In m any social o r po lit ical science p rob lem s, the personal sub ject ive p reference info rm a2 t ion can be the resu lt f rom qualitat ive analysis, w h ich is diff icu lt to be exp ressed in the u t ility fo rm , bu t can be exp ressed in o rdinal fo rm. Based upon o rdinal p reference info rm at ion the decision2m akers exp ressed, in stead of the payoff funct ion o r u t ility level, th is paper developed a rank2o rdering based gam e theo ry o r model, p ropo sed som e concep t s of rank2o rdering equ ilib rium , and gave som e num eri2 cal demon st rat ion s. Th is new gam e theo ry cou ld be con sidered as the necessary and valuab le general2 izat ion and supp lem en t to the t radit ional u t ility o r payoff based gam e theo ry.