Abstract
Efficient allocations in common-pool resources cannot be accomplished when appropriators are selfish. In addition, we find that a system of a common-pool resource is locally unstable if there are four or more appropriators. Such instability most likely makes efficiency worse than that in the Nash equilibrium. These results indicate that equilibrium analyses might not capture the essence of the common-pool resource problem. They may also provide an answer to the unexplained pulsing behavior among appropriators and inefficiency observed in experiments.
Highlights
An open access resource such as a fishing ground, an irrigation system, or a forest is called a common-pool resource (CPR)
The problem is often formalized in terms of game theory and the concept of a Nash equilibrium, where, in general, the resources are overexploited at the Nash equilibria of CPR dilemma games
We investigate the conditions for the dynamic stability of the Nash equilibrium of a CPR dilemma game
Summary
An open access resource such as a fishing ground, an irrigation system, or a forest is called a common-pool resource (CPR). The appropriators’ labor inputs in the time step is x2=(10, 10, 10, 10, 10, 10), which is the Nash equilibrium (e′) Given that this equilibrium is itself located on the best-response curve k-e′, we have r(x−2i )=10, and the system stays at the equilibrium. It reveals that the Nash equilibrium is stable as long as n≤6, but is destabilized for larger n-values, resulting in a cycle with period 2. The best-response function stays unchanged, the width of the box expands to the right and, the jump from b should be amplified from d′ to d This amplification of the response by the total labor inputs results in the destabilization of the Nash equilibrium. The Nash equilibrium is destabilized for n≥4, resulting in a cycle with period 2
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