Game theory based privacy preserving analysis in correlated data publication

Privacy preserving on data publication has been an important research field over the past few decades. One of the fundamental challenges in privacy preserving data publication is the trade-off problem between privacy and utility of the single and independent data set. However, recent research works have 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 the payoff of each player is dependent not only on his privacy parameter, but also on 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, who each publishes the data set sanitized by differential privacy. Next, we analyze the existence and uniqueness of the pure Nash Equilibrium and demonstrate the sufficient conditions in the game. Finally, we refer to a notion, i.e., the price of anarchy, to evaluate efficiency of the pure Nash Equilibrium.