Privacy preservation is one of the greatest concerns in big data. As one of extensive applications in big data, privacy preserving data publication (PPDP) has been an important research field. One of the fundamental challenges in PPDP is the trade-off problem between privacy and utility of the single and independent data set. However, recent research has shown that the advanced privacy mechanism, i.e., differential privacy, is vulnerable when multiple data sets are correlated. In this case, the trade-off problem between privacy and utility is evolved into a game problem, in which payoff of each player is dependent on his and his neighbors’ privacy parameters. In this paper, we firstly present the definition of correlated differential privacy to evaluate the real privacy level of a single data set influenced by the other data sets. Then, we construct a game model of multiple players, in which each publishes data set sanitized by differential privacy. Next, we analyze the existence and uniqueness of the pure Nash Equilibrium. We refer to a notion, i.e., the price of anarchy, to evaluate efficiency of the pure Nash Equilibrium. Finally, we show the correctness of our game analysis via simulation experiments