Contrary to most formal models of decision making under risk and uncertainty that are built on the basis of prescriptive behavioral principles or axioms, this paper derives a descriptive model of decision making under ambiguity based on principles of behavior, i.e. principles that describe how people behave as opposed to how they should behave. The model assumes that the people evaluate the impact of ambiguous probabilities by first anchoring on a given value of the unknown probability and then adjusting this by the net effect of imagining or ‘trying out’ other values the probability could take. The mental simulation process incorporates giving differential weight to the ranges of probability values above and below the anchor where such weight reflects individual and situational variables. In particular, the assumption that people are cautious as opposed to reckless in making decisions leads to attributing more weight to possible values of probabilities below the anchor when considering potential gains, and the reverse when faced with potential losses. Two experiments test implications of the model for situations involving competitive decisions. The first concerns legal decision making, the second involves the purchase and sale of industrial equipment. Both experiments validate predictions that (a) the effects of ambiguity depend on both the sign of payoffs and the level of probabilities, and (b) two parties to a negotiation or transaction may be differently sensitive to ambiguity. Finally, the model is compared to other models of ambiguity proposed in the literature, and directions are suggested for future work.