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Mathematical Problems in Engineering
Volume 2015, Article ID 452042, 10 pages
Research Article

A Study of Prisoner’s Dilemma Game Model with Incomplete Information

1School of Applied Mathematics, Guangdong University of Technology, Guangzhou, Guangdong 510006, China
2Department of Computer Science and Technology, Tsinghua University, Beijing 100084, China

Received 25 May 2014; Revised 22 September 2014; Accepted 23 September 2014

Academic Editor: Yiu-ming Cheung

Copyright © 2015 Xiuqin Deng and Jiadi Deng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Prisoners’ dilemma is a typical game theory issue. In our study, it is regarded as an incomplete information game with unpublicized game strategies. We solve our problem by establishing a machine learning model using Bayes formula. The model established is referred to as the Bayes model. Based on the Bayesian model, we can make the prediction of players’ choices to better complete the unknown information in the game. And we suggest the hash table to make improvement in space and time complexity. We build a game system with several types of game strategy for testing. In double- or multiplayer games, the Bayes model is more superior to other strategy models; the total income using Bayes model is higher than that of other models. Moreover, from the result of the games on the natural model with Bayes model, as well as the natural model with TFT model, it is found that Bayes model accrued more benefits than TFT model on average. This demonstrates that the Bayes model introduced in this study is feasible and effective. Therefore, it provides a novel method of solving incomplete information game problem.