Kuhn’s Theorem for extensive form Ellsberg games

Abstract

We propose the notions of mixed and behavioral Ellsberg strategies for extensive form games and prove that these strategies are outcome-equivalent if and only if mixed Ellsberg strategies satisfy a certain rectangularity condition. In addition, we show that not only the profile of Ellsberg strategies must be appropriately chosen but also the extensive form must satisfy further restrictions beyond those implied by perfect recall in order to ensure that each player will respect his ex ante strategy choice with the evolution of play.