From Monetary to Nonmonetary Mechanism Design via Artificial Currencies

Nonmonetary mechanisms for repeated allocation and decision making are gaining widespread use in many real-world settings. Our aim in this work is to study the performance and incentive properties of simple mechanisms based on artificial currencies in such settings. To this end, we make the following contributions: For a general allocation setting, we provide two black-box approaches to convert any one-shot monetary mechanism to a dynamic nonmonetary mechanism using an artificial currency that simultaneously guarantees vanishing gains from nontruthful reporting over time and vanishing losses in performance. The two mechanisms trade off between their applicability and their computational and informational requirements. Furthermore, for settings with two agents, we show that a particular artificial currency mechanism also results in a vanishing price of anarchy.

Competitive Equilibrium with Indivisible Goods and Generic Budgets

Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods (Foley 1967, Varian 1974). Every agent receives an equal budget of artificial currency with which to purchase goods, and prices match demand and supply. However, a CEEI is not guaranteed to exist when the goods are indivisible even in the simple two-agent, single-item market. Yet it is easy to see that, once the two budgets are slightly perturbed (made generic), a competitive equilibrium does exist. In this paper, we aim to extend this approach beyond the single-item case and study the existence of equilibria in markets with two agents and additive preferences over multiple items. We show that, for agents with equal budgets, making the budgets generic—by adding vanishingly small random perturbations—ensures the existence of equilibrium. We further consider agents with arbitrary nonequal budgets, representing nonequal entitlements for goods. We show that competitive equilibrium guarantees a new notion of fairness among nonequal agents and that it exists in cases of interest (such as when the agents have identical preferences) if budgets are perturbed. Our results open opportunities for future research on generic equilibrium existence and fair treatment of nonequals.

Design of Lotteries and Wait-Lists for Affordable Housing Allocation

We study a setting in which dynamically arriving items are assigned to waiting agents, who have heterogeneous values for distinct items and heterogeneous outside options. An ideal match would both target items to agents with the worst outside options and match them to items for which they have high value. Our first finding is that two common approaches—using independent lotteries for each item and using a waitlist in which agents lose priority when they reject an offer—lead to identical outcomes in equilibrium. Both approaches encourage agents to accept items that are marginal fits. We show that the quality of the match can be improved by using a common lottery for all items. If participation costs are negligible, a common lottery is equivalent to several other mechanisms, such as limiting participants to a single lottery, using a waitlist in which offers can be rejected without punishment, or using artificial currency. However, when there are many agents with low need, there is an unavoidable trade-off between matching and targeting. In this case, utilitarian welfare may be maximized by focusing on good matching (if the outside option distribution is light tailed) or good targeting (if it is heavy tailed). Using a common lottery achieves near-optimal matching, whereas introducing participation costs achieves near-optimal targeting. This paper was accepted by Charles Corbett, operations management.