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

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

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

turnout across democracies world democracies widely differ in legislative executive and legal institutions different institutional environments induce different mappings from electoral outcomes to the distribution of power we explore how these mappings affect voters participation in an election we show that the effect of such institutional differences on turnout depends on the distribution of voters preferences we uncover a novel contest effect given the preferences distribution turnout increases and then decreases when we move from a more proportional to a less proportional power sharing system turnout is maximized for an intermediate degree of power sharing moreover we generalize the competition effect common to models of endogenous turnout given the institutional environment turnout increases in the ex ante preferences evenness and more so when the overall system has lower power sharing these results are robust to a wide range of modeling approaches including ethical voter models voter mobilization models and rational voter models

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

capacity investment under postponement strategies market competition and demand uncertainty we consider duopoly models where firms make decisions on capacity production and price under demand uncertainty capacity and price decisions are made respectively ex ante and ex post demand realizations the interplay between the timings of demand realization and production decision endows firms with different capabilities flexible firms can postpone production decisions until the actual demand curve is observed but inflexible firms cannot under general demand structures and cost functions we characterize the equilibrium for a symmetric duopoly and establish the strategic equivalence of price and quantity competitions when firms are flexible we investigate the stochastic order properties of capacity and profit and show that they both increase for a flexible firm when the market is more volatile we find that flexibility allows a firm to increase investment in capacity and earn a higher profit while benefiting customers by keeping the price in a narrower range strategic equivalence implies that

the price of anarchy in supply chains quantifying the efficiency of price only contracts in this paper we quantify the efficiency of decentralized supply chains that use price only contracts with a price only contract a buyer and a seller agree only on a constant transaction price without specifying the amount that will be transferred it is well known that these contracts do not provide incentives to the parties to coordinate their inventory capacity decisions we measure efficiency with the price of anarchy poa defined as the largest ratio of profits between the integrated supply chain that is fully coordinated and the decentralized supply chain we characterize the efficiency of various supply chain configurations push or pull inventory positioning two or more stages serial or assembly systems single or multiple competing suppliers and single or multiple competing retailers

unimodality of price setting newsvendor s objective function with multiplicative demand and its applications abstract we present a general solution framework for the price setting newsvendor problem with a multiplicative stochastic demand under mild assumptions such as increasing price elasticity on the mean demand function and increasing generalized failure rate on the distribution of the random factor we first prove that both the profit function with respect to price and its derived function with respect to order quantity are quasi concave three applications are then studied under our solution framework 1 we consider a wholesale price only contract by which a manufacturer sets a wholesale price and a newsvendor determines an order quantity and the retail price and show that the manufacturer s profit function is unimodal with respect to retailing price or stocking factor under certain conditions 2 we consider a newsvendor problem in which the demand depends on both the retail price and the level of sales effort and the cost exerting the sales effort is proportional to the order quantity we prove that there exists a unique pair of price and sales effort levels that maximize the total profit this result is established under a set of mild assumptions on the demand and cost functions 3 we identify a property in the single period profit function that satisfies condition 1 of huh and janakiraman 2008 which in turn guarantees the optimality of s s policy for an infinite stationary dynamic inventory price control system with lost sales and fixed order costs finally the unimodality of the newsvendor problem with a general stochastic and price sensitive demand is studied

a note on closure properties of failure rate distributions increasing generalized failure rate igfr distributions were introduced as a tool in the study of contracting mechanisms in supply chains in this note we compare and contrast the closure and the lack thereof of igfr and increasing failure rate ifr distributions with respect to standard operations on random variables some implications of these results for the use of igfr distributions in supply chain models are noted

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

managing local commons theoretical issues in incentive design local commons encompass a wide range of resources whose shared feature is the need for some form of collective management in what follows we shall be concerned mainly with the problems of implementing a collective management plan whatever the mechanisms invoked many recent contributions to the literature have stressed that relatively informal collective management of common property resources can in the right circumstances avoid the severe resource degradation predicted by the tragedy of the commons nevertheless both empirical and theoretical arguments suggest that cooperative behavior may be only partial and the incentives of short term self interest only partially held in check under what circumstances then can more formal implementation mechanisms make good the deficiency and given that formal incentives are typically stronger than informal ones are there any reasons why informal incentives might nevertheless sometimes be preferred

