Entry in quota-managed industries: A global game with placement uncertainty

We present a model of firm entry in an industry that is managed with a cap-and-trade quota regulation. Firms are heterogeneous in their individual productivities; each knows its own productivity but ranks within the firm population sre uncertain. Each firm forms a posterior on the distribution of competing firms’ productivities based on its own productivity. Entry is modeled as a simultaneous move game with incomplete information. Under an industry wide quota, the entry payoff (capital rent) is high if average productivity among the set of all active firms is low. In this case, the quota price is low and the return to vested capital is higher. The opposite holds when the average productivity among the set of active firms is high. In our model, the information structure is irrelevant when the cost of entry is sufficiently low. A firm chooses whether to enter the industry solely based its own productivity. But, when the entry cost is sufficiently high, firms’ entry behavior differs across incomplete vis-à-vis complete information. We derive threshold entry strategies which separate active and inactive firms. We show that placement uncertainty in general increases entry relative to a full information benchmark. Additional comparative statics and efficiency implications are provided. We extend our model to consider placement overconfidence, whereby a firm believes it ranks higher on the productivity continuum than is objectively warranted. We show that this form of overconfidence exacerbates the over-entry problem. Our results explain investment/divestment patterns in overcapitalized industries adopting quota regulations, commercial fisheries in particular. The results can also explain excess entry and investment by overconfident entrepreneurs.