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

is there a glass ceiling in sweden using 1998 data we show that the gender log wage gap in sweden increases throughout the wage distribution and accelerates in the upper tail we interpret this as a strong glass ceiling effect we use quantile regression decompositions to examine whether this pattern can be ascribed primarily to gender differences in labor market characteristics or in the rewards to those characteristics even after extensive controls for gender differences in age education both level and field sector industry and occupation we find that the glass ceiling effect we see in the raw data persists to a considerable extent

tracking the market dynamic pricing and learning in a changing environment dynamic pricing of commodities without knowing the exact relation between price and demand is a much studied problem most existing studies assume that the parameters describing the market are constant during the selling period this severely reduces their practical applicability since in reality market characteristics may change all the time without the firm always being aware of it in the present paper we study dynamic pricing and learning in a changing market environment we introduce a methodology that enables the price manager to hedge against changes in the market and provide explicit upper bounds on the regret a measure of the performance of the firm s pricing decisions in addition this methodology guides the selection of the optimal way to estimate the market process we provide numerical examples from practically relevant situations to illustrate the methodology

will dynamic pricing outperform theoretical analysis and empirical evidence from o2o on demand food service market abstract this study attempts to identify the pricing strategy of three most commonly used on demand food service platforms in china based on detailed information of more than 240 000 orders and further evaluates the impact of pricing strategy on platform performance we find that some platforms adopt dynamic pricing strategies while other platforms adopt static pricing strategies considering the unique structure of the o2o on demand food service market in china we develop a dyadic two sided market theory and demonstrate that compared with static pricing strategies dynamic pricing strategies perform better consistent with our theory our empirical analysis also suggests that platforms adopting dynamic pricing strategies have a significantly higher level of demand compared with platforms adopting static strategies in addition our results indicate the importance of delivery speed red envelopes and ratings in promoting demand

close the gaps a learning while doing algorithm for single product revenue management problems we consider a retailer selling a single product with limited on hand inventory over a finite selling season customer demand arrives according to a poisson process the rate of which is influenced by a single action taken by the retailer such as price adjustment sales commission advertisement intensity etc the relationship between the action and the demand rate is not known in advance however the retailer is able to learn the optimal action on the fly as she maximizes her total expected revenue based on the observed demand reactions using the pricing problem as an example we propose a dynamic learning while doing algorithm that only involves function value estimation to achieve a near optimal performance our algorithm employs a series of shrinking price intervals and iteratively tests prices within that interval using a set of carefully chosen parameters we prove that the performance of our algorithm is among the best of all possible algorithms in terms of the asymptotic regret the relative loss compared to the full information optimal solution our result closes the performance gaps between parametric and nonparametric learning and between the post price mechanism and the customer bidding mechanism important managerial insight from this research is that the values of information on both the parametric form of the demand function as well as each customer s exact reservation price are less important than prior literature suggests our results also suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially

dynamic pricing with real time demand learning in many service industries the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution because the firm can easily monitor the product inventory the success of dynamic pricing relies on an accurate demand forecast in this paper we consider a situation where the firm does not have an accurate demand forecast but can only roughly estimate the customer arrival rate before the sale begins as the sale moves forward the firm uses real time sales data to fine tune this arrival rate estimation we show how the firm can first use this modified arrival rate estimation to forecast the future demand distribution with better precision and then use the new information to dynamically adjust the product price in order to maximize the expected total revenue numerical study shows that this strategy not only is nearly optimal but also is robust when the true customer arrival rate is much different from the original forecast finally we extend the results to four situations commonly encountered in practice unobservable lost customers time dependent arrival rate batch demand and discrete set of allowable prices

simultaneously learning and optimizing using controlled variance pricing price experimentation is an important tool for firms to find the optimal selling price of their products it should be conducted properly since experimenting with selling prices can be costly a firm therefore needs to find a pricing policy that optimally balances between learning the optimal price and gaining revenue in this paper we propose such a pricing policy called controlled variance pricing cvp the key idea of the policy is to enhance the certainty equivalent pricing policy with a taboo interval around the average of previously chosen prices the width of the taboo interval shrinks at an appropriate rate as the amount of data gathered gets large this guarantees sufficient price dispersion for a large class of demand models we show that this procedure is strongly consistent which means that eventually the value of the optimal price will be learned and derive upper bounds on the regret which is the expected amount of money lost due to not using the optimal price numerical tests indicate that cvp performs well on different demand models and time scales this paper was accepted by assaf zeevi stochastic models and simulation

the disparity between willingness to accept and willingness to pay measures of value psychologists have long argued that people are much more averse to a loss than attracted to an equivalent gain this behavior termed loss aversion has been formalized by kahneman and tversky 1979 in their reformulation of expected utility theory prospect theory in prospect theory the utility function is replaced by a value function that evaluates changes in income from the current level increases in income are weighted by a relatively small marginal utility decreases in income are weighted by a much larger marginal utility in effect the value function implies that a kink in the relationship between utility and income occurs at the initial income or reference point and that the slope of the utility function for losses in income is steeper than it is for gains in a recent paper knetsch and sinden 1984 report a series of experiments that demonstrate the existence of a large disparity between willingness to accept wta and willingness to pay wtp measures of value they argue that the psychological theory of loss aversion explains this difference economic theory would suggest that individuals who exhibit a large disparity between wta and wtp are perhaps underperceiving the value of gains or overperceiving the value of losses are behaving in an irrational manner and will consequently achieve a lower level of well being than if they behaved in a true utility maximizing manner this would in contrast to loss aversion usually imply near equal values for wta and wtp see willig 1976 further documentation of a larger than expected disparity between wta and wtp has been obtained in surveys asking for the value of a variety of public goods for example cummings brookshire and schulze 1986 document six

