The analysis of dynamic games hinges on assumptions about players' actions and beliefs at information sets that are not expected to be reached during game play. Under the standard notion of sequential rationality, these assumptions cannot be tested on the basis of observed, on‐path behavior. This paper introduces a novel optimality criterion, structural rationality , which addresses this concern. In any dynamic game, structural rationality implies weak sequential rationality (Reny (1992)). If players are structurally rational, assumptions about on‐path and off‐path beliefs concerning off‐path actions can be tested via suitable “side bets.” Structural rationality also provides a theoretical rationale for the use of a novel version of the strategy method (Selten (1967)) in experiments.

This paper proposes a model of decision under ambiguity deemed vector expected utility, or VEU. In this model, an uncertain prospect, or Savage act, is assessed according to (a) a baseline expected-utility evaluation, and (b) an adjustment that reflects the individual's perception of ambiguity and her attitudes toward it. The adjustment is itself a function of the act's exposure to distinct sources of ambiguity, as well as its variability. The key elements of the VEU model are a baseline probability and a collection of random variables, or adjustment factors, which represent acts exposed to distinct ambiguity sources and also reflect complementarities among ambiguous events. The adjustment to the baseline expected-utility evaluation of an act is a function of the covariance of its utility profile with each adjustment factor, which reflects exposure to the corresponding ambiguity source. A behavioral characterization of the VEU model is provided. Furthermore, an updating rule for VEU preferences is proposed and characterized. The suggested updating rule facilitates the analysis of sophisticated dynamic choice with VEU preferences.

This paper considers local and global multiple-prior representations of ambiguity for preferences that are (i) monotonic, (ii) Bernoullian, that is, admit an affine utility representation when restricted to constant acts, and (iii) locally Lipschitz continuous. We do not require either certainty independence or uncertainty aversion. We show that the set of priors identified by Ghirardato, Maccheroni, and Marinacci's (2004) “unambiguous preference” relation can be characterized as a union of Clarke differentials. We then introduce a behavioral notion of “locally better deviation” at an act and show that it characterizes the Clarke differential of the preference representation at that act. These results suggest that the priors identified by these preference statements are directly related to (local) optimizing behavior.

We provide a behavioral foundation to the notion of 'mixture' of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully subjective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may 'distort' the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley's model of choice with incomplete preferences.