Group Size and Threshold Uncertainty in Common-Pool Resource Dilemmas

Abstract

We present the first analysis of the common-pool resource dilemma game under group size uncertainty. In our model, the number of active players and the size of the resource are random variables, but the distributions are common knowledge. All active players privately and simultaneously choose an amount of the resource to request. If the sum of all requests is less than or equal to the realized resource size, then all players receive utility equal to their request; otherwise, all players receive zero utility. The introduction of group size uncertainty makes the traditional analysis intractable. We exploit the mixed continuous/discrete nature of the game to obtain the set of potential equilibria, of which only a subset can be classified as equilibria in the Nash sense. We compare our predictions to the data of several experimental studies ex post. Theoretically, an increase in group size uncertainty increases equilibrium resource requests. Overall, the data supports a reversal of the prediction: an increase in group size uncertainty decreases resource requests, provided resource uncertainty is not too extreme. A large portion of the data can be rationalized with simple pessimistic decision-making, whereby individuals optimize in a subjective probability framework that places nearly all mass on the worst-case scenario threshold and group size realizations.

Keywords: common-pool resource, group size uncertainty, environmental uncertainty, experiment, pessimism

JEL Classification: C72, C91, D71, D80, Q20, Q50