THE COMMON PROPERTY RESOURCE AS A DYNAMIC GAME (EXTERNALITIES, AQUIFER, COMMON PROPERTY, RESOURCE ALLOCATION)

This thesis analyzes common property resource models with congestion and stock externalities. In the basic model, output prices are exogenous; current extraction costs of the firm with access to the commons are assumed to depend on the level of extraction of the firm, aggregate extraction of all firms, and the reserve stock of the resource. Open-loop and subgame perfect equilibria are compared qualitatively and quantitatively under three different industry structures: restricted access and the polar extremes of sole ownership and free access competition. Where access to the commons is restricted, the two equilibria yield qualitatively different extraction strategies. The subgame perfect equilibrium captures the inefficiency associated with the strategic scramble to capture the resource reserves, the open loop does not. Under sole ownership, the two equilibria coincide with the surplus maximizing extraction strategy. In free access, when the stock is non-renewable, or when the growth of the stock is governed by constant regeneration independent of the population size, the extraction strategies under both equilibrium concepts coincide with the free access equilibrium solution to the static problem. This is a fortunate circumstance since it means that free access perfect equilibrium extraction can be deduced without recourse either to game theory or to dynamic analysis. Aggregate extraction in each period is simply that unique quantity which completely dissipates industry profits. This is precisely the assumption which is implicit in the extensive literature on the commons which preceded widespread understanding of multistage games.; But is this assumption of industry rent dissipation in free access always valid? Granted that as the number of extractors grows, the rent per period for a given stock of each of them converges to zero. This alone, however, does not assure that the sum of the rents also converges to zero. The matter is settled by the example in Chapter 3. When the analysis is extended to a model where regeneration of the stock is governed by proportional growth, industry rents in a free access, perfect equilibrium are shown to converge to a positive number. Hence, the traditional assumption of complete rent dissipation under free access is erroneous and would lead to erroneous conclusions. In particular, larger aggregate extraction would be predicted using the traditional approach than would in fact occur in the free access, perfect equilibrium. Therefore, until conditions sufficient to eliminate such cases are discovered, there is no substitute for dynamic strategic analysis of the commons problem.