Credit rating dynamics and competition

I analyze the market for credit ratings with competition between more than two rating agencies. How can honest rating behavior be achieved, and under which conditions can a new honest rating agency successfully invade a market with inflating incumbents? My model predicts cyclic dynamics if sophisticated investors have a high impact on agencies' reputation. In contrast, if trusting investors have the main impact, then the dynamics exhibits a saddle point rather than cycles. In this case, regulatory support for honest rating agencies is only needed for a limited time, but the effect is sustainable in the long run.