结构化多人博弈的分析框架

摘要

结构化多人博弈是一种把博弈方嵌入到具体的社会关系之中，在两两博弈的基础上求解整体博弈均衡状态的分析框架。和现有的合作博弈(Cooperative Game Theory)、网络博弈(Network Games)、进化图论(Evolutionary Graph Theory， EGT)、计算博弈论(Computational Game Theory)等多人博弈分析框架相比，结构化博弈既有和它们相似的地方，也有非常重要的差别。结构化博弈更适合用来分析政治问题和社会现象中的多人博弈局面。作为最简单的情况，本文先给出了一个三人结构化博弈的一般分析框架，然后根据这个分析框架对传统的联盟博弈进行了新的分析，发现经典的“三人分300元”博弈事实上有稳定的均衡解，即三人各分100元。作为一个简单的应用，文章分析了三个国家之间的“战争-同盟博弈”，我们发现该博弈有两个稳定的均衡解，在这两个稳定的均衡解中，超级大国和小国总是选择结盟，而小国总是选择和地区大国进行战争。从这两个例子可以看出，结构化多人博弈在分析复杂的政治、经济、社会问题上具有传统博弈论方法所不具备的很多优势，其获得的均衡解也更符合社会实际。%Structured multi-player game is an analytical framework, which assumed that each player is embedded in the so-cial relations, analyzing the whole game based on thepair-wise games between players with an equilibrium status. Compared with the existing multi-player game theory framework, such as Cooperative Game Theory, Network Games, Evolutionary Graph The-ory and Computational Game Theory, the structured multi-player game has the same characteristics with them, at the same time, there are lots of vital differences with those methods. Structured multi-player game is more suitable to analyze the political problems and social issues. At the beginning, an analytical framework for the most fundamental 3-player structured game is provided as the general situation, then, according to the generalanalytical framework, a classical cooperative game is analyzed with the discovery of the game called "3 players distribute 300 Yuan", which has a stable Nash Equilibrium in fact-each player gets 100Yuan. As a simple application, the results of "war and coalition game" between 3 nations can be explored. As the results, there are two stable NEs in the game. In the two NEs, the super powers always make alliances with the small country, while, the small country always chooses"war"with the local hegemony.From the two examples above, the structured multi-player game has some advantages on analyzing political problems, social issues, and economics situations, compared with some traditional game theories. The solutions of the structured multi-player game look more suitable to facts in the real society.