The process of allocating rights to resources can be viewed as a contest: parties compete with each other for the right to claim a larger allocation. In some situations, the amount of the resource that is available to allocate may be unknown when parties are competing for shares and perhaps not realized until contestants actually attempt to claim their shares of the resource. For example, fishing quotas may be awarded based on estimated fish populations, but if there are fewer fish than anticipated, those who are last to harvest may not be able to fill their quota. We model contests of this form and test the predictions of the model using a controlled laboratory experiment. The general result, supported by both theory and experimental data, is that participants compete less intensively for shares of the resource when uncertainty regarding the size of the prize is resolved later in the process.