optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

optimal dynamic pricing for perishable assets with nonhomogeneous demand we consider a dynamic pricing model for selling a given stock of a perishable product over a finite time horizon customers whose reservation price distribution changes over time arrive according to a nonhomogeneous poisson process we show that at any given time the optimal price decreases with inventory we also identify a sufficient condition under which the optimal price decreases over time for a given inventory level this sufficient condition requires that the willingness of a customer to pay a premium for the product does not increase over time in addition to shedding managerial insight these structural properties enable efficient computation of the optimal policy numerical studies are conducted to show the revenue impact of dynamic price policies price changes are set to compensate for statistical fluctuations of demand and to respond to shifts of the reservation price for the former our examples show that using optimal dynamic optimal policies achieves 2 4 7 3 revenue improvement over the optimal single price policy for the latter the revenue increase can be as high as 100 these results explain why yield management has become so essential to fashion retailing and travel service industries

the probability of sale and price premiums in withdrawn auctioned properties this paper examines the impact of the auction process of residential properties that whilst unsuccessful at auction sold subsequently the empirical analysis considers both the probability of sale and the premium of the subsequent sale price over the guide price reserve and opening bid the findings highlight that the final achieved sale price is influenced by key price variables revealed both prior to and during the auction itself factors such as auction participation the number of individual bidders and the number of bids are significant in a number of the alternative specifications

revenue management with forward looking buyers a seller wishes to sell multiple goods by a deadline for example the end of a season potential buyers enter over time and can strategically time their purchases each period the profit maximizing mechanism awards units to the buyers with the highest valuations exceeding a sequence of cutoffs we show that these cutoffs are deterministic depending only on the inventory and time remaining in the continuous time limit the optimal mechanism can be implemented by posting anonymous prices when incoming demand decreases over time the optimal cutoffs satisfy a one period look ahead property and prices are defined by an intuitive differential equation

optimal dynamic pricing with inventories abstract we characterize optimal dynamic pricing by a monopolist with a finite stock of goods to sell we show that the monopolist finds it optimal to charge a price that increases monotonically as his stock depletes

managing online auctions current business and research issues the internet s computational power and flexibility have made auctions a widespread and integral part of both consumer and business markets though online auctions are a multi billion dollar annual activity with a growing variety of sophisticated trading mechanisms scientific research on them is at an early stage this paper analyzes the current state of management science research on online auctions it develops a broad research agenda for issues such as the behavior of online auction participants the optimal design of online auctions the integration of auctions into the ongoing operation of firms and the use of the data generated by online auctions to inform future trading mechanisms these research areas will draw from applied and theoretical work spanning management science economics and information systems

optimal dynamic auctions for revenue management we analyze a dynamic auction in which a seller withc units to sell faces a sequence of buyers separated intot time periods each group of buyers has independent private values for a single unit buyers compete directly against each other within a period as in a traditional auction and indirectly with buyers in other periods through the opportunity cost of capacity assessed by the seller the number of buyers in each period as well as the individual buyers valuations are random the model is a variation of the traditional single leg multiperiod revenue management problem in which consumers act strategically and bid for units of a fixed capacity over time for this setting we prove that dynamic variants of the first price and second price auction mechanisms maximize the seller s expected revenue we also show explicitly how to compute and implement these optimal auctions the optimal auctions are then compared to a traditional revenue management mechanism in which list prices are used in each period together with capacity controls and to a simple auction heuristic that consists of allocating units to each period and running a sequence of standard multiunit auctions with fixed reserve prices in each period the traditional revenue management mechanism is proven to be optimal in the limiting cases when there is at most one buyer per period when capacity is not constraining and asymptotically when the number of buyers and the capacity increases the optimal auction significantly outperforms both suboptimal mechanisms when there are a moderate number of periods capacity is constrained and the total volume of sales is not too large the benefit also increases when variability in the dispersion in buyers valuations or in the number of buyers per period increases

auctions an introduction abstract this is a detailed introduction to auction theory it begins with a simple analysis of standard auctions and then uses a strikingly simple general solution of symmetric private values auctions to prove the payoff equivalence of many auction rules the basic framework is then modified to admit risk aversion multi unit and repeated auctions as well as collusion then follows an introduction to optimal auctions with and without stochastic entry and to common value auctions and the winner s curse problem the survey closes with a sample of applications from the regulation of natural monopolies to price competition in oligopoly and the government securities market