real time dynamic pricing with minimal and flexible price adjustment we study a standard dynamic pricing problem where the seller a monopolist possesses a finite amount of inventories and attempts to sell the products during a finite selling season despite the potential benefits of dynamic pricing many sellers still adopt a static pricing policy because of 1 the complexity of frequent reoptimizations 2 the negative perception of excessive price adjustments and 3 the lack of flexibility caused by existing business constraints in this paper we develop a family of pricing heuristics that can be used to address all these challenges our heuristic is computationally easy to implement it requires only a single optimization at the beginning of the selling season and automatically adjusts the prices over time moreover to guarantee a strong revenue performance the heuristic only needs to adjust the prices of a small number of products and do so infrequently this property helps the seller focus his effort on the prices of the most important products instead of all products in addition in the case where not all products are equally admissible to price adjustment due to existing business constraints such as contractual agreement strategic product positioning etc our heuristic can immediately substitute the price adjustment of the original products with the price adjustment of similar products and maintain an equivalent revenue performance this property provides the seller with extra flexibility in managing his prices

game theoretic pricing models in hotel revenue management an equilibrium choice based conjoint analysis approach abstract this paper explores a game theoretically founded approach to conjoint analysis that determines equilibrium room rates under differentiated price competition in an oligopolistic hotel market competition between hotels is specified in terms of market share functions that can be estimated using multinomial logit models of consumer choice the approach is based on choice based conjoint analysis that permits the estimation of attributes weights part worths for an additive utility formulation of the utility function from this room rates that equilibrate the market conditioned on the differences in services and facilities offered by competing hotels can be determined the approach is illustrated by an example

price dispersion and incomplete learning in the long run abstract in each period a seller chooses a price and the customer for that period buys either one unit or nothing the relationship between price and purchase probability is one of two linear functions it is shown that the seller behaving optimally does not necessarily learn which function is the actual relationship since there can be a positive probability of sequences of prices converging to the price at which the two functions give the same purchase probability

bubbles crashes and endogenous expectations in experimental spot asset markets1 spot asset trading is studied in an environment in which all investors receive the same dividend from a known probability distribution at the end of each of t 15 or 30 trading periods fourteen of twenty two experiments exhibit price bubbles followed by crashes relative to intrinsic dividend value when traders are experienced this reduces but does not eliminate the probability of a bubble the regression of changes in mean price on lagged excess bids number of bids minus the number of offers in the previous period p pt a f b 1 o l supports the hypothesis that a e d the one period expected value of the dividend and that f 0 where excess bids is a surrogate measure of excess demand arising from homegrown capital gains losses expectations thus when bt 1 o goes to zero we have convergence to rational expectations in the sense of fama 1970 that arbitrage becomes unprofitable the observed bubble phenomenon can also be interpreted as a form of temporary myopia tirole 1982 from which agents learn that capital gains expectations are only temporarily sustainable ultimately inducing common expectations or priors tirole 1982 four of twenty six experiments all using experienced subjects yield outcomes that appear to the chart s eye to converge early to rational expectations although even in these cases we get 0 and small price fluctuations of a few cents that invite scalping

is there a glass ceiling over europe exploring the gender pay gap across the wages distribution using harmonised data from the european union household panel we analyse gender pay gaps by sector across the wages distribution for ten countries we find that the mean gender pay gap in the raw data typically hides large variations in the gap across the wages distribution we use quantile regression qr techniques to control for the effects of individual and job characteristics at different points of the distribution and calculate the part of the gap attributable to differing returns between men and women we find that first gender pay gaps are typically bigger at the top of the wage distribution a finding that is consistent with the existence of glass ceilings for some countries gender pay gaps are also bigger at the bottom of the wage distribution a finding that is consistent with sticky floors third the gender pay gap is typically higher at the top than the bottom end of the wage distribution suggesting that glass ceilings are more prevalent than sticky floors and that these prevail in the majority of our countries fourth the gender pay gap differs significantly across the public and the private sector wages distribution for each of our eu countries

dynamic pricing of inventory capacity with infrequent price changes we consider a problem of dynamically pricing a single product sold by a monopolist over a short time period if demand characteristics change throughout the period it becomes attractive for the company to adjust price continuously to respond to such changes i e price discriminate intertemporally however in practice there is typically a limit on the number of times the price can be adjusted due to the high costs associated with frequent price changes if that is the case instead of a continuous pricing rule the company might want to establish a piece wise constant pricing policy in order to limit the number of price adjustments such a pricing policy which involves optimal choice of prices and timing of price changes is the focus of this paper we analyze the pricing problem with a limited number of price changes in a dynamic deterministic environment in which demand depends on the current price and time and there is a capacity inventory constraint that may be set optimally ahead of the selling season the arrival rate can evolve in time arbitrarily allowing us to model situations in which prices decrease increase or neither we consider several plausible scenarios where pricing and or timing of price changes are endogenized various notions of complementarity single crossing property supermodularity and total positivity are explored to derive structural results conditions sufficient for the uniqueness of the solution and the monotonicity of prices throughout the sales period furthermore we characterize the impact of the capacity constraint on the optimal prices and the timing of price changes and provide several other comparative statics results additional insights are obtained directly from the solutions of various special cases

