Abstract Complex systems appear everywhere, including in economics (winning and losing) 、in biology (evolution) 、in social science (learning and segregation), in nature and are focus of many researches. Physicist have constructed a simple binomial game, called the “Minority Game”, to simulate the systems. In the minority game, minority is the winner. Every member of a group of agents seems independent from one another, whereas affected by others’ behavior. A few interesting statistical results were discovered in the minority game. I will give an analytical explanation for the properties shown in the phase diagrams of the game. In particular, we explain why is a good parameter and how one can determine its critical value . All properties we found in the game are originated from the na?ve rule –every agent uses his best strategy (it seems to be a reasonable choice, is it?).
