Does an increase in the number of solvers benefit the seeker in heterogeneous contests?

In this paper, we analyze whether increasing the number of solvers benefits the seeker in heterogeneous contests. We show that if the number of solvers is large, the expected average quality (resp., expected maximum quality) of solutions is decreasing (resp., increasing). However, the results may not hold when the number of solvers is below a certain threshold. These imply that the seeker should adopt the restricted-entry policy or not based on different measure criteria and sizes of solvers.     

Revenue deficiency under second-price auctions in a supply-chain setting

Consider a firm, called the buyer, that satisfies its demand over two periods by assigning both demands to a supplier via a second-price procurement auction; call this the Standard auction. In the hope of lowering its purchase cost, the firm is considering an alternative procedure in which it will also allow bids on each period individually, where there can be either one or two winners covering the two demands; call this the Multiple Winner auction. Choosing the Multiple Winner auction over the Standard auction can in fact result in a higher cost to the buyer. We provide a bound on how much greater the buyer’s cost can be in the Multiple Winner auction and show that this bound is tight. We then sharpen this bound for two scenarios that can arise when the buyer announces his demands close to the beginning of the demand horizon. Under a monotonicity condition, we achieve a further sharpening of the bound in one of the scenarios. Finally, this monotonicity condition allows us to generalize this bound to the T-period case in which bids are allowed on any subset of period demands.     

All-pay auctions with pre- and post-bidding options

Motivated by the emergence of online penny or pay-to-bid auctions, in this study, we analyze the operational consequences of all-pay auctions competing with fixed list price stores. In all-pay auctions, bidders place bids, and highest bidder wins. Depending on the auction format, the winner pays either the amount of their bid or that of the second-highest bid. All losing bidders forfeit their bids, regardless of the auction format. Bidders may visit the store, both before and after bidding, and buy the item at the fixed list price. In a modified version, we consider a setting where bidders can use their sunk bid as a credit towards buying the item from the auctioneer at a fixed price (different from the list price). We characterize a symmetric equilibrium in the bidding/buying strategy and derive optimal list prices for both the seller and auctioneer to maximize expected revenue. We consider two situations: (1) one firm operating both channels (i.e. fixed list price store and all-pay auction), and (2) two competing firms, each operating one of the two channels.     

Revenue management for low-cost providers

Low-cost providers have emerged as important players in many service industries, the most predominant being low-cost, or the so-called discount airlines. This paper presents models and results leading toward understanding the revenue management outlook for a discount pricing firm. A framework and model is formulated specifically for the airline industry, but is generalizable to low-cost providers in similar revenue management settings. We formulate an optimal pricing control model for a firm that must underprice to capture a segment of exogenous demand. Two specific model formulations are considered: a continuous deterministic version, and a discrete stochastic version. Structural results are derived for the deterministic case, providing insight into the general form of optimal underpricing policies. The stochastic results support the structural insight from the deterministic solution, and illuminate the effect of randomness on the underpricing policies.     

模糊需求下的供应链收益共享契约模型

在模糊需求环境下,研究由单一供应商和零售商组成的两级供应链系统的协调机制问题。将市场需求视为模糊变量,建立不确定理论下,基于可信性分布的集成供应链模型和收益共享契约模型,并给出了模型中的最优策略。最后,以三角形模糊变量为例,通过数值算例对模型中的参数进行了求解,并分析批发价格和收益系数对其他参数的影响。研究结果表明,零售商的最优订购量在模糊需求中心点的左、右浮动,并随着零售价格的提高而增加;不同的收益系数对应不同的批发价格策略;通过改变收益系数可以实现供应链成员之间的完美协调。     

Revenue management for a supply chain with two streams of customers

In this paper, we consider revenue management for a service supply chain with one supplier and one retailer. The supplier has a limited capacity of a perishable product and both the supplier and the retailer face customers. Each customer may choose to buy a product from either the supplier or the retailer by considering prices and the cost associated with switching. For the centralized model, the supplier determines the selling prices for both herself and the retailer, and the retailer simply collects a commission fee for each product sold. We derive monotone properties for the revenue functions and pricing strategies. Further, we show that the commission fee increases the retailer’s price while decreasing the supplier’s and leads to efficiency loss of the chain. For the decentralized decision-making model, the supplier and the retailer compete in price over time. Two models are considered. In the first, the retailer buys products from the supplier before the selling season and in the second the retailer shares products with the supplier in retailing. For both models, we discuss the existence of the equilibrium and characterize the optimal decisions. Numerical results are presented to illustrate properties of the models and to compare the supply chain performance between the centralized and the decentralized models.     

