Manna from Heaven or Forty Years in the Desert: Optimal Allocation without Transfer Payments

Abstract

Often an organization or government must allocate goods without collecting payment in return. This may pose a di¢ cult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known di¤erences is not a viable option. In this paper, we …nd an optimal mechanism to allocate goods when the designer is benevolent. While the designer cannot charge agents, he can receive a costly but wasteful signal from them. We …nd conditions for which ignoring these costly signals by giving agents equal share (or using lotteries if the goods are indivisible) is optimal. In other cases, those that send the highest signal should receive the goods; however, we then show that there exist cases where more complicated mechanisms are superior. Finally, we show that the optimal mechanism is independent of the scarcity of the goods being allocated.

Optimal mechanism design and money burning

“…The characterization unifies results in the economics literature [5,26] and also extends them in two important directions. First, the results in [5,26] concern only multi-unit auctions, where k identical units of an item can be allocated to agents who each desire at most one unit.…”

“…The characterization unifies results in the economics literature [5,26] and also extends them in two important directions. First, the results in [5,26] concern only multi-unit auctions, where k identical units of an item can be allocated to agents who each desire at most one unit. Our characterization applies to the general, possibly asymmetric, setting of single-parameter agents; for example, agents could be seeking disjoint paths in a multicommodity network.…”

“…Independently from our work, Chakravarty and Kaplan [5] describe the optimal Bayesian auction in multi-unit money-burning settings. Our work extends this analysis to general single-parameter agent settings with explicit focus on the case where the hazard rate is not monotone in either direction.…”

Efficient Money Burning in General Domains

“…money burning, instead of actual monetary transfers. One could think of the time wasted in "computational" challenges (e.g., captcha) or in waiting queues or lists (e.g., in hospitals [2] or in popular events or places), where each agent's waiting time serves as an implicit proof of how much the agent values the service (see also [13,4] for more examples in the same direction). Assuming that the value of the wasted resources is measured in the same unit as the agent valuations, the natural objective in such settings is to maximize the net gain of the agents.…”

What Money Can't Buy: Allocations with Priority Lists, Lotteries and Queues

“…In contrast to the papers above, I provide, within the same environment, a closed form solution to the problem of designing an optimal mechanism. Closely related environments, where agent compete for a set of homogenous goods by engaging in costly effort or money burning, are studied in a number of papers in the context of different applications: McAfee and McMillan (1992), Chakravarty and Kaplan (2006), Yoon (2009), and Hartline and Roughgarden (2008). My results are significantly more gen-3 If an institution has a direct interest in screening individuals on the basis of specific characteristics a distribution based on the willingness to pay may not be optimal (e.g.…”