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A seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either good. The value of the bundle and the ratio are the agent's private information. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price or a posted price mechanism for a class of distributions. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio are independently distributed. [ABSTRACT FROM AUTHOR]

We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(\epsilon,\delta)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(\epsilon,\delta)$-DP, improving upon previous results that only apply to at most three colors and for $\epsilon$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.

There is a strong demand for multi-attribute auctions in real-world scenarios for non-price attributes that allow participants to express their preferences and the item's value. However, this also makes it difficult to perform calculations with incomplete information, as a single attribute—price—no longer determines the revenue. At the same time, the mechanism must satisfy individual rationality (IR) and incentive compatibility (IC). This paper proposes an innovative dual network to solve these problems. A shared MLP module is constructed to extract bidder features, and multiple-scale loss is used to determine network status and update. The method was tested on real and extended cases, showing that the approach effectively improves the auctioneer's revenue without compromising the bidder. [ABSTRACT FROM AUTHOR]

We study sequential auctions as optimal mechanisms for selling multiple heterogeneous items to unit‐demand buyers. We find that as long as the items can be ordered in decreasing variation of the buyers' values, any combination of static standard auctions in this sequence achieves full efficiency and the constrained optimal revenue, subject to (BIC), (IIR), and the all‐sold constraint. In addition, with increasing threshold types and optimal static reserve prices, any l‐th price auctions in the same sequence can achieve the optimal revenue subject to (BIC) and (IIR). Our results have implications for practical auction design, such as sponsored search auctions. [ABSTRACT FROM AUTHOR]

Integrating Cost Reduction and Supplier Selection Activities Manufacturers who outsource production may find ways to reduce suppliers' cost to lower the contract price. Conventionally, this is done after supplier selection. However, in practice, a sizable portion of the degree to which the manufacturer can help a supplier reduce cost could be learned before the supplier starts production. This opens up a possibility to better integrate supplier selection and cost-reduction activities. In "Procurement Mechanisms with Postauction Preaward Cost-Reduction Investigations," Chen, Beil, and Duenyas explore an alternative procurement process wherein, after suppliers' initial pricing bids are collected, the manufacturer investigates suppliers' cost-saving potential and then leverages this information to select the contract winner. They provide analytical and numerical evidence that this integrated procurement process not only helps the manufacturers reduce cost significantly, but also benefits the suppliers in many plausible scenarios. A buyer seeking to outsource production may be able to find ways to reduce a potential supplier's cost, for example, by suggesting improvements to the supplier's proposed production methods. We study how a buyer could use such cost-reduction investigations by proposing a three-step supplier selection mechanism: First, each of several potential suppliers submits a price bid for a contract. Second, for each potential supplier, the buyer can exert an effort to see if the buyer can identify how the supplier could reduce their cost to perform the contract; the understanding is that if savings are found, they are passed on to the buyer if the supplier is awarded the contract. Third, the buyer awards the contract to whichever supplier has the lowest updated bid (the supplier's initial bid price minus any cost reduction the buyer is able to identify for that supplier). For this proposed process, we characterize how the buyer's decision on which suppliers for which to investigate cost reductions in step 2 is affected by the aggressiveness of the suppliers' bids in step 1. We show that, even if the buyer does not share the cost savings the buyer identifies in step 2, ex ante symmetric suppliers are actually better off (ex ante) in our proposed mechanism than in a setting without such cost-reduction investigations, resulting in a win–win for the buyer and suppliers. When suppliers' cost and cost-reduction distributions become very heterogeneous, the win–win situation may no longer hold, but every supplier still has an incentive to allow the buyer to investigate them in step 2 because it increases their chance of winning the contract. Using an optimal mechanism analysis, our numerical studies show that our proposed bid–investigate–award mechanism helps the buyer achieve near-optimal performance despite its simplicity. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2349. [ABSTRACT FROM AUTHOR]

A main challenge that service providers face when managing service systems is how to generate value and regulate congestion at the same time. To this end, classical queueing models suggest managers charge per-use fees and invest in capacity to speed up the service. However, in discretionary services, in which consumers value time in service and choose how long to stay, per-use fees result in suboptimal performance and speeding up does not apply. We study a queueing model of a service provider and rational consumers who are heterogenous in their requirements for service duration. Consumers incur disutility from waiting and choose whether to join and how long to spend in service. We consider time limits as a novel mechanism that may help in controlling congestion. Time limits put a cap on the maximum time that customers can spend in service. We analyze their effectiveness when combined with two price schemes: per-use fees and price rates. Time limits are effective because they reduce time in service and impact waiting times and joining behavior. Revenue maximizing firms and social planners who maximize social welfare benefit from implementing time limits in addition to price rates. Social planners who seek to maximize consumer welfare, however, focus on regulating congestion and should, therefore, offer the service for free but implement time limits if congestion levels are high. The attractiveness of time limits goes further. We show that time limits are not only a useful lever that works well when combined with simple price mechanisms, but they are in fact optimal when congestion is high. Service providers can achieve the first-best outcome and extract all customer surplus by coupling a time limit with an optimal price mechanism. The attractiveness of time limits stems from their ability to reduce not only the average time spent in service, but also its variance. This is highly effective in settings in which customers' service times impose externalities on others' waiting times. Thus, we conclude that providers of discretionary services should set time limits when congestion is an issue. This paper was accepted by Vishal Gaur, operations management. [ABSTRACT FROM AUTHOR]

