Generation method for adversarial strategies in underwater incomplete information games

The Nash differential strategy is suitable for complete information scenarios, but in the underwater environment with incomplete information, the complexity of obtaining solutions and the associated computational cost increase significantly. Therefore, the paper proposes a generation method to seek the solutions for the game adversarial strategy in the underwater environment. First, the relative motion relationship in a bilateral pursuit-evasion game was established, and the incomplete information characteristics were described using discrete and non-uniform time sequences, thus providing a foundation for constructing the expressions of the strategy. Secondly, based on the separation theorem of the secondary payment function and its minimum and maximum principles, the forms of the strategy within discrete time intervals were derived, and the strategy expressions for state estimation is presented. Finally, the Markov method was employed to construct the state transfer payment function, and key state transfer nodes were selected using threshold conditions, effectively reducing strategy update frequency and achieving efficient approximate solutions. The simulation results demonstrate that the proposed generation method exhibits good game effects in the underwater environment with incomplete information, which can quickly generate adversarial strategies.