Local differential privacy (LDP) is an effective privacy-preserving model to address the problems which do not have a trusted entity. The main idea of the LDP is to add randomness in real data to guarantee individual's private sensitive information. Here, the technology of randomized response is an effective method to realize the LDP mechanism. In fact, the randomized response is a probabilistic mapping from the real data to perturbed data, which can be modeled as an information-theoretic lossy compression mechanism. What's more, the privacy budget ε has become a de facto standard to quantify the worstcase privacy leakage. However, such a metrics can not capture the question that which one is the optimal privacy mechanism in a set of equivalent ε-privacy mechanisms. Besides, the privacy and utility are closely correlated with the privacy mechanism, and existing methods do not consider the strategic adversary's behavior. In this paper, we tackle the problem of tradeoffs privacy and utility under the rational framework within an information-theoretic approach as the metrics. To address the problem, we first formulate this trade-off as a minimax information leakage problem. Then, we propose a privacy preserving attack and defense (PPAD) game framework, that is, a two-person zero-sum (TPZS) game. Further, we develop an alternating optimization algorithm to compute the saddle point of the proposed PPAD game. As a case study, we apply our method to compare several alternative ln 2-privacy mechanisms, the experimental result demonstrates that can provide an effective method to compare equivalent ε-privacy mechanisms. Furthermore, the numeric simulation result confirms that the proposed method also be useful for the protector to assess privacy disclosure risks.

Federated learning (FL) is a distributed machine learning framework that can effectively help multiple players to use data to train federated models while complying with their privacy, data security, and government regulations. Due to federated model training, an accurate model should be trained, and all federated players should actively participate. Therefore, it is crucial to design an incentive mechanism; however, there is a conflict between fairness and Pareto efficiency in the incentive mechanism. In this paper, we propose an incentive mechanism via the combination of the Shapley value and Pareto efficiency optimization, in which a third party is introduced to supervise the federated payoff allocation. If the payoff can reach Pareto optimality, the federated payoff is allocated by the Shapley value method; otherwise, the relevant federated players are punished. Numerical and simulation experiments show that the mechanism can achieve fair payoff allocation and Pareto optimality payoff allocation. The Nash equilibrium of this mechanism is formed when Pareto optimality payoff allocation is achieved.