Inverse Cooperative and Non-Cooperative Dynamic Games Based on Maximum Entropy Inverse Reinforcement Learning
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Dynamic game theory provides mathematical means for modeling the interaction between several players, where their decisions are explained by individual cost functions. The inverse problem of dynamic games, where cost functions are sought which explain observed behavior, has recently gained attention due to its potential application for identification of biological systems and the possibility of generalizing inverse optimal control results. In this paper, we extend maximum entropy inverse reinforcement learning to the N-player case in order to solve inverse dynamic games with continuous-valued state and control spaces. On this basis, we first present a method for identification of cost function parameters in a cooperative game. Afterwards, we propose an approach for identifying cost function parameters which explain the behavior of the players in a non-cooperative setting, i.e. open-loop and feedback Nash equilibrium behaviors. Furthermore, we give results on the unbiasedness of the estimation of cost function parameters for each class of inverse dynamic game. The applicability of the methods is demonstrated with simulation examples of a nonlinear and a linear-quadratic dynamic game.
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