Kuhn's Theorem for Extensive Games with Unawareness
22 Pages Posted: 3 Nov 2017
Date Written: November 1, 2017
Abstract
We extend Kuhn's Theorem to extensive games with unawareness. This extension is not entirely obvious: First, extensive games with non-trivial unawareness involve a forest of partially ordered game trees rather than just one game tree. An information set at a history in one tree may consist of histories in a less expressive tree. Consequently, perfect recall takes a more complicated form as players may also become aware of new actions during the play. Second, strategies can only be partially an object of ex-ante choice in games with unawareness. Finally, histories that a player may expect to reach with a strategy profile may not be the histories that actually occur with this strategy profile, requiring us to define appropriate notions of equivalence of strategies.
Keywords: perfect recall, mixed strategy, behavior strategy, unawareness
JEL Classification: C72, D83
Suggested Citation: Suggested Citation