Rationalizability and interactivity in evolutionary OLG models

We use the theory of rationalizable choices to study the survival and the extinction of types (or traits) in evolutionary OLG models. Two properties of evolutionary processes are introduced: rationalizability by a fitness ordering (i.e. only the most fit types survive) and interactivity (i.e. a withdrawal of types affects the survival of other types). Those properties are shown to be logically incompatible. We then examine whether the evolutionary processes at work in canonical evolutionary OLG models satisfy rationalizability or interactivity. We study n-types versions of the evolutionary OLG models of Galor and Moav (2002) and Bisin and Verdier (2001), and show that, while the evolutionary process at work in the former is generally rationalizable by a fitness ordering, the opposite is true for the latter, which exhibits, in general, interactivity.