a simple solution to the identification problem in detailed wage decompositions i introduction oaxaca and ransom 1999 show that the oaxaca decomposition suffers from one nagging conceptual problem the detailed oaxaca decomposition of wage differentials is not invariant to the choice of reference group when dummy variables are used 1 that is if one uses dummy variable s then the detailed coefficients effect attributed to dummy variables is not invariant to the choice of the omitted group s 2 this invariance or identification problem is well known to labor economists and has plagued decomposition and discrimination analysis for a long time 3 this article proposes a simple and practical solution to this identification invariance problem the solution is based on the intuitive idea that if alternative reference groups yield different estimates of the characteristics and coefficients effects for each individual variable then it is natural to obtain estimates of the two effects for every possible specification of the reference groups and take the average of the estimates of the two effects with various reference groups as the true contributions of individual variables to wage differentials a close inspection shows that averaging the two effects in the decomposition equation with varying reference groups the averaging approach is equivalent to finding average estimates of constant and dummy variables in wage equations with varying reference groups and then using the average estimates to calculate the oaxaca decomposition equation researchers may react a bit negatively to this suggestion because it could be quite cumbersome and tedious to estimate wage equations permuting the choice of reference groups this article shows that there is no need to estimate multiple wage equations one set of regression estimates is sufficient to resolve the identification problem in the detailed decompositions that is the average of the estimates with varying reference groups can be easily calculated by using only one set of regression estimates with any specific reference group s the identification problem for the detailed decomposition disappears once the contribution of the dummy variables and the constant in the regression equations are identified 4 ii identification problem and invariant decomposition an illustration to understand what the identification problem in the detailed wage decomposition is i will first illustrate the problem with a simple example suppose that there are three categories and the regression equation has only a constant and two dummy variables on the right hand side where the reference group is the first category 5 that is 1 y sub i alpha sub i 3 summation over k 2 d sub ki beta sub ki e sub i where y is log wages and i a or b for two comparison groups coefficients for two dummy variables taking category one as the reference group are estimated using ordinary least squares ols regression and are reported in the second column of table 1 for sample a and for sample b note that the coefficient of the reference group category 1 is restricted to zero similarly i may change my reference group specification and estimate the wage equation two more times the estimates taking category 2 or 3 as the reference group are reported on the next two columns because i have three sets of estimates with varying reference groups i may decompose the wage differentials 0 15 0 76 0 61 into characteristics and coefficients effects three times the characteristics effect delta sub x 1 and coefficients effects delta sub beta 1 are specified as follows when category 1 is the reference group delta sub x 1 summation sup 3 sub k 2 bar d sub ka bar d sub kb beta sub kb and delta sub beta 1 alpha sub a alpha sub b summation sup 3 sub k 2 bar d sub ka beta sub ka beta sub kb

investment timing with incomplete information and multiple means of learning we consider a firm that can use one of several costly learning modes to dynamically reduce uncertainty about the unknown value of a project each learning mode incurs cost at a particular rate and provides information of a particular quality in addition to dynamic decisions about its learning mode the firm must decide when to stop learning and either invest or abandon the project using a continuous time bayesian framework and assuming a binary prior distribution for the project s unknown value we solve both the discounted and undiscounted versions of this problem in the undiscounted case the optimal learning policy is to choose the mode that has the smallest cost per signal quality when the discount rate is strictly positive we prove that an optimal learning and investment policy can be summarized by a small number of critical values and the firm only uses learning modes that lie on a certain convex envelope in cost rate versus signal quality space we extend our analysis to consider a firm that

actively learning about demand and the dynamics of price adjustment by observing the quantity demanded at particular prices a firm may learn about the parameters of its demand curve in such an environment price changes obstruct the learning process by inducing additional noise the authors paper constructs a dynamic model where a price setting firm endogenously controls the speed of learning the model provides a possible explanation for price inertia as a stable pricing policy allows the firm to learn more rapidly which improves future expected profits furthermore even in the long run learning continues to affect the firm s optimal price copyright 1990 by royal economic society

the gender wage gap among recent post secondary graduates in canada a distributional approach using the national graduates survey we examine the trends in the gender wage gap among recent post secondary graduates in canada between 1988 and 2007 female graduates earn on average 6 14 less than males during the period two to five years after graduation decompositions show that observable personal characteristics and job attributes can explain only a small portion of the wage gap we also find that men earn more than women at every point of the distribution interestingly the wage difference shrank in the lower half of the distribution in recent years while it increased in the upper half l ecart salarial entre les sexes chez les nouveaux diplomes postsecondaires une approche distributionnelle a l aide de l enquete nationale aupres des diplomes nous examinons les tendances dans l ecart salarial entre les sexes chez les nouveaux diplomes postsecondaires au canada entre 1988 et 2007 les femmes diplomees gagnent en moyenne de 6 a 14 moins que les hommes durant les 2 a 5 ans suivant l obtention du diplome des decompositions montrent que les caracteristiques personnelles et les attributs de l emploi observables ne peuvent expliquer qu une petite partie de l ecart salarial nous trouvons aussi que les hommes touchent plus que les femmes a chaque point de la distribution salariale de maniere interessante la difference de salaire a diminue dans la moitie inferieure de la distribution lors des annees recentes alors qu elle a augmente dans la moitie superieure

on the surprising sufficiency of linear models for dynamic pricing with demand learning we consider a multiperiod single product pricing problem with an unknown demand curve the seller s objective is to adjust prices in each period so as to maximize cumulative expected revenues over a given finite time horizon in doing so the seller needs to resolve the tension between learning the unknown demand curve and maximizing earned revenues the main question that we investigate is the following how large of a revenue loss is incurred if the seller uses a simple parametric model that differs significantly i e is misspecified relative to the underlying demand curve we measure performance by analyzing the price trajectory induced by this misspecified model and quantifying the magnitude of revenue losses as a function of the time horizon relative to an oracle that knows the true underlying demand curve the price of misspecification is expected to be significant if the parametric model is overly restrictive somewhat surprisingly we show under reasonably general conditions that this need not be the case this paper was accepted by gerard cachon stochastic models and simulation

dynamic pricing and learning with finite inventories we study a dynamic pricing problem with finite inventory and parametric uncertainty on the demand distribution products are sold during selling seasons of finite length and inventory that is unsold at the end of a selling season perishes the goal of the seller is to determine a pricing strategy that maximizes the expected revenue inference on the unknown parameters is made by maximum likelihood estimation we show that this problem satisfies an endogenous learning property which means that the unknown parameters are learned on the fly if the chosen selling prices are sufficiently close to the optimal ones we show that a small modification to the certainty equivalent pricing strategy which always chooses the optimal price w r t current parameter estimates satisfies regrett olog2t where regrett measures the expected cumulative revenue loss w r t a clairvoyant who knows the demand distribution we complement this upper bound by showing an instance for which the regret of any pricing policy satisfies i log t

on the minimax complexity of pricing in a changing environment we consider a pricing problem in an environment where the customers willingness to pay wtp distribution may change at some point over the selling horizon customers arrive sequentially and make purchase decisions based on a quoted price and their private reservation price the seller knows the wtp distribution pre and postchange but does not know the time at which this change occurs the performance of a pricing policy is measured in terms of regret the loss in revenues relative to an oracle that knows the time of change prior to the start of the selling season we derive lower bounds on the worst case regret and develop pricing strategies that achieve the order of these bounds thus establishing the complexity of the pricing problem our results shed light on the role of price experimentation and its necessity for optimal detection of changes in market response wtp our formulation allows for essentially arbitrary consumer wtp distributions and purchase request patterns

