Study on the model of the standard grey matrix game based on pure-strategy solution

Abstract

The problem of game in the real-life is not all a simple decision-making problem, which the process of game is only related to precision whitenization number, because of that there are a lot of uncertainty factors. This paper defines conceptions of pure-strategy solution (grey saddle-point) and optimal pure-strategy in the standard grey matrix game based on hypothesis of sense behavior and un-precision discursion characteristics for players, which the deduction process of players in the game are not the same as exactness calculation of the computers. In the grey matrix Atilde(ominus) of the grey matrix game Gtilde(ominus) = {S1, S2; Atilde(ominus)}, the strategies of line i* and the column j* of a grey saddle-point (i*, j*) are respectively a grey optimum pure-strategy alphai. of play-1 and betaj. of play-2, and the grey element [ai.j., bi.j.] of the grey saddle-point (i*, j*) in Atilde(ominus) is an optimum grey game values of the Gtilde(ominus). Furthermore, the paper proves necessary and sufficient conditions of that there exit pure-strategies, and researches characters, which if there are multi-saddle of Gtilde(ominus), then there are properties of no-difference and changeable among these grey saddles. In fact, the standard grey matrix game Gtilde(ominus) is directly generalization of classical matrix game in the field of grey system, which the later is a special example of the former