Traveling waves for a nonlocal KPP equation and mean-field game models of knowledge diffusion

We analyze a mean-field game model proposed by economists R.E. Lucas and B. Moll (2014) to describe economic systems where production is based on knowledge growth diffusion. This reduces PDE system backward Hamilton-Jacobi-Bellman equation coupled with forward KPP-type nonlocal reaction term. study the existence of traveling waves for this system, obtaining both critical supercritical waves. In particular we prove conjecture raised balanced path described economy, supposed be expected stable in long run. also provide nonexistence results which clarify role parameters model.