Ambiguity aversion, games against nature, and dynamic consistency

Several papers, adopting an axiomatic approach to study decision making under ambiguity aversion, have produced conflicting predictions about how decision makers would behave in simple dynamic urn problems. We explore the concepts of ambiguity aversion and dynamic consistency, with examples of dynamic games against nature. Basically, a malevolent nature puts balls into the urn, and a fair nature draws them out. Depending on the game, various choices that seem inconsistent with static notions of ambiguity aversion or dynamic consistency are consistent with subgame perfection. In the dynamic 3-color Ellsberg urn problem with 30 red balls and 60 blue or green balls, the decision maker could strictly prefer to bet on blue-green at time 0, and to switch to red-green after learning that the ball is not green.