Study on Matrix Solution Method of Grey Matrix Game Based on Full Rank Grey Payoff Matrix

Abstract

Game theory based on the theory and thought of classical math has brought far-reaching affects in the field of economics, sociology, and so on. However, classical game theory can find no way out when game circumstance faces to uncertainty condition, such as finite logos, finite knowledge, small sample, and inadequate information, the payoff value of game can only be described with grey number. So study on grey matrix game has the most important theoretic value and actualistic meaning. How to solve the grey matrix game with high efficiency is the key problem which must be solved in the theory research and application of this field. Matrix solution method of grey matrix game is simple and effective. This paper has defined grey full rank payoff value expansion square matrix of grey matrix game, and has also proved that besides the value of grey element at the right and bottom edge of inverse matrix of grey full rank expansion square matrix, the value of grey element at its last line and right column is corresponding the optimal grey game strategies of player 1 and 2 separately.