收入管理的MMV动态拍卖机制研究

随着互联网上交易的增多,多单位同质产品销售的拍卖机制成为了一个新的研究方向.针对易逝性服务产品的收入管理问题,提出将产品销售分为多个拍卖期的MMV(Multi-period and Multi-unit Vickrey(Auction with Reserve Pricing)动态拍卖机制,给出每期最优拍卖单位数和保留价格的确定方法,证明了最优拍卖单位数分别关于剩余存量和销售时间单增的性质,以及保留价格关于剩余存量的单降性.最后证明MMV机制的每期实际成交价格将高于Vulcano(2002)提出的MSP(Modified Second-Price)机制,根据易逝性服务产品的需求特点得到MMV机制优于MSP机制的结论.     

Revenue management approach to stochastic capacity allocation problem

To formulate stochastic capacity allocation problems in a manufacturing system, the concept and techniques of revenue management is applied in this research. It is assumed the production capacity is stochastic and hence its exact size cannot be forecasted in advance, at the time of planning. There are two classes of “frequent” and “occasional” customers demanding this capacity. The price rate as well as the penalty for order cancellation caused by overbooking is different for each class. The model is developed mathematically and we propose an analytical solution method. The properties of the optimal solution as well as the behavior of objective function are also analyzed. The objective function is not concave, in general. However, we prove it is a unimodal function and by taking advantage of this property, the optimal solution is determined.     

Revenue management model for on-demand IT services

This paper presents a model for applying revenue management to on-demand IT services. The multinomial logit model is used to describe customer choice over multiple classes with different service-level agreements (SLAs). A nonlinear programming model is provided to determine the optimal price or service level for each class. Through a numerical analysis, we examine the impacts of system capacity and customer waiting incentives on the service provider’s profit and pricing strategies.     

Revenue-maximizing Dutch auctions with discrete bid levels

This paper is concerned with setting a predetermined number of bid levels in a Dutch auction to maximize the auctioneer’s expected revenue. As a departure from the traditional methods used by applied economists and game-theorists, a novel approach is taken in this study to tackle the problem by formulating the auctioning process as a constrained nonlinear program and applying standard optimization techniques to solve it. Aside from proposing respective closed-form formulae for computing the optimal bid levels and the auctioneer’s maximum expected revenue, we also show that the bid decrements should be increasing if there are two or more bidders in the Dutch auction. Additionally, the auctioneer’s maximum expected revenue increases with the number of bidders as well as the number of bid levels. Finally, managerial implications of the key findings as well as limitations of this research work are discussed.     

Contractivity of Bellman operator in risk averse dynamic programming with infinite horizon

The paper deals with a risk averse dynamic programming problem with infinite horizon. First, the required assumptions are formulated to have the problem well defined. Then the Bellman equation is derived, which may be also seen as a standalone reinforcement learning problem. The fact that the Bellman operator is contraction is proved, guaranteeing convergence of various solution algorithms used for dynamic programming as well as reinforcement learning problems, which we demonstrate on the value iteration and the policy iteration algorithms.     

All-pay auctions with risk-averse players

We study independent private-value all-pay auctions with risk-averse players. We show that: (1) Players with low values bid lower and players with high values bid higher than they would bid in the risk neutral case. (2) Players with low values bid lower and players with high values bid higher than they would bid in a first-price auction. (3) Players’ expected utilities in an all-pay auction are lower than in a first-price auction. We also use perturbation analysis to calculate explicit approximations of the equilibrium strategies of risk-averse players and the seller’s expected revenue. In particular, we show that in all-pay auctions the seller’s expected payoff in the risk-averse case may be either higher or lower than in the risk neutral case.     

Dynamic pricing and warranty policies for products with fixed lifetime

We consider a repairable product with known market entry and departure times. A warranty policy is offered with product purchase, under which a customer can have a failed item repaired free of charge in the warranty period. It is assumed that customers are heterogeneous in their risk attitudes toward uncertain repair costs incurred after the warranty expires. The objective is to determine a joint dynamic pricing and warranty policy for the lifetime of the product, which maximizes the manufacturer’s expected profit. In the first part of the analysis, we consider a linearly decreasing price function and a constant warranty length. We first study customers’ purchase patterns under several different pricing strategies by the manufacturer and then discuss the optimal pricing and warranty strategy. In the second part, we assume that the warranty length can be altered once during the product lifetime in developing a joint pricing and warranty policy. Numerical studies show that a dynamic warranty policy can significantly outperform a fixed-length warranty policy.     