bilateral bargaining pareto optimality and the empirical frequency of impasse abstract an experimental bilateral bargaining mechanism is developed for use on a computer and then studied under two types of time constraint first a single buyer and single seller are allowed to negotiate a market contract during one long experimental session the relative pareto optimality results of these negotiations are comparable to the benchmark siegel and fourakel bargaining experiments then by shortening the time of each contract negotiation period and replicating these periods over one long experimental session a multiperiod version of the bilateral mechanism is examined using this repetitive mechanism the occurrence of an impasse as a bargaining tool becomes important the multiple contract pareto optimality results and multiple impasse occurrences are then compared to the original single contract results

blind network revenue management we consider a general class of network revenue management problems where mean demand at each point in time is determined by a vector of prices and the objective is to dynamically adjust these prices so as to maximize expected revenues over a finite sales horizon a salient feature of our problem is that the decision maker can only observe realized demand over time but does not know the underlying demand function that maps prices into instantaneous demand rate we introduce a family of blind pricing policies that are designed to balance trade offs between exploration demand learning and exploitation pricing to optimize revenues we derive bounds on the revenue loss incurred by said policies in comparison to the optimal dynamic pricing policy that knows the demand function a priori and we prove that asymptotically as the volume of sales increases this gap shrinks to zero

the distribution of the male female earnings differential 1970 1990 the authors examine the male female earnings differential between 1970 and 1990 their objective is to provide consistent estimates that can be compared and interpreted over time and to assess the sensitivity of their results to alternative specifications the authors find that women made modest gains over the period standard decomposition techniques reveal that gender differences in observable characteristics do not explain much of the earnings differential most of the improvement in women s relative earnings has come by a decline in the unexplained component the authors also find that the differential varies systematically across age and education groups and across high and low income women coauthors are dwayne benjamin andree desaulniers and mary grant

gender role attitudes and the labour market outcomes of women across oecd countries this paper uses data from the world value surveys 1990 1995 1999 to investigate the impact of gender role attitudes and work values on women s labour market outcomes across 25 oecd countries anti egalitarian views are found to display the strongest negative association with female employment rates and the gender pay gap these views are however softening among recent cohorts on the other hand perceptions of women s role as homemakers which are likely formed in youth and linked to religious ideology are more persistent over time they could be implicated in the recent slowdown of the gender convergence in pay finally the unavoidable clash between family values and egalitarian views that takes the form of an inner conflict for many women the so called mother s guilt is another obstacle in the path towards greater gender equality in the labour market copyright 2005 oxford university press

analytical solutions to the dynamic pricing problem for time normalized revenue abstract in this work we consider dynamic pricing for the case of continuous replenishment an essential ingredient in such a formulation is the use of time normalized revenue or profit function in other words revenue or profit per unit time this provides the incentive to sell many items in the shortest time and of course at a high price moreover for most firms what matters most is how much revenue or profit is achieved in a certain time frame for example per year this changes the problem qualitatively and methodologically we develop a new dynamic pricing model for this formulation we derive an analytical solution to the pricing problem in the form of a simple to solve ordinary differential equation ode equation the trajectory of this ode gives the optimal pricing curve unlike many of the models existing in the literature that rely on computationally demanding dynamic programming type solutions our model is relatively simple to solve also we apply the derived equation to two commonly used price demand functions the exponential and the power functions and derive closed form pricing curves for these functions

dynamic monopoly pricing under a poisson type uncertain demand this article explores dynamic pricing strategies in the presence of uncertainty diffusion dynamics experience curve effects and a poisson type of uncertainty in the demand are incorporated in a model using the framework of a stochastic control problem the results indicate that the movement of the expected price depends on the relative strength of the contingent effects and the effects of the experience if the direction of the former is opposite to the latter and is substantial enough to dominate it the expected price path will show a pattern different from the one predicted by a deterministic model copyright 1992 by university of chicago press

in and out of the labour market long term income consequences of child related interruptions to women s paid work why do canadian mothers have lower incomes than women who have never had children microdata from the 1995 gss allow examination of two hypotheses 1 mothers have spent more time out of the labour force thus acquiring less human capital 2 higher levels of unpaid work lead to fatigue and or scheduling difficulties measuring work history does little to account for the family gap the estimated child penalty is reduced by allowing for human capital depreciation and controlling for unpaid work hours but the two hypotheses together cannot entirely explain the gap jel classification j0 j3 entrees et sorties marche du travail et consequences a long terme des interruptions dans l experience sur le marche du travail a cause des enfants ce memoire se demande pourquoi les femmes canadiennes qui ont eu des enfants ont des revenus plus bas que ceux des femmes qui n en ont pas eus les microdonnees de l enquete sociale generale de 1995 de statistiques canada permettent d examiner deux hypotheses 1 les meres ont passe plus de temps en dehors de la main d oeuvre active et donc ont accumule moins de capital humain ou 2 des niveaux plus eleves de travail non remunere peuvent entrainer fatigue ou difficultes d organisation du temps des efforts pour construire une meilleure image de l experience de travail des femmes ne permettent pas d expliquer cet ecart familial meme si la possibilite qu il y ait depreciation du capital humain reduit la penalisation attachee au fait d avoir un enfant en particulier si l interruption dans l experience sur le marche du travail est suivie d un changement d emploi le nombre hebdomadaire d heures de travail non paye est relie negativement aux revenus et si l on normalise pour tenir compte des heures de travail non paye cela reduit la penalisation attachee au fait d avoir un enfant cependant les deux hypotheses combinees ne suffisent pas pour expliquer l ecart

