基于完全信息博弈的“沙漠掘金”游戏策略  

“Desert Nuggets”game strategy based on complete information game

作　　者：曾梓怡 张世雄 冀成知远 李厚彪[1] ZENG Ziyi;ZHANG Shixiong;JI Chengzhiyuan;LI Houbiao(School of Mathematical Sciences,University of Electronic Science and Technology of China,Chengdu Sichuan 610051,China;School of Automation Engineering,University of Electronic Science and Technology of China,Chengdu Sichuan 610051,China;School of Information and Software Engineering,University of Electronic Science and Technology of China,Chengdu Sichuan 610051,China)

机构地区：[1]电子科技大学数学科学学院,成都610051 [2]电子科技大学自动化工程学院,成都610051 [3]电子科技大学信息与软件工程学院,成都610051

出　　处：《计算机应用》2021年第S02期93-97,共5页journal of Computer Applications

基　　金：国家自然科学基金资助项目(11101071,11271001);四川省科技支撑计划项目(2016CC0036)。

摘　　要：为寻求益智类游戏"沙漠掘金"在多人参与下的游戏策略,针对具体的游戏规则进行了深入的分析,分别提出了基于完全信息静态博弈与完全信息动态博弈的游戏策略。首先,通过简化游戏规则将其转变为一个非合作博弈问题。其次,考虑单人游戏中的最优化问题,分析单人游戏的策略并在此基础上采用博弈论的方法对多人游戏的情况进行求解。最后,针对第一关,满足完全信息静态博弈的情况,模拟玩家行动,得出博弈支付矩阵,通过混合策略纳什均衡的方法计算最优策略;针对第二关,满足完全信息动态博弈的情况,构建博弈树并通过逆向递归求解得出最佳的游戏攻略,并分析了多人竞争策略。In order to seek the game strategy of the puzzle game“Desert Nuggets”with multi-player participation,an indepth analysis of specific game rules was carried out,and the game strategies based on a static game with complete information and a dynamic game with complete information were respectively proposed. First,it was transformed into a noncooperative game problem by simplifying the rules of the game. Secondly,considering the optimization problem in the single player game,the strategy of the single player game was analyzed and the game theory method was used to solve the multiplayer game situation on this basis. Finally,for the first level which satisfied the complete information static game situation,by simulating the player’s actions,the game payout matrix was obtained,and the optimal strategy was calculated by the method of mixed strategy Nash equilibrium;for the second level which satisfied the complete information dynamic game situation,the game tree was constructed and the best game strategy was obtained through reverse recursion,and the multiplayer competition strategy was analyzed.

关 键 词：完全信息动态博弈 完全信息静态博弈 博弈论 纳什均衡 博弈支付矩阵 

分 类 号：F224.32[经济管理—国民经济]