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

摘要

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) (Ã⊗ of the grey matrix game)} (G̃(⊗) = {S1, S2; Ã(⊗)}, the strategies of line i* and the column j* of a grey saddle-point (i*, j*) are respectively a grey optimum pure-strategy αi*of play-1 and βj*of play-2, and the grey element, [ai*j*,bi*j*] of the grey saddle-point (i*, j*) in Ã(⊗) is an optimum grey game values of the G̃(⊗). Furthermore, the paper proves necessary and sufficient conditions of that there exit pure-strategies, and researches characters, which if there are multi-saddle of G̃(⊗), then there are properties of no-difference and changeable among these grey saddles. In fact, the standard grey matrix game G̃(⊗) is directly generalization of classical matrix game in the field of grey system, which the later is a special example of the former.