Algorithmic Combinatorial Game Theory

Motivation

Games are as old as humanity. The combinatorial game theory community has studied games extensively, resulting in powerful tools for their analysis, like the notion of game-theoretic value. This theory provides a high-level understanding of how to play combinatorial games, but to completely solve specific games requires algorithmic techniques. So far, algorithmic results are rare and mainly negative, e.g., the proofs that Chess and Go are EXPTIME-complete. There are also some positive results on endgames of Go and on various classes of impartial games. But most games lie in "Wonderland4, i.e., we are wondering about their complexity/efficiency. (We are not normally interested in exhaustive approaches like the recent world-class computer players for Checkers and Chess.)

The two large communities of combinatorial game theory and algorithmics rarely interact. This is unfortunate. Game theory could benefit from applying algorithmic techniques to games with known outcomes but no known efficient strategies, e.g., Hex and poset games such as Chomp. On the other hand, better knowledge of the game-theoretic tools could help researchers in algorithmics to develop more efficient or more general algorithms for games whose complexity is barely known, e.g., Hex and Chomp and epidemiography games such as Nimania. Maybe the game-theoretic framework can even be extended to non combinatorial games, like geometric games.

There has been a recent surge of interest in algorithmic combinatorial game theory from both communities. The goal of this seminar is to bring these two communities together, to advance the area of algorithmic combinatorial game theory from infancy to maturity. We will invite a few keynote speakers from both communities; so far, Elwyn Berlekamp has confirmed his participation.