Towards Strategic 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, compared to the existing approaches, is to model the opponent as a competent player and to predict his likely moves. The moves of our own player can then be computed based on these predictions. The problem is challenging because, first, there are many possible world states the agent has to keep track of. Second, one may be unsure about the characteristics of the other player which could influence his behavior, such as his level of expertise or his evaluation function. To keep the size of the state space manageable we consider a scaled down version of Kriegspiel played on 4 by 4 chessboard with only a king and a queen on both sides. To deal with an opponent with uncertain characteristics we use the notion of quantal responses developed in behavioral game theory. This allows us to consider only one prototypical opponent while modeling a whole ensamble of possible opponents. We implemented our approach using influence diagrams, and discuss results in example situations.