Departmental Bulletin Paper The Tragedy of the Commons : The Dynamic Adjustment under Unregulated Population Growth

早川 弘晃

Vol.23pp.51 - 83 , 2015-03-30
The tragedy of the commons is often represented in terms of Nash equilibrium of a static game of complete information. Such elucidation is misleading since it does not capture the dynamics of an underlying process that eventually invites the tragedy as the number of the users increases without limit. Using a bucolic case as an example, this paper examines Hardin’s thesis from the standpoint of a dynamic process by elucidating the inherent logic of entry that is inevitable.The key to this process is the devaluation cost that an added number imposes on the average value of cattle.When a finite number of herdsmen use the commons, the stock carried by each herdsman reaches the state of equilibrium when an additional benefit from an added number equals an additional cost comprised of the private marginal cost and the devaluation cost that this number induces on this stock. But, this equilibrium is constantly disrupted by the entry of another herdsman, for at the point of entry there is no need for this entrant to consider the devaluation cost induced by his own action. As the entrant increases his stock and imposes the devaluation cost on all existing stocks, the incumbent herdsmen are forced to cut down their stocks. The adjustment ceases when an additional benefit is balanced again with an additional cost. This process of entry and adjustment continues until the stock of all herdsmen combined approaches its maximum size allowable under a given private marginal cost, while each herdsman’s share of this total falls to zero. Thus, the logic of entry and an accompanying adjustment account for the eventual arrival of the day of reckoning unless population growth is checked. The process itself has little to do with a simultaneous move game which has Nash equilibrium, but a temporary equilibrium reached with a finite number of herdsmen isidentical to this equilibrium. The problem is that this number increases without limit and that an entrant at any stage finds it profitable to enter the commons. The analysis confirms Hardin’s insight that it is overpopulation that eventually leads to the tragedy. The paper also places the issue and the literature in a historical perspective.

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