a minmax regret price control model for managing perishable products with uncertain parameters abstract conventional revenue management assumes that demand parameters used in the models are known the control policy derived based on such a premise however guarantees no optimality as the real parameters can significantly deviate from their estimates this article proposes a robust price control model for managing perishable products it attempts to find a policy that minimizes the worst case regret due to imperfect information distribution of each uncertain parameter is assumed arbitrary with only the lower and upper bound available we formulate the dynamic price control problem as a continuous time model under fairly mild conditions we derive the optimality condition for the control policy and develop a recursive procedure for the optimal solution our analysis shows that the proposed minmax regret price control model is equivalent to conventional rm models when demand parameters are deterministic we examine structural properties of the solution and managerial insights they imply numerical results show that the proposed robust model outperforms the conventional rm model when parameters are unknown in particular it significantly reduces the variation in revenues without sacrificing the average revenue

disequilibrium economic dynamics a post schumpeterian contribution abstract adaptive economizing in a decentralized economy with alternative technologies and scarce resources leads to various kinds of locally unstable behavior economic disequilibrium is the rule in such a world and requires the presence of market mechanisms that make possible continued viability if in addition to local instability economies are also globally unstable as considerable evidence suggests then the discovery and application of new structure is essential a complete dynamic theory of economic change must therefore be based not only on conventional rationality and routinely adapting behavior but on a superior faculty which may perhaps best be called creative intelligence

bargaining in the absence of property rights an experiment abstractthe coase theorem posits that if 1 property rights are perfect 2 contracts are perfectly enforceable 3 transaction costs are zero 4 preferences are common knowledge and 5 parties are rational then the initial allocation of entitlements matters only for distribution not for efficiency we study in an experimental setting whether condition 1 is necessary our results suggest that property rights have a limited effect on efficiency

joint inventory and markdown management for perishable goods with strategic consumer behavior in this paper we formulate and analyze a novel model on a firm s dynamic inventory and markdown decisions for perishable goods we consider a dynamic stochastic setting where every period consists of two phases clearance phase and regular sales phase in the clearance phase the firm decides how much to order for regular sales as well as whether to markdown some or all of the leftover inventory from the previous period that will be disposed otherwise since strategic consumers may buy the product during clearance sales for future consumption markdown may cannibalize future sales at regular price hence the firm needs to make a trade off between product spoilage and intertemporal demand substitution we show that the firm should either put all of the leftover inventory on discount or dispose all of it and the choice depends on the amount of leftover inventory from the previous period in particular the firm should introduce markdown when the amount of leftover inventory is higher than a certain th

innovation and technology diffusion in competitive supply chains abstract innovations in consumer products frequently rely on technological advances across multiple tiers in a supply chain considering the consumer market demand and downstream investment conditions as input we model a game in a two tier supply chain where downstream firms choose to adopt different levels of an upstream technology and an upstream technology leader determines its pricing policy we identify two necessary but distinct elements for the successful development adoption and diffusion of upstream technologies that are sold to lower tiers as components within final products 1 the level of technology demanded by the market we develop a measure technological potential which describes the highest level of an upstream technology demanded by consumer markets 2 a sufficiently rich return to an upstream innovator as a function of different levels of technology from these two elements we show that the relative magnitudes of two competing sets of consumer market factors determine the technological potential whereas the overall magnitude of the factors in both sets determines the return to the upstream developer we discuss how this difference in consumer market factors influence on these two elements may determine how different technologies fare in the supply chain our results have managerial implications for investors in research and development project selection in identifying profitable technologies that are also demanded at higher capability levels and for governments in defining more targeted public policies for example in choosing the right tier of a supply chain to provide subsidies to encourage market support for certain technologies

technical note dynamic pricing and demand learning with limited price experimentation in a dynamic pricing problem where the demand function is not known a priori price experimentation can be used as a demand learning tool existing literature usually assumes no constraint on price changes but in practice sellers often face business constraints that prevent them from conducting extensive experimentation we consider a dynamic pricing model where the demand function is unknown but belongs to a known finite set the seller is allowed to make at most m price changes during t periods the objective is to minimize the worst case regret i e the expected total revenue loss compared with a clairvoyant who knows the demand distribution in advance we demonstrate a pricing policy that incurs a regret of ologmt or m iterations of the logarithm furthermore we describe an implementation of this pricing policy at groupon a large e commerce marketplace for daily deals the field study shows significant impact on revenue and bookings the e companion is available at https doi org 10 1287 opre 2017 1629

performance pay and the white black wage gap we show that the reported tendency for performance pay to be associated with greater wage inequality at the top of the earnings distribution applies only to white workers this results in the white black wage differential among those in performance pay jobs growing over the earnings distribution even as the same differential shrinks over the distribution for those not in performance pay jobs we show that this remains true even when examining suitable counterfactuals that hold observables constant between whites and blacks we explore reasons behind our finding focusing on the interactions between discrimination unmeasured ability and selection

innovation diffusion uncertainty advertising and pricing policies we develop and analyze a normative and structurally stochastic model of innovation diffusion by depicting the market at an aggregate level model dynamics are defined through the flow pattern of individuals that move from the innovation unaware stage to the innovation aware and ultimately to the adopter stages the stochastic evolution of this stage wise transition unfolds according to tractable stochastic processes and is influenced by such factors as price word of mouth and advertisement efforts in this environment techniques of contingent claims analysis and stochastic control theory are employed to obtain optimal pricing or advertising policies that maximize the value of the innovation to account for their optimal adjustment over time these policies are modeled as positive real valued adapted processes given this setting policy adjustments over time i e advertising or pricing are viewed as a value additive sequence of nested real options we present closed form analytic results regarding the optimal policies simulations provide a numeric insight to the models behavior

the effect of transaction costs on double auction markets abstract the ability of the continuous double auction to attain the competitive equilibrium outcome is one of the most robust results in experimental economics in this paper we study the sensitivity of the behavior of the double auction to the imposition of a monetary cost on the submission of offers to buy and sell we find that even with the transaction cost prices converge toward the competitive equilibrium level however the presence of the transaction cost leads to lower quantity exchanged and market efficiency than in the competitive equilibrium

