Volunteering for heterogeneous tasks

We model the search for volunteers as a war of attrition. Every player is tempted to wait for someone else to volunteer for the tasks. When tasks are not equivalent, it may be optimal to volunteer quickly to perform an easy task. We analyze the trade-off between volunteering for an easy task and taking the risk of having to perform a more strenuous task in order to get the chance of avoiding all tasks. When the cost of waiting is borne by agents until every task has found a volunteer, we show that it may be optimal to volunteer for the difficult task even if an easier task is available, in order to speed up the process and reduce the costs of waiting.