Successful solid-waste management relies heavily on citizen involvement and cooperation, particularly through effective source separation. By ensuring that waste is sorted correctly at source, costs are reduced, the quality of recycled products is improved, and waste handling becomes more efficient—resulting in significant cost savings for municipal authorities (MAs) and mitigating causes of air pollution, water pollution, and soil contamination. This study explores enhancing waste separation in local authorities populated by traditional minority groups through stakeholder cooperation. The aim is to improve economic, social, and environmental utilities while identifying the mechanism that best maximizes the well-being of all players involved. Employing mixed methods and game-theory tools, we conduct twenty-one in-depth interviews with local minority leaders to define the parameters of the service function. The utility functions of all players serve as a basis for game-theory modeling that allow us to identify Nash equilibria, compare their efficiency, and formulate the mechanism optimally. The results of the study show that when an influential local player fosters cooperation and trust among residents, effective waste separation is achieved, enhancing the well-being of all involved. [ABSTRACT FROM AUTHOR]

There is a strong demand for multi-attribute auctions in real-world scenarios for non-price attributes that allow participants to express their preferences and the item’s value. However, this also makes it difficult to perform calculations with incomplete information, as a single attribute—price—no longer determines the revenue. At the same time, the mechanism must satisfy individual rationality (IR) and incentive compatibility (IC). This paper proposes an innovative dual network to solve these problems. A shared MLP module is constructed to extract bidder features, and multiple-scale loss is used to determine network status and update. The method was tested on real and extended cases, showing that the approach effectively improves the auctioneer’s revenue without compromising the bidder.

We examine new mechanisms that introduce environmentally friendly ecochanges involving the elimination of noxious commodities and take into account the structure of demand without a detrimental effect to agents' position. In the era of the fourth industrial revolution, these mechanisms allow eliminating unnecessary services or goods that are being replaced by modern technologies. We define optimal mechanisms under the criterion of distance minimization, when a small number of detrimental commodities is excluded from production processes as well as when producers are change-averse. The results have the form of theorems with rigorous proofs. [ABSTRACT FROM AUTHOR]

Sellers with one unit of land each are located at the nodes of a graph. Two sellers are contiguous if they are connected by an edge in the graph. The buyer realizes a positive value only if he can purchase plots that constitute a path of given length. We characterize the optimal mechanism when the buyer and sellers have independently distributed private valuations. [ABSTRACT FROM AUTHOR]

This study considers a mechanism design problem in which service slots are allocated over time to buyers arriving in different periods. Buyers have a multidimensional type representing their valuation and patience level. Some buyers can accept delayed service, whereas others cannot. The seller fully commits to a deterministic mechanism. We show that a mechanism is periodic ex-post incentive compatible if and only if the allocation rule is monotone in valuation and "price equivalence" holds. The dynamic pivot mechanism with reserve prices maximizes the seller's expected revenue if and only if the virtual valuation function is affine. [ABSTRACT FROM AUTHOR]

This paper studies the use of posted prices and auctions in a large dynamic market with many short-lived sellers and long-lived buyers. Although a reserve-price auction maximizes the expected revenue, the optimal revenue decreases when the market becomes more buyer-friendly; namely, when buyers survive longer, face fewer competitors, and become more patient. As the market becomes more buyer-friendly, the revenue advantage of a reserve-price auction over posting a price also decreases, but using posted prices would lead to sale and allocative inefficiencies. [ABSTRACT FROM AUTHOR]

This paper studies a principal-agent relationship when both are risk-neutral and in the presence of adverse selection and moral hazard. Contracts must satisfy the limited-liability and monotonicity conditions. We provide sufficient conditions under which the optimal contract is simple, in the sense that each type is offered the same contract. These are: the action and the agent's type are complements, and the output's cumulative distribution function is such that the marginal rate of substitution between the action and the agent's type is the same for each possible output realization. Furthermore, under the average monotone likelihood ratio property, the optimal contract is a call-option contract as in Innes (J Econ Theory 52(1):45–67, 1990). The results shed light on the fact that sometimes contracts are not highly dependent on individual characteristics as predicted in most pure moral hazard and pure adverse selection settings. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we propose an optimal mechanism to reduce congestion when information is asymmetric. Each car driver receives a quantity of traffic rights such that his adjusted marginal benefit is equal to the marginal cost of congestion and payments are based on willingness to pay. We show that the level of congestion achieved is lower and each car user can receive more or fewer rights than under complete information. With symmetric beliefs, the payment rule results from a second‐degree price discrimination. When beliefs are asymmetric, it results simultaneously from a second‐degree price discrimination and from a third‐degree price discrimination and high willingness‐to‐pay car users are discriminated against. The revenue raised can be used to reduce distortionary taxes, thereby gaining public acceptability. [ABSTRACT FROM AUTHOR]

We investigate when a buyer seeking to procure multiple units of an input may find it advantageous to run a "test auction" in which she has incumbent suppliers bid on a portion of the desired units. The test auction reveals incumbent supplier cost information that helps the buyer determine how many entrants (if any) to recruit at a cost prior to awarding the remaining units. The optimal number of entrant suppliers to recruit follows a threshold policy that is monotonic in the test auction's clearing price unless the underlying supplier cost distribution is not regular. When setting her reserve price in the test auction, the buyer uses supplier recruitment as her "outside option": if the reserve price is not met in the test auction, the buyer recruits new suppliers and runs a second auction. We compare the attractiveness of the test auction procedure relative to the more conventional procedure in which the buyer auctions off her entire demand in one auction. Since the buyer can choose ex ante which procedure to use, we propose using whichever has lower ex ante total (purchase plus recruitment) cost. Finally, using an optimal mechanism analysis, we find a lower bound on the buyer's cost, and use that cost as a benchmark to show that our proposed sourcing strategy performs well given its ease of implementation. [ABSTRACT FROM AUTHOR]