learning and pricing with models that do not explicitly incorporate competition in revenue management research and practice demand models are used that describe how demand for a seller s products depends on the decisions such as prices of that seller even in settings where the demand for a seller s products also depends on decisions of other sellers the models often do not explicitly account for such decisions it has been conjectured in the revenue management literature that such monopoly models may incorporate the effects of competition because the parameter estimates of the monopoly models are based on data collected in the presence of competition in this paper we take a closer look at such a setting to investigate the behavior of parameter estimates and decisions if monopoly models are used in the presence of competition we consider repeated pricing games in which two competing sellers use mathematical models to choose the prices of their products over the sequence of games each seller attempts to estimate the values of the parameters of a demand model that expresses demand as a function only of its own price using data comprised only of its own past prices and demand realizations we analyze the behavior of the sellers parameter estimates and prices under various assumptions regarding the sellers knowledge and estimation procedures and we identify situations in which a the sellers prices converge to the nash equilibrium associated with knowledge of the correct demand model b the sellers prices converge to the cooperative solution and c the sellers prices have many potential limit points that are neither the nash equilibrium nor the cooperative solution and that depend on the initial conditions we compare the sellers revenues at potential limit prices with their revenues at the nash equilibrium and the cooperative solution and we show that it is possible for sellers to be better off when using a monopoly model than at the nash equilibrium

matching as a tool to decompose wage gaps abstract this paper presents a methodology that uses matching comparisons to explain gender wage differences the approach emphasizes gender differences in the supports of the distributions of observable characteristics and provides insights into the distribution of unexplained gender pay differences this nonparametric alternative to the blinder oaxaca bo decomposition does not require the estimation of earnings equations and divides the gap into four additive elements two of these are analogous to the elements of the bo decomposition but computed only over the common support of the distributions of characteristics while the other two account for differences in the supports

dynamic pricing with a prior on market response we study a problem of dynamic pricing faced by a vendor with limited inventory uncertain about demand and aiming to maximize expected discounted revenue over an infinite time horizon the vendor learns from purchase data so his strategy must take into account the impact of price on both revenue and future observations we focus on a model in which customers arrive according to a poisson process of uncertain rate each with an independent identically distributed reservation price upon arrival a customer purchases a unit of inventory if and only if his reservation price equals or exceeds the vendor s prevailing price we propose a simple heuristic approach to pricing in this context which we refer to as decay balancing computational results demonstrate that decay balancing offers significant revenue gains over recently studied certainty equivalent and greedy heuristics we also establish that changes in inventory and uncertainty in the arrival rate bear appropriate directional impacts on decay balancing prices in contrast to these alternatives and we derive worst case bounds on performance loss we extend the three aforementioned heuristics to address a model involving multiple customer segments and stores and provide experimental results demonstrating similar relative merits in this context

optimal starting times for end of season sales and optimal stopping times for promotional fares many industries face the problem of selling a fixed stock of items over a finite horizon these industries include airlines selling seats before planes depart hotels renting rooms before midnight theaters selling seats before curtain time and retailers selling seasonal goods such as air conditioners or winter coats before the end of the season given a fixed number of seats rooms or coats the objective for these industries is to maximize revenues in excess of salvage value when demand is price sensitive and stochastic pricing is an effective tool to maximize revenues in this paper we address the problem of deciding the optimal timing of a single price change from a given initial price to either a given lower or higher second price under mild conditions we show that it is optimal to decrease resp to increase the initial price as soon as the time to go falls below resp above a time threshold that depends on the number of yet unsold items

bayesian dynamic pricing policies learning and earning under a binary prior distribution motivated by applications in financial services we consider a seller who offers prices sequentially to a stream of potential customers observing either success or failure in each sales attempt the parameters of the underlying demand model are initially unknown so each price decision involves a trade off between learning and earning attention is restricted to the simplest kind of model uncertainty where one of two demand models is known to apply and we focus initially on performance of the myopic bayesian policy mbp variants of which are commonly used in practice because learning is passive under the mbp that is learning only takes place as a by product of actions that have a different purpose it can lead to incomplete learning and poor profit performance however under one additional assumption a constrained variant of the myopic policy is shown to have the following strong theoretical virtue the expected performance gap relative to a clairvoyant who knows the underlying demand model is bounded by a constant as the number of sales attempts becomes large this paper was accepted by gerard p cachon stochastic models and simulation

wage discrimination in the nba evidence using free agent signings this article takes a step toward understanding potential causes of wage discrimination in an economy highly dependent on the service industry traditionally categorized within the service industry professional sport leagues such as the national basketball association nba provides a unique setting to examine the potential impact of race on salary we analyze free agency contract signings which allow us to better capture the determinants of players wages from 2011 to 2017 to investigate the prominence of wage discrimination in the nba using weighted linear regression models and the oaxaca blinder decomposition we find that black athletes are paid significantly less than their counterparts in addition we also identify the presence of consumer discrimination after controlling the exposure of a player to the audience which is observed through the interaction term between the share of msa population which is white and an identifier for whether a player is black

the immigrant and native born wage distributions evidence from united states censuses recent studies document a large widening of the immigrant native born mean wage gap since about 1970 a trend that some observers ascribe to post 1965 changes in u s immigration policy these studies are limited however by their exclusive focus on men which ignores important gender differences in the wage gap and by the inadequacy of the mean wage for characterizing the gap when as in recent decades the wage distribution dramatically changes this study of recent immigrants examines changes across the entire wage distribution for both genders the authors find evidence based partly on gender differences that minimum wages strongly influenced the gap a counterfactual analysis also indicates that if recent immigrants in 1970 had faced the 1990 wage structure their wage distribution would have closely resembled that of recent immigrants in 1990 these and other results suggest that the increasing wage gap is linked to changes in the wage structure

pay differences among the highly paid the male female earnings gap in lawyers salaries this article uses very detailed information on graduates of the university of michigan law school to examine male female pay differences in that population men and women in this population have virtually identical human capital on graduation from law school allowing us to examine carefully the different impact of children and work history on men s and women s careers and earnings taking time from work in order to care for children reduces wages significantly but a rich set of controls including childcare work history school performance and job setting measures still leave one fourth to one third of the earnings gap unexplained

