A New Algorithm for Generating Equilibria in Massive Zero-Sum Games

Martin Zinkevich, Michael Bowling, Neil Burch

In normal scenarios, computer scientists often consider the number of states in a game to capture the difficulty of learning an equilibrium. However, players do not see games in the same light: most consider Go or Chess to be more complex than Monopoly. In this paper, we discuss a new measure of game complexity that links existing state-of-the-art algorithms for computing approximate equilibria to a more human measure. In particular, we consider the range of skill in a game, i.e. how many different skill levels exist. We then modify existing techniques to design a new algorithm to compute approximate equilibria whose performance can be captured by this new measure. We use it to develop the first near Nash equilibrium for a four round abstraction of poker, and show that it would have been able to win handily the bankroll competition from last year's AAAI poker competition.

Subjects: 1.8 Game Playing; 7.1 Multi-Agent Systems

Submitted: Apr 24, 2007

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