We present a model of firm entry in an industry that is managed with an aggregate production quota or cap-and-trade (CAT) regulation. Firms are heterogeneous in productivity; each knows its own costs of production but is uncertain about where its costs rank among an entrant population. Entry is modeled as a simultaneous move game with incomplete information. Under CAT, firms compete to secure shares of a fixed number of production permits. Entry payoffs are determined by own and rival entrant productivity. We derive the Bayesian Nash entry equilibrium and show conditions under which placement uncertainty leads to excess entry relative to full information. We derive conditions where the reverse, inefficiency due to under entry, occurs. Whereas the behavioral IO literature has attributed over-entry and over-investment to bias, i.e., entrepreneurs are overconfident believing that they are better than average, we show that rational uncertainty regarding post entry competition is sufficient. Our results offer a new explanation for often-observed rational exuberance and for rational pessimism in investment by entrepreneurs.