reoptimization and self adjusting price control for network revenue management we consider a standard dynamic pricing problem with finite inventories finite selling horizon and stochastic demands where the objective of the seller is to maximize total expected revenue we introduce a simple improvement of the popular static price control known in the literature the proposed heuristic only requires a single optimization at the beginning of the selling horizon and does not require any reoptimization at all this provides an advantage over the potentially heavy computational burden of reoptimization especially for very large applications with frequent price adjustments in addition our heuristic can be implemented in combination with a few reoptimizations to achieve a high level revenue performance this hybrid of real time adjustment and reoptimization allows the seller to enjoy the benefit of reoptimization without overdoing it

optimal experimentation in a changing environment this paper studies optimal experimentation by a monopolist who faces an unknown demand curve subject to random changes and who maximizes profits over an infinite horizon in continuous time we show that there are two qualitatively very different regimes determined by the discount rate and the intensities of demand curve switching and the dependence of the optimal policy on these parameters is discontinuous one regime is characterized by extreme experimentation and good tracking of the prevailing demand curve the other by moderate experimentation and poor tracking moreover in the latter regime the agent eventually becomes trapped into taking actions in a strict subset of the feasible set

dynamic pricing with online learning and strategic consumers an application of the aggregating algorithm we study the problem faced by a monopolistic company that is dynamically pricing a perishable product or service and simultaneously learning the demand characteristics of its customers in the learning procedure the company observes the sales history over consecutive learning stages and predicts consumer demand by applying an aggregating algorithm aa to a pool of online stochastic predictors numerical implementation uses finite sample distribution approximations that are periodically updated using the most recent sales data these are subsequently altered with a random step characterizing the stochastic predictors the company s pricing policy is optimized with a simulation based procedure integrated with aa the methodology of the paper is general and independent of specific distributional assumptions we illustrate this procedure on a demand model for a market in which customers are aware that pricing is dynamic may time their purchases strategically and compete for a limited product supply we derive the form of this demand model using a game theoretic consumer choice model and study its structural properties numerical experiments demonstrate that the learning procedure is robust to deviations of the actual market from the model of the market used in learning

an experimental investigation of transaction costs abstract this research builds on hoffman and spitzer 1982 and 1986 and coursey hoffman and spitzer 1987 and investigates how transaction costs may alter price patterns and economic efficiency in markets sixteen experimental markets were conducted which were designed to have different levels of transaction costs the transaction costs were of two types either as a consequence of strategic price setting due to potential holdouts or due to the number of traders who had to contract to trigger a synergistic payoff the results of the markets indicated that transaction costs had the anticipated influence on the price patterns and the efficiency of the markets

periodic pricing of seasonal products in retailing this paper studies intertemporal pricing policies when selling seasonal products in retail stores we first present a continuous time model where a seller faces a stochastic arrival of customers with different valuations of the product for this model we characterize the optimal pricing policies as functions of time and inventory we use this model as a benchmark against which we compare more realistic models that consider periodic pricing reviews we show that the structure of the optimal pricing policies in this case is consistent with the procedures observed in practice retail stores successively discount the product during the season and promote a liquidation sale at the end of the planning horizon we also show that the loss experienced when implementing periodic pricing reviews instead of continuous policies is small when the appropriate number of reviews is chosen several interesting economic insights emerge from our analysis for example uncertainty in the demand for new products leads to higher prices larger discounts and more unsold inventory finally we study the effect of announced discount policies on prices and profits we show that stores that have adopted this type of strategy usually set prices such that with high probability the merchandise is sold during the first periods and the largest discounts rarely take place

adaptive data driven inventory control with censored demand based on kaplan meier estimator using the well known product limit form of the kaplan meier estimator from statistics we propose a new class of nonparametric adaptive data driven policies for stochastic inventory control problems we focus on the distribution free newsvendor model with censored demands the assumption is that the demand distribution is not known and there are only sales data available we study the theoretical performance of the new policies and show that for discrete demand distributions they converge almost surely to the set of optimal solutions computational experiments suggest that the new policies converge for general demand distributions not necessarily discrete and demonstrate that they are significantly more robust than previously known policies as a by product of the theoretical analysis we obtain new results on the asymptotic consistency of the kaplan meier estimator for discrete random variables that extend existing work in statistics to the best of our knowledge this is the first application of the kaplan meier estimator within an adaptive optimization algorithm in particular the first application to stochastic inventory control models we believe that this work will lead to additional applications in other domains

dynamic pricing under a general parametric choice model we consider a stylized dynamic pricing model in which a monopolist prices a product to a sequence of t customers who independently make purchasing decisions based on the price offered according to a general parametric choice model the parameters of the model are unknown to the seller whose objective is to determine a pricing policy that minimizes the regret which is the expected difference between the seller s revenue and the revenue of a clairvoyant seller who knows the values of the parameters in advance and always offers the revenue maximizing price we show that the regret of the optimal pricing policy in this model is theta sqrt t by establishing an omega sqrt t lower bound on the worst case regret under an arbitrary policy and presenting a pricing policy based on maximum likelihood estimation whose regret is cal o sqrt t across all problem instances furthermore we show that when the demand curves satisfy a well separated condition the t period regret of the optimal policy is log t numerical experiments show that our policies perform well

nonparametric advertising budget allocation with inventory constraint abstract in this paper we study the optimization problem of the advertising budget allocation for revenue management faced by a marketer besides the advertising budget the marketer is subject to an inventory constraint during the promotion season the marketer can affect sales by spending on advertising but does not initially know the relationship between the advertising expense and consequent sales we propose a nonparametric learning while doing budget allocation policy for the problem specifically we first conduct a sequence of advertising experiments to learn predict the market sales response through observing realized sales exploration then based on the learned sales function determine the following budget allocation planning exploitation in particular during the exploration and exploitation phases we need to balance the advertising and inventory budgets simultaneously we show that our policy is asymptotically optimal as the size of the market increases by constructing a worst case example we show that our policy achieves near best asymptotic performance we also provide numerical illustrations to show how our policy works and discuss how its performance changes as the system parameters vary we also glen some managerial implications of our model and policy from the numerical results