optimal minimum bids and inventory scrapping in sequential single unit vickrey auctions with demand learning abstract retailers often conduct sequential single unit auctions and need to decide the minimum bid in each auction to reduce inventory costs it may be optimal to scrap some of the inventory rather than holding it until it is auctioned off in some auctions the seller may be uncertain about the market response and hence may want to dynamically learn the demand by observing the number of posted bids we formulate a markov decision process mdp to study this dynamic auction design problem under the vickrey mechanism we first develop a clairvoyant model where the seller knows the demand distribution we prove that it is optimal to scrap all inventory above a certain threshold and then auction the remaining units we derive a first order necessary condition whereby the bidders virtual value at an optimal minimum bid equals the seller s marginal profit this is a generalization of riley and samuelson s result from the one single unit auction case when the virtual value is strictly increasing this necessary condition is also sufficient and leads to a structured value iteration algorithm we then assume that the number of bidders is poisson distributed but the seller does not know its mean the seller uses a mixture of gamma prior on this mean and updates this belief over several auctions this results in a high dimensional bayesian mdp whose exact solution is intractable we therefore propose and compare two approximation methods called certainty equivalent control cec and q function approximation numerical experiments suggest that q function approximation can attain higher revenues than cec

reconsidering carbon permits auction mechanism an efficient dynamic model one of major concerns for china and developing countries is the new international trade rule concerning carbon emissions which one needs to know its suitable mechanism and the possible implication on china s carbon trading market precisely in an emission and trade scheme an important question is whether the auction outcome is efficient since this is closely related with the economic costs of emissions reduction due to the unique features of carbon permits existing auction mechanisms do not seem to be suitable for their distribution inspired by the t tonnement process this paper proposes a new auction mechanism for them for both practical application and theoretical extension the discrete and continuous situations are examined respectively the result shows that the proposed auction converges to pareto optimal equilibria and that without ties the equilibrium is unique for bidders the straightforward bidding strategy is the most preferred one in the sense that the strategy makes them avoid the risk of loss intuitively the auctioneer s utility is increasing in the number of bidders while bidders pay off is increasing in permits to a certain extent the proposed auction mechanism resolves the confliction between efficiency and revenue in the multi item auction theory while it increases people s understanding for carbon emission auction mechanism design

a dynamic model for optimal design quality and return policies abstract a clearly explained and generous return policy has been established as a competitive weapon to enhance sales from the firm s point of view a generous return policy will increase sales revenue but will also increase cost due to increased likelihood of return design quality of the product has been used as a competitive weapon for a long time this paper recognizes the relationship between design quality and price of the product and the firm s return policy quality level in the product would influence the amount of return directly when the product quality is higher the customer satisfaction rate will increase and the probability of return will decrease we develop a profit maximization model to jointly obtain optimal policies for the product quality level price and the return policy over time the model presented in this paper is dynamic in nature and considers the decisions as the product moves through the life cycle we obtain a number of managerial guidelines for using marketing and operational strategy variables to obtain the maximum benefit from the market we mention several future research possibilities

dual mechanism for an online retailer abstract while posted price and auction have typically been seen as alternatives to each other we observe web stores selling a product at a posted price and simultaneously running auctions for the identical product a phenomenon that has not been studied fully in this article we study a dual mechanism where an online retailer combines the two conventional mechanisms posted price and auction for multiple units of a product we demonstrate that the dual mechanism can be used to achieve market segmentation when customers discount the expected utility of auctions we characterize the customer s decision rule and formulate a retailer s profit function under the dual mechanism finally we compare the performance of three selling mechanisms posted price auction and dual through computational experiments

the dynamic vickrey auction abstract we study the efficient allocation of a single object over a finite time horizon buyers arrive randomly over time are long lived and have independent private values the valuation of a buyer may depend on the time of the allocation in an arbitrary way we construct an incentive compatible mechanism in which a there is a single financial transaction with the buyer b ex post participation constraints are fulfilled c there is no positive transfer to any agent and d payments are determined online we exploit that under the efficient allocation rule there is a unique potential winning period for each buyer this reduces the multidimensional type to one dimension and the payment of the winner can be defined as the lowest valuation for the potential winning period with which the buyer would have won the object in a static model this payment rule coincides with the payment rule of the vickrey auction

active labour market policies in germany do regional labour markets benefit abstractthis article examines on a regional level whether active labour market policies almp improve the matching process to take the fact of heterogeneous search effectiveness during programme

research note strategic bid shading and sequential auctioning with learning from past prices this paper analyzes sequential auctioning of single units of an indivisible good to a fluctuating population composed of overlapping generations of unit demand bidders two phenomena emergent in such a market are investigated forward looking bidding strategies and closed loop selling strategies that involve learning from past prices the buyers shade their bids down i e bid less than they would in a single isolated auction whenever they expect the seller to sell another unit of the good in the near future unlike in exogenous sequences of auctions the optimal bidding strategy thus depends on the seller s selling strategy the converse dependence also occurs the seller can learn about current demand from past realized prices and sell only in periods with high enough demand such learning depends on the extent of bid shading because the seller needs to invert the bidding strategy to learn in equilibrium buyer bid shading persists even when the seller does not sell in every period but it is self regulating in that it eventually vanishes when the existence of the market is threatened by low seller profits in this sense auction markets have a self preservation instinct general properties of learning about current demand from past auction prices are also investigated and characterized

