Kuhn's Theorem for Extensive Form Ellsberg Games

The paper generalizes Kuhn's Theorem to extensive form games in which players condition their play on the realization of ambiguous randomization devices and use a maxmin decision rule to evaluate the consequences of their decisions. It proves that ambiguous behavioral and ambiguous mixed strategies are payoff and outcome equivalent only if the latter strategies satisfy a rectangularity condition. The paper also discusses dynamic consistency. In particular, it shows that not only the profile of ambiguous 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 respects her ex ante contingent choice with the evolution of play.