Abstract: With the rapid development of the Internet, online sales not only become an important part of the sales market, but also influence the traditional sales model (offline sales) changes. However, the online and offline sales will exist in the market for a long time, because the online and offline have irreplaceable advantages. And more, fairness concerns effect the decision-making behavior of participants in the market competition. Thus, the game model between online and offline sales is constructed in order to analyze the impact of fair concern on decision behavior and competitive strategy. Firstly, the decision and profits are comparably analyzed from the four conditions of fairness concerns based on the game model. Secondly, the evolutionary game model is constructed based on the four conditions of fairness concerns in order to analyze the influence of different equity concerns on the decision-making behavior of the participants in the sales channel. The main results are as follows:the other sales profit will be reduced when fairness concerns are adopted by online or offline; offline taking fairness concerns or unfair concern strategy is closely related to the online strategies, i.e. the offline takes unfair concerns when online takes fairness concerns of probability is greater than a certain threshold, on the contrary, adopt fairness concerns; the evolutionary equilibrium stability strategy is to adopt fair concern on both sides after a long period of evolutionary game between online and offline sales. The scientific decisions could be provided to online and offline sales through this study.

Key words: online and offline, fair concern, evolutionary game