optimal deficit and debt in the presence of foreign aid summary external revenue in the form of foreign aid constitutes an important component of the government s budget constraint in many developing countries we derive optimal public spending and the resulting optimal deficit and debt in an optimal control framework when the government seeks to maximize the utility of constituents in the presence of external revenue that cannot be influenced by the government directly but is contingent on public revenue and debt we find that in this context a policy of running budget deficits and accumulating debt becomes optimal in simulations we characterize the size and the path dependency of the optimal deficit and debt

technical note revenue management with bargaining static game theoretic models of bilateral bargaining assume that the seller knows his valuation for the item that is up for sale that is how the seller may determine this quantity is exogenous to these models in this paper we develop and analyze a stylized markov decision process that endogenizes the seller s computation of his marginal inventory valuation in an infinite horizon revenue management setting when each sale occurs according to a given bilateral bargaining mechanism we use this model to compare both analytically and numerically the seller s performance under four basic bilateral bargaining mechanisms with a tractable information structure these comparisons provide insights into the seller s performance under the following trading arrangements buyer and seller posted pricing negotiated pricing and rule based pricing

auctions and bidding a primer maybe the contractor was right to think bid jobs are different but it is more likely that he suffered from too simple a view of what is involved in preparing a competitive bid our analysis will show that even an experienced estimator working in familiar terrain can lose money if he doesn t understand the subtleties of competitive bidding the phenomenon experienced by the painting contractor known as the winner s curse is just one of the surprising and puzzling conclusions that have been turned up by modern research into auctions another is the theoretical proposition supported also by some experimental evidence that for example a sealed bid treasury bill auction in which each buyer pays a price equal to the highest rejected bid would yield more revenue to the treasury than the current procedure in which the winning bidder pays the seemingly higher amount equal to his own bid there are also subtle results that demonstrate the equivalence of such apparently different institutions as the standard sealed bid auction in which the auctioneer seller sells the goods to the highest bidder for a price equal to his bid and the dutch auction in which the auctioneer seller begins by asking a high price and gradually lowers the price until

inventory management with auctions and other sales channels optimality of s s policies we study periodic review inventory replenishment problems with fixed ordering costs and show the optimality of s s inventory replenishment policies inventory replenishment is instantaneous i e the lead time is zero we consider several sales mechanisms e g auction mechanisms name your own price mechanisms and multiple heterogeneous sales channels we prove this result by showing that these models satisfy a recently established sufficient condition for the optimality of s s policies thus this paper shows that the optimality of s s policies extends well beyond the traditional sales environments studied so far in the inventory literature

rational frenzies and crashes most markets clear through a sequence of sales rather than through a walrasian auctioneer because buyers can decide whether to buy now or later rather than only now or never their current willingness to pay is much more sensitive to price than the demand curve is a consequence is that markets will be extremely sensitive to new information leading to both frenzies in which demand feeds on itself and crashes in which price drops discontinuously the paper also shows how a result from static auction theory the revenue equivalence theorem can be applied to solve for a dynamic price path

optimal price skimming by a monopolist facing rational consumers this paper considers the intertemporal pricing problem for a monopolist marketing a new product the key feature differentiating this paper from the extant management science literature on intertemporal pricing is the assumption that consumers are intertemporal utility maximizers a subgame perfect nash equilibrium pricing policy is characterized and shown to involve intertemporal price discrimination we compare this policy to the optimal policy for a monopolist facing myopic consumers and find that for any given state prices are always lower with rational consumers than with myopic consumers for plausible parameter values the assumption of consumer rationality can be shown to lead to large differences in optimal prices moreover if a monopolist facing rational consumers implements the optimal myopic consumer pricing policy profits can be significantly less than if the monopolist follows the equilibrium pricing policy for rational consumers

airline seat allocation with multiple nested fare classes this paper addresses the problem of determining optimal booking policies for multiple fare classes that share the same seating pool on one leg of an airline flight when seats are booked in a nested fashion and when lower fare classes book before higher ones we show that a fixed limit booking policy that maximizes expected revenue can be characterized by a simple set of conditions on the subdifferential of the expected revenue function these conditions are appropriate for either the discrete or continuous demand cases these conditions are further simplified to a set of conditions that relate the probability distributions of demand for the various fare classes to their respective fares the latter conditions are guaranteed to have a solution when the joint probability distribution of demand is continuous characterization of the problem as a series of monotone optimal stopping problems proves optimality of the fixed limit policy over all admissible policies a comparison is made of the optimal solutions

modeling competitive bidding a critical essay in analyzing bidding modeling matters this paper is a critical analysis of the models available to aid competitive bidding decision making bidding strategy and auction design in real transactions after an introductory overview this paper describes the contexts in which auctions arise reviews the mainstream theory of single isolated auctions and discusses the important work involved in enrichment of this theory in doing so it indicates results that have been obtained and the sort of changes in analytical approach that are needed to tackle other critical enrichments the paper summarizes briefly what is known about the direct use of models by bidders and auction designers a general theme of this paper is that enriched models are needed to bring bidding theory closer to direct applicability in decision making