Learning implicit information in Bayesian games with knowledge transfer
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Control Theory and Technology http://link.springer.com/journal/11768
Learning implicit information in Bayesian games with knowledge transfer Guanpu CHEN† , Kai CAO, Yiguang HONG Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China; School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China Received 18 December 2018; revised 3 February 2020; accepted 10 February 2020
Abstract In this paper, we consider to learn the inherent probability distribution of types via knowledge transfer in a two-player repeated Bayesian game, which is a basic model in network security. In the Bayesian game, the attacker’s distribution of types is unknown by the defender and the defender aims to reconstruct the distribution with historical actions. It is difficult to calculate the distribution of types directly since the distribution is coupled with a prediction function of the attacker in the game model. Thus, we seek help from an interrelated complete-information game, based on the idea of transfer learning. We provide two different methods to estimate the prediction function in different concrete conditions with knowledge transfer. After obtaining the estimated prediction function, the defender can decouple the inherent distribution and the prediction function in the Bayesian game, and moreover, reconstruct the distribution of the attacker’s types. Finally, we give numerical examples to illustrate the effectiveness of our methods. Keywords: Bayesian game, repeated game, knowledge transfer, security DOI https://doi.org/10.1007/s11768-020-0086-2
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Introduction
The incomplete-information game is one of the important categories in game theory because the players may not have the whole information of the game [1–3]. The Bayesian game, whose concept was established in [4] by translating a class of incomplete-information
games into imperfect-information games, is the most widely accepted model among incomplete-information games. In Bayesian games, players’ strategies depend on his/her own type with an inherent probability distribution. Specifically, different types of one player can be regarded as different players acting simultaneously, and the probability distribution of types is private knowl-
† Corresponding author. E-mail: [email protected]. This work was supported by the National Key Research and Development Program (No. 2016YFB0901900) and the National Natural Science Foundation of China (No. 61733018).
© 2020 South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature
G. Chen et al. / Control Theory Tech, Vol.
edge for opponents in most cases. Researchers have investigated various incomplete-information games in the framework of Bayesian games [5–8]. Meanwhile, repeated Bayesian games practically provide mathematical tools and models in network security [9, 10], including jamming and eavesdropping attacks, mobile ad hoc networks and intrusion detectio
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