Application of Mean Field Games to Growth Theory

Abstract

Recent theories of economic growth, following the Schumpeterian model developed essentially by P. Aghion and P. Howitt ([AH92]), mainly focus on research and industrial innovation as the only way to generate a non decreasing growth process. Here, we are back to former ideas to explain growth with human capital accumulation only. However, our framework is quite new since we use the theory designed by J.-M. Lasry and P.-L. Lions on mean-field games ([LL06a, LL06b, LL07a]). This new framework allows us to model in a simple way the interaction between people and growth will be a byproduct of the interaction and competition between people to improve their welfare. We basically model a continuum of individuals whose wages depend not only on their own human capital but also on the whole distribution of human capital. This distribution dependency is important in two different ways. First, we take into account a competition effect in the labor market. Second we model the easiness or difficulty to improve human capital depending on the proximity to the technological frontier. Like in the recent paper by Aghion et al (2001) ([AHHV01]) or as in Aghion and Howitt ([AH]), growth is fostered by an escape competition effect. However, in our setting, it is the threat of competition that forces people to improve their human capital and not competition by itself: because individuals less skilled than a given person represent a threat for this person, she is forced to accumulate human capital. That leads evenhal-00348376,