The tragedy of the commons: the logic of entry and the dynamic process under two scenarios

Abstract

This paper analyzes the dynamics of entry and adjustment that underlies the process leading to the tragedy of the commons under two scenarios, one in which the users only react ex post to the entry of other users and the other in which the users anticipate and proact to such entry. The key to our analysis is the logic of entry based on the devaluation cost, which explains (1) why entry takes place when the incumbent users are in temporary equilibrium, (2) how this equilibrium shifts sequentially with the entry of new users, (3) why such equilibria resemble either the Cournot-Nash equilibrium of a static game or the Stackelberg type equilibrium of a dynamic game depending on the reactive or the proactive nature of the users, (4) why the stocks owned by the users in the proactive case depend on the order of entry and remain unchanged once determined at the point of entry. The speed of depletion, cumulative profits of the users, and the distribution pattern of the ownership differ significantly between the two scenarios. Our theory also explains why and how duopoly and oligopoly emerge through the process of entry and adjustment and acquire different equilibrium features.