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This paper explores the idea of Bertrand duopoly in a context of bounded rationality, where two content providers (CP) endeavor to maximize their own profit. Each CP varies his price and fixes the level of his credibility of content. We suppose that one CP adjusts his price strategy according to a kind of smoothed information which average his marginal profit in the previous period and the one in a delayed period, while another CP makes its price strategy as the best response, which is a function the opponent action in the current period. Through a detailed analysis, we calculate explicitly the equilibrium points of the dynamical system, and we show the stability of its Nash equilibrium under some conditions. Numerical results reveal that while varying the model parameters (speed of adjustment and side payment), complex dynamic behaviors would occur, such as chaos. In addition, an appropriate method of chaos …