Evolutionary Framework for Solving Simultaneous Continuous Games with Multi-Objective Players

抄録

Game theory provides a mathematical framework for analyzing interactive situations between multiple decision-makers. In the field of cybersecurity, it is frequently applied to model the interactions between attackers and defenders, with the goal of developing effective defensive strategies. However, the complexity of the models often leads to exact methods being impractical, especially when the players have multiple objectives and continuous decision spaces. Also, intrinsic features of the game may prevent the use of existing numerical methods. In this work, we present a generic framework for approximating Nash equilibria, the model solutions, in continuous games of simultaneous decision with multi-objective players. The framework is based on the decomposition of the decision space into one set of optimization problems for each player, the concurrent solution of these problems using numerical methods such as evolutionary algorithms, and the merging of the Pareto-optimal solutions from different players into a single set of Nash equilibria approximations. We demonstrate the effectiveness of the framework by applying it to an extension of the widely studied FlipIt game, using standard, unmodified evolutionary algorithms. The results show that the resulting approximations improve in diversity and accuracy as the number of optimization problems increases, as prescribed by the framework. This points to the robustness of the proposed method, which shall appear familiar to both the game-theoretic and the evolutionary computation communities. It has the potential to be used as a general-purpose framework for other games.