Product safety for a monopolist under strict liability

This paper views strict producer liability as essentially requiring the producer to provide a tie-in sale of full coverage insurance to its customers. The output and safety levels under strict producer liability are compared to those that would exist when the consumer retains all liability. The risk averseness of the producer and the availability of commercial liability coverage are shown to affect the producer's output and safety decision. In general, a shift from consumer to producer liability might not encourage the production of safer products, either with or without the availability of commercial liability insurance to the producer.     

On cross-risk vulnerability

We introduce the notion of cross-risk vulnerability to generalize the concept of risk vulnerability introduced by Gollier and Pratt [Gollier, C., Pratt, J.W. 1996. Risk vulnerability and the tempering effect of background risk. Econometrica 64, 1109–1124]. While risk vulnerability captures the idea that the presence of an unfair financial background risk should make risk-averse individuals behave in a more risk-averse way with respect to an independent financial risk, cross-risk vulnerability extends this idea to the impact of a non-financial background risk on the financial risk. It provides an answer to the question of the impact of a background risk on the optimal coinsurance rate and on the optimal deductible level. We derive necessary and sufficient conditions for a bivariate utility function to exhibit cross-risk vulnerability both toward an actuarially neutral background risk and toward an unfair background risk. We also analyze the question of the sub-additivity of risk premia and show to what extent cross-risk vulnerability provides an answer.     

Cost,Revenue and Profit Efficiency Models in Generalized Fuzzy Data Envelopment Analysis

One of the most important information given by data envelopment analysis models is the cost, revenue and profit efficiency of decision making units (DMUs). Cost efficiency is defined as the ratio of minimum costs to current costs, while revenue efficiency is defined as the ratio of maximum revenue to current revenue of the DMU. This paper presents a framework where data envelopment analysis (DEA) is used to measure cost, revenue and profit efficiency with fuzzy data. In such cases, the classical models cannot be used, because input and output data appear in the form of ranges. When the data are fuzzy, the cost, revenue and profit efficiency measures calculated from the data should be uncertain as well. Fuzzy DEA models emerge as another class of DEA models to account for imprecise inputs and outputs for DMUs. Although several approaches for solving fuzzy DEA models have been developed, numerous deficiencies including the $\alpha$-cut approaches and types of fuzzy numbers must still be improved. This scheme embraces evaluation method based on vector for proposed fuzzy model. This paper proposes generalized cost, revenue and profit efficiency models in fuzzy data envelopment analysis. The practical application of these models is illustrated by a numerical example.     

Random queues and risk averse users

We analyze Nash equilibrium in time of use of a congested facility. Users are risk averse with general concave utility. Queues are subject to varying degrees of random sorting, ranging from strict queue priority to a completely random queue. We define the key “no residual queue” property, which holds when there is no queue at the time the last user arrives at the queue, and prove that this property holds in equilibrium under all queueing regimes considered. The no residual queue property leads to simple results concerning the equilibrium utility of users and the timing of the queue.     

Would a risk-averse newsvendor order less at a higher selling price?

We model a risk-averse newsvendor’s decision-making behavior with some commonly used classes of utility functions within the expected utility theory (EUT) framework. Under fairly general conditions of EUT, we show that a risk-averse newsvendor will order less than an arbitrarily small quantity as selling price gets larger if price is higher than a threshold value, i.e., the optimal order quantity decreases as the selling price increases.     

Duopolistic competition under risk aversion and uncertainty

A monopolist typically defers entry into an industry as both price uncertainty and the level of risk aversion increase. By contrast, the presence of a rival typically hastens entry under risk neutrality. Here, we examine these two opposing effects in a duopoly setting. We demonstrate that the value of a firm and its entry decision behave differently with risk aversion and uncertainty depending on the type of competition. Interestingly, if the leader’s role is defined endogenously, then higher uncertainty makes her relatively better off, whereas with the roles exogenously defined, the impact of uncertainty is ambiguous.     

Two-person insurance negotiation

This paper considers a risk-neutral insurer and a risk-averse individual who bargain over the terms of an insurance contract. The Core and the Nash solution to this bargaining game are characterized. It is shown that the insurer's expected profit is higher when bargaining with a more risk-averse individual.