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

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

a note on pricing with risk aversion abstract we consider the pricing problem of a risk averse seller facing uncertain demand demand uncertainty stems from buyers valuations being privately observed by imposing very mild restrictions on the distribution of buyers valuations an increasing generalized failure rate distribution and the bernoulli utility function we show that a risk averse seller will unambiguously post a lower price than a risk neutral counterpart

exploring the effect of cap and trade mechanism on firm s production planning and emission reduction strategy abstract cap and trade mechanism has a significant effect on firm s production and operation decisions and carbon emissions this study develops a mathematical model to examine the effect of cap and trade mechanism on firm s production planning and emission reduction strategy based on the model the firm s critical production planning decisions such as the optimal production quantity optimal allowance selling price and the maximum profit under the cap and trade mechanism are derived firstly then based on the cost benefit analysis the conditions under which the firm makes the optimal emission reduction strategy between buying carbon allowance from the carbon trading market and conducting low carbon processing are identified the result suggests that when the low carbon processing cost is greater than the potential opportunity benefit the firm is inclined to purchase carbon allowance from the carbon trading market and vice versa finally a numerical analysis is conducted to investigate the effects of relevant factors such as carbon quotas carbon emission rate low carbon processing cost and transaction cost on firm s production and operation decisions the results indicate that under the cap and trade mechanism the transaction cost has a positive effect on allowance selling price the firm s optimal production quantity and maximum profit is positively related to carbon quotas while negatively related to carbon emission rate and low carbon processing cost this research contributes to enrich related literature and knowledge with regard to carbon emissions reduction at the firm level and highlight the critical importance of cap and trade mechanism in reducing carbon emissions

choice simplification a theory of mental budgeting and naive diversification we develop a theory of how an agent makes basic multiproduct consumption decisions in the presence of taste consumption opportunity and price shocks that are costly to attend to we establish that the agent often simplifies her choices by restricting attention to a few important considerations which depend on the decision at hand and affect her consumption patterns in specific ways if the agent s problem is to choose the consumption levels of many goods with different degrees of substitutability then she may create mental budgets for more substitutable products e g entertainment in some situations it is optimal to specify budgets in terms of consumption quantities but when most products have an abundance of substitutes specifying budgets in terms of nominal spending tends to be optimal if the goods are complements in contrast then the agent may consistent with naive diversification choose a fixed unconsidered mix of products and if the agent s problem is to choose one of multiple products to fulfill a given consumption need e g for gasoline or a bed then it is often optimal for her to allocate a fixed sum for the need

relationships among three assumptions in revenue management this note discusses the relationships among three assumptions that appear frequently in the pricing revenue management literature these assumptions are mostly needed for analytical tractability and they have the common property of ensuring a well behaved revenue function the three assumptions are decreasing marginal revenue with respect to demand decreasing marginal revenue with respect to price and increasing price elasticity of demand we provide proofs and examples to show that none of these conditions implies any other however they can be ordered from strongest to weakest over restricted regions and the ordering depends upon the region

optimal price and product quality decisions in a distribution channel this paper studies a joint pricing and product quality decision problem in a distribution channel in which a manufacturer sells a product through a retailer the manufacturer jointly determines the wholesale price and quality of the product and the retailer determines the retail price we find that if the marginal revenue function is strictly concave then the manufacturer chooses a lower product quality level than if selling the product directly to customers if the marginal revenue function is affine then the manufacturer s optimal product quality decision is independent of the distribution channel structure if the marginal revenue function is strictly convex then the manufacturer chooses a higher product quality level than if selling the product directly to customers

bundling strategies when products are vertically differentiated and capacities are limited we consider a seller who owns two capacity constrained resources and markets two products components corresponding to these resources as well as a bundle comprising the two components in an environment where all customers agree that one of the two components is of higher quality than the other and that the bundle is of the highest quality we derive the seller s optimal bundling strategy we demonstrate that the optimal solution depends on the absolute and relative availabilities of the two resources as well as upon the extent of subadditivity of the quality of the products the possible strategies that can arise as equilibrium behavior include a pure components strategy a partial or full spectrum mixed bundling strategy and a pure bundling strategy where the latter strategy is optimal when capacities are unconstrained these conclusions are contrary to findings in the prior literature on bundling that demonstrated the unambiguous dominance of the full spectrum mixed bundling strategy thus our work expands the frontier of bundling to an environment with vertically differentiated components and limited resources we also explore how the bundling strategies change as we introduce an element of horizontal differentiation wherein different types of customers value the available components differently

