Learning to Win in Evolutionary Two-person Boolean Game with Fixed Strategy Updating Rule*

This paper introduces an algorithm to learn the strategy updating rule for a two- person Boolean game using the records of the history strategies and game results. The two-person game in this paper is introduced as a zero-sum game along with a Boolean strategy set, and the strategies are governed by fixed Boolean functions whose arguments are the history strategies and game results with additive binary noise, which can be modeled as a stochastic Boolean dynamic system. However, for this easy-to-play game, there is no effective convenient methods to win more often. To achieve this goal, a learning algorithm based on Boolean regression and maximum-likelihood estimation is put forward to learn the strategy updating rule and the noise property using the records of the history strategies and game results. In addition, extensive simulations via actual examples have illustrated the effectiveness of the proposed learning algorithm.