Optimal Allocation without Transfer Payments

Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known differences is not a viable option. In this paper, we find 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 find 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.mechanism design; efficient allocation; waiting lines; lotteries; all-pay auctions

Optimal Allocation without Transfer Payments

Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known differences is not a viable option. In this paper, we …nd an optimal mechnnism 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.mechanism design; efficient allocation; waiting lines; lotteries; all-pay auctions

Optimal allocation without transfer payments

Author's draft dated February 2010 issued as discussion paper by University of Exeter Business School. Final version published by Elsevier; available online at http://www.sciencedirect.com/Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs. In this paper, we find 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 find conditions for cases in 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. Also, we show that the optimal mechanism is independent of the scarcity of the goods being allocated

Optimal Allocation without Transfer Payments

Often an organization or government must allocate goods without collecting payment in return. This may pose a difficult problem either when agents receiving those goods have private information in regards to their values or needs or when discriminating among agents using known differences is not a viable option. In this paper, we find 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 find 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

Manna from heaven or forty years in the desert: optimal allocation without transfer payments

Often an organization, government or entity must allocate goods without collecting payment in return. This may pose a difficult problem when agents receiving those goods have private information in regards to their values or needs or discriminating among agents is not an option. In this paper, we search for 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 show that for a large class of distributions of valuations, ignoring these costly signals by giving agents equal share (or using lotteries if the goods are indivisible) maximizes the social surplus. 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

What money can't buy: allocations with priority lists, lotteries and queues

I study the welfare optimal allocation of a number of identical and indivisible objects to a set of heterogeneous risk-neutral agents under the hypothesis that money is not available. Agents have independent private values, which represent the maximum time that they are will- ing to wait in line to obtain a good. A priority list, which ranks agents according to their expected values, is optimal when hazard rates of the distributions of values are increasing. Queues, which allocates the ob- ject to those who wait in line the longest, are optimal in a symmetric setting with decreasing hazard rates.rationing; queues; priority lists; lotteries.

Optimal-in-expectation redistribution mechanisms

AbstractMany important problems in multiagent systems involve the allocation of multiple resources among the agents. If agents are self-interested, they will lie about their valuations for the resources if they perceive this to be in their interest. The well-known VCG mechanism allocates the items efficiently, is strategy-proof (agents have no incentive to lie), and never runs a deficit. Nevertheless, the agents may have to make large payments to a party outside the system of agents, leading to decreased utility for the agents. Recent work has investigated the possibility of redistributing some of the payments back to the agents, without violating the other desirable properties of the VCG mechanism.Previous research on redistribution mechanisms has resulted in a worst-case optimal redistribution mechanism, that is, a mechanism that maximizes the fraction of VCG payments redistributed in the worst case. In contrast, in this paper, we assume that a prior distribution over the agents' valuations is available, and our goal is to maximize the expected total redistribution.In the first part of this paper, we study multi-unit auctions with unit demand. We analytically solve for a mechanism that is optimal among linear redistribution mechanisms. We also propose discretized redistribution mechanisms. We show how to automatically solve for the optimal discretized redistribution mechanism for a given discretization step size, and show that the resulting mechanisms converge to optimality as the step size goes to zero. We present experimental results showing that for auctions with many bidders, the optimal linear redistribution mechanism redistributes almost everything, whereas for auctions with few bidders, we can solve for the optimal discretized redistribution mechanism with a very small step size.In the second part of this paper, we study multi-unit auctions with nonincreasing marginal values. We extend the notion of linear redistribution mechanisms, previously defined only in the unit demand setting, to this more general setting. We introduce a linear program for finding the optimal linear redistribution mechanism. This linear program is unwieldy, so we also introduce one simplified linear program that produces relatively good linear redistribution mechanisms. We conjecture an analytical solution for the simplified linear program

The Benefits of Costly Voting

We present a costly voting model in which each voter has a private valuation for their preferred outcome of a vote. When there is a zero cost to voting, all voters vote and hence all values are counted equally regardless of how high they may be. By having a cost to voting, only those with high enough values would choose to incur this cost. Hence, the outcome will be determined by voters with higher valuations. We show that in such a case welfare may be enhanced. Such an effect occurs when there is both a large enough density of voters with low values and a high enough expected value