Competitive Repeated Allocation without Payments

We study the problem of allocating a single item repeatedly among multiple competing agents, in an environment where monetary transfers are not possible. We design (Bayes-Nash) incentive compatible mechanisms that do not rely on payments, with the goal of maximizing expected social welfare. We first focus on the case of two agents. We introduce an artificial payment system, which enables us to construct repeated allocation mechanisms without payments based on one-shot allocation mechanisms with payments. Under certain restrictions on the discount factor, we propose several repeated allocation mechanisms based on artificial payments. For the simple model in which the agents’ valuations are either high or low, the mechanism we propose is 0.94-competitive against the optimal allocation mechanism with payments. For the general case of any prior distribution, the mechanism we propose is 0.85-competitive. We generalize the mechanism to cases of three or more agents. For any number of agents, the mechanism we obtain is at least 0.75-competitive. The obtained competitive ratios imply that for repeated allocation, artificial payments may be used to replace real monetary payments, without incurring too much loss in social welfare.