  We study Monte Carlo tree search (MCTS) in zero-sum extensive-form games with
perfect information and simultaneous moves. We present a general template of
MCTS algorithms for these games, which can be instantiated by various selection
methods. We formally prove that if a selection method is $\epsilon$-Hannan
consistent in a matrix game and satisfies additional requirements on
exploration, then the MCTS algorithm eventually converges to an approximate
Nash equilibrium (NE) of the extensive-form game. We empirically evaluate this
claim using regret matching and Exp3 as the selection methods on randomly
generated games and empirically selected worst case games. We confirm the
formal result and show that additional MCTS variants also converge to
approximate NE on the evaluated games.
