Lossless abstraction of imperfect information games

abstraction of imperfect information games ANDREW GILPIN and TUOMAS SANDHOLM Computer Science Department Carnegie Mellon University Pittsburgh, PA, USA Finding an equilibrium of an extensive form game of imperfect information is a fundamental problem in computational game theory, but current techniques do not scale to large games. To address this, we introduce the ordered game isomorphism and the related ordered game isomortraction transformation. For a multi-player sequential game of imperfect information with observable actions and an ordered signal space, we prove that any Nash equilibrium in an ed smaller game, obtained by one or more applications of the transformation, can be easily converted into a Nash equilibrium in the original game. We present an algorithm, GameShrink, racting the game using our isomorphism exhaustively. Its complexity is ˜O(n2), where n is the number of nodes in a structure we call the signal tree. It is no larger than the game tree, and on nontrivial games...

• Type: Journal
• Year: 2007
• Where: JACM
• Authors: Andrew Gilpin, Tuomas Sandholm
• Keywords: Game, Imperfect Information, JACM 2007, Ordered Game