Assessing the Truth Axiom under incomplete information

Within an incomplete information framework (where the primitives are the individuals' belief hierarchies) the Truth Axiom is stated locally as the hypothesis that no individual has any false beliefs and that this fact is common belief. We decompose this 'Truth Condition' into three parts: Truth of common belief, Truth about common belief and 'quasi-coherence' (the common possibility of common belief in no error). We show the latter to be equivalent to the absence of unbounded gains from betting for 'moderately risk averse' agents as well as to a qualitative impossibility of 'agreeing to disagree'. We show that these characterizations may not hold in more general non-Bayesian models of decision-making under uncertainty. (C) 1998 Elsevier Science B.V. All rights reserved.