume 13, Issue 4, December 2012

Optimization and Engineering : Volume 13, Issue 3, September 2012

Special issue on applications of variational inequality problems

An inverse variational inequality approach to the evolutionary spatial price equilibrium problem

Control nonlinear diffusion macro-hybrid mixed variational problems

Combined methods for dynamic spatial auction market models

A variational inequality model of the spatial price network problem with uncertain data

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

Variational inequalities in stock loan models

Multiperiod competitive supply chain networks with inventorying and a transportation network equilibrium reformulation

Dynamic vaccination games and hybrid dynamical systems

Retarded weighted quasi-variational inequalities for traffic equilibrium problems

Optimization and Engineering : Volume 13, Issue 2, June 2012

Optimization and Engineering : Volume 13, Issue 1, March 2012

Optimization and Engineering : Volume 12

Optimization and Engineering : Volume 11

Optimization and Engineering : Volume 10

Optimization and Engineering : Volume 9

Optimization and Engineering : Volume 8

Optimization and Engineering : Volume 7

Optimization and Engineering : Volume 6

Optimization and Engineering : Volume 5

Optimization and Engineering : Volume 4

Optimization and Engineering : Volume 3

Optimization and Engineering : Volume 2

Optimization and Engineering : Volume 1

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

Content Provider	Springer Nature Link
Author	Krishnamurthy, Nagarajan Parthasarathy, Thiruvenkatachari Ravindran, Gomatam
Copyright Year	2011
Abstract	We briefly survey some results on the orderfield property of 2-player and multi-player stochastic games and their mixtures. Some of these classes of stochastic games can be solved by formulating them as a Linear Complementarity Problem (LCP) or (Generalized) Vertical Linear Complementarity Problem (VLCP). We discuss some of these results and prove that certain new subclasses and mixtures of multi-player (or n-person) stochastic games can be solved via LCP formulations.Mohan, Neogy and Parthasarathy (in Proceedings of the International Conference on Complementarity Problems, 1997) proposed an LCP formulation of β-discounted (multi-player) polystochastic games where the transitions are controlled by one player, and proved that this LCP is processible by Lemke’s algorithm. Using this formulation repeatedly, we prove that we can solve a subclass of β-discounted switching control polystochastic games. As our proof is constructive, we have an algorithm for solving this subclass. This algorithm only involves iteratively solving different LCPs and hence, it follows that this subclass has the orderfield property, a question left open in the paper on orderfield property of mixtures of stochastic games by Krishnamurthy et al., (Indian J. Stat. 72:246–275, 2010). Furthermore, we use results from Krishnamurthy et al., Indian J. Stat. 72:246–275, (2010) to solve some mixture classes using LCP (or VLCP) formulations.We also propose two different VLCP formulations for β-discounted zero-sum perfect information stochastic games, the underlying matrices of both formulations being R $_{0}$. As a result, we also have an alternative proof of the orderfield property of such games.
Starting Page	435
Ending Page	457
Page Count	23
File Format	PDF
ISSN	13894420
Journal	Optimization and Engineering
Volume Number	13
Issue Number	3
e-ISSN	15732924
Language	English
Publisher	Springer US
Publisher Date	2011-09-21
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Multi-player stochastic game Mixture class Perfect information Switching control Polystochastic game Linear complementarity problem Operations Research/Decision Theory Systems Theory, Control Engineering Environmental Management Agriculture Optimization
Content Type	Text
Resource Type	Article
Subject	Software Civil and Structural Engineering Control and Optimization Mechanical Engineering Aerospace Engineering Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Orderfield property of mixtures of stochastic games

Simple stochastic games and P-matrix generalized linear complementarity problems (2005)

Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems

Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies

Generalized principal pivot transforms, complementarity theory and their applications in stochastic games

A shape and topology optimization technique for solving a class of linear complementarity problems in function space

Nonlinear complementarity problems for n-player strategic chance-constrained games

Stationary Anonymous Sequential Games with Undiscounted Rewards

The multi-player nonzero-sum Dynkin game in discrete time

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results

Similar Documents

Orderfield property of mixtures of stochastic games

Simple stochastic games and P-matrix generalized linear complementarity problems (2005)

Feasible Semismooth Newton Method for a Class of Stochastic Linear Complementarity Problems

Existence of Stationary Markov Perfect Equilibria in Stochastic Altruistic Growth Economies

Generalized principal pivot transforms, complementarity theory and their applications in stochastic games

A shape and topology optimization technique for solving a class of linear complementarity problems in function space

Nonlinear complementarity problems for n-player strategic chance-constrained games

Stationary Anonymous Sequential Games with Undiscounted Rewards

The multi-player nonzero-sum Dynkin game in discrete time

Solving subclasses of multi-player stochastic games via linear complementarity problem formulations—a survey and some new results