Monte Carlo Tree Search (MCTS) is a widely-used technique for game-tree search in sequential turn-based games. The extension to simultaneous move games, where all players choose moves simultaneously each turn, is non-trivial due to the complexity of this class of games. In this paper, we describe simultaneous move MCTS and analyze its application in a set of nine disparate simultaneous move games. We use several possible variants, Decoupled UCT, Sequential UCT, Exp3, and Regret Matching. These variants include both deterministic and stochastic selection strategies and we characterize the game-play performance of each one. The results indicate that the relative performance of each variant depends strongly on the game and the opponent, and that parameter tuning can also not be as straightforward as the purely sequential case. Overall, Decoupled UCT performs best despite its theoretical shortcomings.
Tak, M. J. W., Lanctot, M., & Winands, M. H. M. (2014). Monte Carlo Tree Search variants for simultaneous move games. In IEEE Conference on Computatonal Intelligence and Games, CIG. IEEE Computer Society. https://doi.org/10.1109/CIG.2014.6932889