| 摘要: | 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 [1], 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 [2,3]. In this paper, we 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 . We also give an analytic explanation for the appearance of the quasi-periodic structure in the time sequence of population when is small [4]. We also find a strategy for an agent to obtain the higher gain than others [5]. All properties we found in the game are originated from the na?ve rule –every agent uses his best strategy. References: 1. D. Challet and Y. C. Zhang, Emergence of cooperation and organization in an evolutionary game , Physica A 246, 407-418(1997). 2. M.A.R.de Cara, O.Pla and F.Guinea, Competition, efficiency and collective behavior in the “EI Farol” bar model, Euro. Phy. J. B10,187(1999) 3. R.Savit, R.Manuca and R.Riolo, Adaptive competition, market efficiency, and phase transitions, Phys. Rev. Lett.82,2203(1999). 4. Sy-Sang Liaw and Ching Liu, The quasi-periodic time sequence of the population in minority game, Physica A 351, 571-579(2005). 5. Ching Liu and Sy-Sang Liaw, Maximize personal gain in the minority game, Physica A 359, 641-649(2006) |
