Search

Simultaneous move games model discrete, multistage interactions where at each stage players simultaneously choose their actions. At each stage, a player does not know what action the other player will take, but otherwise knows the full state of the game. This formalism has been used to express games in general game playing and can also model many discrete approximations of real-world scenarios. In this paper, we describe both novel and existing algorithms that compute strategies for the class of two-player zero-sum simultaneous move games. The algorithms include exact backward induction methods with efficient pruning, as well as Monte Carlo sampling algorithms. We evaluate the algorithms in two different settings: the offline case, where computational resources are abundant and closely approximating the optimal strategy is a priority, and the online search case, where computational resources are limited and acting quickly is necessary. We perform a thorough experimental evaluation on six substantially different games for both settings. For the exact algorithms, the results show that our pruning techniques for backward induction dramatically improve the computation time required by the previous exact algorithms. For the sampling algorithms, the results provide unique insights into their performance and identify favorable settings and domains for different sampling algorithms.

In this paper forward-pruning methods, such as multi-cut and null move, are tested at so-called ALL nodes. We improved the principal variation search by four small but essential additions. The new PVS algorithm guarantees that forward pruning is safe at ALL nodes. Experiments show that multi-cut at ALL nodes (MC-A) when combined with other forward-pruning mechanisms give a significant reduction of the number of nodes searched. In comparison, a (more) aggressive version of the null move (variable null-move bound) gives less reduction at expected ALL nodes. Finally, it is demonstrated that the playing strength of the lines of action program MIA is significantly (scoring 21% more winning points than the opponent) increased by MC-A.