Title: Rough set approach to bi-matrix game

Authors: Sankar Kumar Roy; Prasanta Mula

Addresses: Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India ' ISRO Satellite Centre, Old Airport Road, Vimanapura Post, Bangalore-560017, India

Abstract: The paper attempts to solve the bi-matrix game under rough set environment. The elements of the bi-matrix game are characterised by rough variables and defined as rough bi-matrix game (RBG). To handle RBG, we introduce the rough measurable function denoted as trust in it. Based on trust measure and rough expected operator, trust equilibrium strategies are defined for RBG. Then using rough set theory and game theory, the RBG converts into crisp quadratic programming problem (QPP) which depends upon the confidence level. Finally, using Wolfe's modified simplex method, the solution of RBG is derived. The numerical examples are presented to illustrate the methodology.

Keywords: bi-matrix game; trust measures; rough constraints; quadratic programming; Wolfe's modified simplex method; rough sets; game theory.

DOI: 10.1504/IJOR.2015.069182

International Journal of Operational Research, 2015 Vol.23 No.2, pp.229 - 244

Received: 27 Nov 2012
Accepted: 28 Jul 2013
Published online: 01 May 2015 *

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