Combinatorial Games with Incomplete Information

Abstract

Games with incomplete information model multi-agent interaction in which players do not have common knowledge of the game they play. We propose a minimal generalisation of combinatorial games to incorporate incomplete information, called combinatorial game with incomplete information (CGII). The most important feature of CGIIs is that all actions are public, which allows better visualisation of each player's knowledge and incomplete information. To further motivate the study of this new formalism, we show that computing optimal strategies for CGIIs has the same computational complexity as for general extensive-form games.