Particle Filtering Approximation of Kriegspiel Play with Opponent Modeling

Kriesgpiel, or partially observable chess, is appealing to the AI community due to its similarity to real-world applications in which a decision maker is not a lone agent changing the environment. This paper applies the framework of interactive POMDPs to design a competent Kriegspiel player. The novel element proposed here is a way to handle complexity in I-POMDPs by using the notion of quantal response developed in behavioral game theory. This allows us to model only one (or a few) prototypical opponents while representing a whole ensemble of possible levels of expertise of the opponent’s evaluation functions. The model is used to predict the opponent’s likely moves. The moves of our own player can then be computed based on these predictions. Furthermore, we explore practical considerations when approximating I-POMDP solutions. Due to the immense number of possible states in a game of chess, we approximate the distribution over states using a sampling of possible states. We show the practical viability of our approach by testing a Kriegspiel playing agent against human players.