In this paper, I pick up on an important theme in Mario Rizzo’s work: that rationality should be understood more broadly than the rational choice model as learning to adjust behaviour in the light of experience and the mistakes that it yields. In particular, I focus on learning-by-doing (LBD). I argue in the first part of the paper that it should be regarded as one of the central insights in economics, alongside those that are more usually recognised like the gains from trade and the importance of unintended consequences. I use Smith and Hirschman’s discussion of LBD to ground this claim. In the second part of the paper, I turn to the determinants of LBD in teams. I argue that the key rule or constitutional/policy design question is how best to embrace the diversity that is central to LBD within teams without this undermining the social origins of co-operation in teams.

Using a variation of the rainbow construction and various pebble and colouring games, we prove that RRA, the class of all representable relation algebras, cannot be axiomatised by any first-order relation algebra theory of bounded quantifier depth. We also prove that the class At(RRA) of atom structures of representable, atomic relation algebras cannot be defined by any set of sentences in the language of RA atom structures that uses only a finite number of variables.