dynamic pricing with an unknown demand model asymptotically optimal semi myopic policies we consider a monopolist who sells a set of products over a time horizon of t periods the seller initially does not know the parameters of the products linear demand curve but can estimate them based on demand observations we first assume that the seller knows nothing about the parameters of the demand curve and then consider the case where the seller knows the expected demand under an incumbent price it is shown that the smallest achievable revenue loss in t periods relative to a clairvoyant who knows the underlying demand model is of order t in the former case and of order log t in the latter case to derive pricing policies that are practically implementable we take as our point of departure the widely used policy called greedy iterated least squares ils which combines sequential estimation and myopic price optimization it is known that the greedy ils policy itself suffers from incomplete learning but we show that certain variants of greedy ils achieve the minimum asymptotic loss rate to highlight the essential features of well performing pricing policies we derive sufficient conditions for asymptotic optimality

learning and pricing models for repeated generalized second price auction in search advertising abstract in search advertising how much an advertiser is willing to pay for a click or tap on his search ad is private information which hampers an ad seller s ability to set the best reserve price to increase the revenue for the generalized second price gsp auctions used to allocate ad slots we present a series of learning and pricing models for repeated gsp auctions selling multiple heterogeneous items this paper contributes to the literature in dynamic pricing with learning and complements the existing off line studies on impact of the reserve price in the multi billion dollar online advertising business with few restrictions on the distribution function of the unknown parameter algorithms are developed to estimate the empirical distribution function and determine the best reserve price to reduce the revenue loss regret over time when bidders bid in the locally envy free equilibrium we present an algorithm that has the best attainable regret upper bound when bidders do not bid in the locally envy free equilibrium we propose a gsp auction with position specific reserve prices and develop an algorithm with the same regret bound to mitigate the risk of strategic bidding with a high volatility involved learning becomes more active while earning is more effective when bidders coordinate bidding the properly selected starting reserve prices can substantially reduce the revenue loss from possible collusive bidding behaviors

information acquisition for capacity planning via pricing and advance selling when to stop and act this paper investigates a capacity planning strategy that collects commitments to purchase before the capacity decision and uses the acquired advance sales information to decide on the capacity in particular we study a profit maximization model in which a manufacturer collects advance sales information periodically prior to the regular sales season for a capacity decision customer demand is stochastic and price sensitive once the capacity is set the manufacturer produces and satisfies customer demand to the extent possible from the installed capacity during the regular sales period we study scenarios in which the advance sales and regular sales season prices are set exogenously and optimally for both scenarios we establish the optimality of a control band or a threshold policy that determines when to stop acquiring advance sales information and how much capacity to build we show that advance selling can improve the manufacturer s profit significantly we generate insights into how operating conditions such as the capacity building cost and market characteristics such as demand variability affect the value of information acquired through advance selling from this analysis we identify the conditions under which advance selling for capacity planning is most valuable finally we study the joint benefits of acquiring information for capacity planning through advance selling and revenue management of installed capacity through dynamic pricing

a multiproduct dynamic pricing problem and its applications to network yield management a firm has inventories of a set of components that are used to produce a set of products there is a finite horizon over which the firm can sell its products demand for each product is a stochastic point process with an intensity that is a function of the vector of prices for the products and the time at which these prices are offered the problem is to price the finished products so as to maximize total expected revenue over the finite sales horizon an upper bound on the optimal expected revenue is established by analyzing a deterministic version of the problem the solution to the deterministic problem suggests two heuristics for the stochastic problem that are shown to be asymptotically optimal as the expected sales volume tends to infinity several applications of the model to network yield management are given numerical examples illustrate both the range of problems that can be modeled under this framework and the effectiveness of the proposed heuristics the results provide several fundamental insights into the performance of yield management systems

dynamic pricing in the presence of inventory considerations research overview current practices and future directions the benefits of dynamic pricing methods have long been known in industries such as airlines hotels and electric utilities where the capacity is fixed in the short term and perishable in recent years there has been an increasing adoption of dynamic pricing policies in retail and other industries where the sellers have the ability to store inventory three factors contributed to this phenomenon 1 the increased availability of demand data 2 the ease of changing prices due to new technologies and 3 the availability of decision support tools for analyzing demand data and for dynamic pricing this paper constitutes a review of the literature and current practices in dynamic pricing given its applicability in most markets and its increasing adoption in practice our focus is on dynamic intertemporal pricing in the presence of inventory considerations

a partially observed markov decision process for dynamic pricing in this paper we develop a stylized partially observed markov decision process pomdp framework to study a dynamic pricing problem faced by sellers of fashion like goods we consider a retailer that plans to sell a given stock of items during a finite sales season the objective of the retailer is to dynamically price the product in a way that maximizes expected revenues our model brings together various types of uncertainties about the demand some of which are resolvable through sales observations we develop a rigorous upper bound for the seller s optimal dynamic decision problem and use it to propose an active learning heuristic pricing policy we conduct a numerical study to test the performance of four different heuristic dynamic pricing policies in order to gain insight into several important managerial questions that arise in the context of revenue management

robust new product pricing we study the pricing decision for a monopolist launching a new innovation at the time of launch we assume that the monopolist has incomplete information about the true demand curve despite the lack of objective information the firm must set a retail price to maximize total profits to model this environment we develop a novel two period non bayesian framework where the monopolist sets the price in each period based only on a nonparametric set of all feasible demand curves optimal prices are dynamic as prices in any period allow the firm to learn about demand and improve future pricing decisions our main results show that the direction of dynamic introductory prices versus static prices depends on the type of heterogeneity in the market we find that 1 when consumers have homogeneous preferences introductory dynamic price is higher than the static price 2 when consumers have heterogeneous preferences and the monopolist has no ex ante information the introductory dynamic price is the same as

monopolist pricing with dynamic demand and production cost this paper deals with pricing of a new product over time by a monopolist who maximizes the discounted profit stream the interdependency of cost and demand on cumulative production makes the problem inherently dynamic cost is assumed to be declining with cumulative production learning curve effect while demand is a function of price and cumulative sales representing word of mouth and saturation effects the paper addresses this problem in a general framework that includes several previous results as special cases and provides new insights in other situations while the learning curve and word of mouth effect cause prices to be lower than the price that maximizes immediate revenues the saturation factor has the opposite effect the price path over time is affected by these factors and the interest rate we characterize the price path under several different situations and interpret the results for policy guidelines