Extreme Nash equilibrium of polymatrix games in electricity market

Kailash Chand Sharma; Rohit Bhakar; Harpal Tiwari

doi:10.1109/ICRAIE.2014.6909279

Extreme Nash equilibrium of polymatrix games in electricity market

Kailash Chand Sharma, Rohit Bhakar, Harpal Tiwari

Department of Electronic & Electrical Engineering

Research output: Chapter or section in a book/report/conference proceeding › Chapter in a published conference proceeding

5 Citations (SciVal)

235 Downloads (Pure)

Abstract

Game theoretical approaches are widely used for the analysis of oligopolistic electricity markets. Nash equilibrium is a solution concept of game theoretical approaches. Due to existence of mixed strategy equilibrium and large number of multiple players, finding Nash equilibrium for problems in electricity market is a difficult task. To resolve these difficulties, this paper proposes a simplified approach for finding extreme Nash equilibrium, based on payoff matrix approach and mixed integer linear programming (MILP). To illustrate the proposed approach, a practical case study of Cournot poly-matrix game is considered. Eliminating constraints are appended on the proposed approach to find a global optimal solution. Obtained results show the strength of proposed approach, in terms of simplicity and computational time.

Original language	English
Title of host publication	International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014
Publisher	IEEE
ISBN (Print)	9781479940400
DOIs	https://doi.org/10.1109/ICRAIE.2014.6909279
Publication status	Published - 1 Jan 2014
Event	International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014 - Jaipur, UK United Kingdom Duration: 9 May 2014 → 11 May 2014

Conference

Conference	International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014
Country/Territory	UK United Kingdom
City	Jaipur
Period	9/05/14 → 11/05/14

Keywords

Electricity market
mixed-integer linear programming
Nash equilibrium
payoff matrix approach
poly-matrix game

Access to Document

10.1109/ICRAIE.2014.6909279

Accepted Version
© 2014 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works
Accepted author manuscript, 215 KB

Cite this

Sharma, KC, Bhakar, R & Tiwari, H 2014, Extreme Nash equilibrium of polymatrix games in electricity market. in International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014., 6909279, IEEE, International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014, Jaipur, UK United Kingdom, 9/05/14. https://doi.org/10.1109/ICRAIE.2014.6909279

@inproceedings{91f85b813ae64d7096833121c0bf9355,

title = "Extreme Nash equilibrium of polymatrix games in electricity market",

abstract = "Game theoretical approaches are widely used for the analysis of oligopolistic electricity markets. Nash equilibrium is a solution concept of game theoretical approaches. Due to existence of mixed strategy equilibrium and large number of multiple players, finding Nash equilibrium for problems in electricity market is a difficult task. To resolve these difficulties, this paper proposes a simplified approach for finding extreme Nash equilibrium, based on payoff matrix approach and mixed integer linear programming (MILP). To illustrate the proposed approach, a practical case study of Cournot poly-matrix game is considered. Eliminating constraints are appended on the proposed approach to find a global optimal solution. Obtained results show the strength of proposed approach, in terms of simplicity and computational time.",

keywords = "Electricity market, mixed-integer linear programming, Nash equilibrium, payoff matrix approach, poly-matrix game",

author = "Sharma, {Kailash Chand} and Rohit Bhakar and Harpal Tiwari",

year = "2014",

month = jan,

day = "1",

doi = "10.1109/ICRAIE.2014.6909279",

language = "English",

isbn = "9781479940400",

booktitle = "International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014",

publisher = "IEEE",

address = "USA United States",

note = "International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014 ; Conference date: 09-05-2014 Through 11-05-2014",

}

TY - GEN

T1 - Extreme Nash equilibrium of polymatrix games in electricity market

AU - Sharma, Kailash Chand

AU - Bhakar, Rohit

AU - Tiwari, Harpal

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Game theoretical approaches are widely used for the analysis of oligopolistic electricity markets. Nash equilibrium is a solution concept of game theoretical approaches. Due to existence of mixed strategy equilibrium and large number of multiple players, finding Nash equilibrium for problems in electricity market is a difficult task. To resolve these difficulties, this paper proposes a simplified approach for finding extreme Nash equilibrium, based on payoff matrix approach and mixed integer linear programming (MILP). To illustrate the proposed approach, a practical case study of Cournot poly-matrix game is considered. Eliminating constraints are appended on the proposed approach to find a global optimal solution. Obtained results show the strength of proposed approach, in terms of simplicity and computational time.

AB - Game theoretical approaches are widely used for the analysis of oligopolistic electricity markets. Nash equilibrium is a solution concept of game theoretical approaches. Due to existence of mixed strategy equilibrium and large number of multiple players, finding Nash equilibrium for problems in electricity market is a difficult task. To resolve these difficulties, this paper proposes a simplified approach for finding extreme Nash equilibrium, based on payoff matrix approach and mixed integer linear programming (MILP). To illustrate the proposed approach, a practical case study of Cournot poly-matrix game is considered. Eliminating constraints are appended on the proposed approach to find a global optimal solution. Obtained results show the strength of proposed approach, in terms of simplicity and computational time.

KW - Electricity market

KW - mixed-integer linear programming

KW - Nash equilibrium

KW - payoff matrix approach

KW - poly-matrix game

UR - http://www.scopus.com/inward/record.url?scp=84908637505&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1109/ICRAIE.2014.6909279

U2 - 10.1109/ICRAIE.2014.6909279

DO - 10.1109/ICRAIE.2014.6909279

M3 - Chapter in a published conference proceeding

AN - SCOPUS:84908637505

SN - 9781479940400

BT - International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014

PB - IEEE

T2 - International Conference on Recent Advances and Innovations in Engineering, ICRAIE 2014

Y2 - 9 May 2014 through 11 May 2014

ER -

Extreme Nash equilibrium of polymatrix games in electricity market

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this