optimal pricing and inventory control policy with quantity based price differentiation a firm facing price dependent stochastic demand aims to maximize its total expected profit over a planning horizon in addition to the regular unit selling price the firm can utilize quantity discounts to increase sales we refer to this dual pricing strategy as quantity based price differentiation at the beginning of each period the firm needs to make three decisions replenish the inventory set the unit selling price if the unit sales mode is deployed and set the quantity discount price if the quantity sales mode is deployed or the combination of the two modes of sales we identify conditions under which the optimal inventory control policy and selling pricing strategy is well structured remarkably under a utility based demand framework these conditions can be unified by a simple regularity assumption that has long been used in the auction and mechanism design literature moreover sharper structural results are yielded for the optimal selling strategy we also examine the comparative advantag

a dual self model of impulse control we propose that a simple dual self model gives a unified explanation for several empirical regularities including the apparent time inconsistency that has motivated models of quasi hyperbolic discounting and rabin s paradox of risk aversion in the large and small the model also implies that self control costs imply excess delay as in the o donoghue and rabin models of quasi hyperbolic utility and it explains experimental evidence that increased cognitive load makes temptations harder to resist the base version of our model is consistent with the gul pesendorfer axioms but we argue that these axioms must be relaxed to account for the effect of cognitive load

income shocks and suicides causal evidence from indonesia we examine how income shocks affect the suicide rate in indonesia we use a difference in differences approach exploiting the cash transfer s nationwide rollout and corroborate the findings using

competitive price matching guarantees equilibrium analysis of the availability verification clause under demand uncertainty price matching guarantees involve a retailer matching the lower price of a competitor for an identical product in reality retailers often make such guarantees contingent on the verification of product availability at the competitor s location and decline a price match request if the product is not available there this creates certain consternation on the part of customers in this paper we investigate the availability contingency strategy from the perspectives of both the retailers and the customers our analysis shows that availability contingency clauses intensify inventory competition between retailers and reinstitutes price competition which is otherwise eliminated by unconditional price matching guarantees consequently despite what customers may think about the availability verification it actually increases their surplus on the other hand such a clause reduces profits and hence is not the equilibrium strategy for retailers subsequently we discuss how a likely customer behaviour pattern may be a plausible explanation regarding the use of the clause by the retailers in practice this paper was accepted by yossi aviv operations management

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

a damage based tax mechanism for regulation of non point emissions in a recent paper segerson 1988 proposed a novel incentive mechanism for stochastic non point emissions based on ambient pollution concentrations in nature for specification of the mechanism when the damage function is nonlinear the regulator must know polluters cost and emission functions the mechanism also gives incentives to form coalitions among polluters which if they are formed render the mechanism inefficient in this paper we propose a revised mechanism which eliminates the need for knowledge of polluters cost and emission functions and reduces the probability of coalition forming a standards and pricing version of the revised mechanism with both properties mentioned is also developed

the regulation of non point source pollution under imperfect and asymmetric information abstract this paper develops a bayesian framework for discussing the role of information in the design of non point source pollution control mechanisms an ambient concentration tax is examined allowing for spatial transport among multiple zones imposition of the tax requires costly measurement of concentrations in selected zones and the selection of zones for measurement must be undertaken without perfect information regarding several parameters of the problem potentially crucial information issues discussed include a the impact of asymmetric priors regarding fate and transport b the cost of measuring ambient concentration and c the optimal acquisition of information regarding fate and transport

an integrated revenue management framework for a firm s greening pricing and inventory decisions abstract there is a growing interest on developing efficient ways of incorporating environmental considerations into business practices in order to meet both consumers demand for green products services and the firms sustainable profitability the main contribution of this article is in developing an integrated revenue management framework to address a firm s greening investment effort pricing and inventory decisions it is assumed that the firm inaugurates a green product along with its existing product even though the firm offers both the green and regular product at differentiated prices the market segmentation as a result of this price differentiation is regarded as imperfect this imperfect market segmentation causes a demand leakage mainly due to the heterogeneity among the customers willingness to pay these effects are included in our proposed model and simplified analytical solutions are developed to solve the same additional scenarios where a firm experiences a price dependent stochastic demand with an unknown distribution is also modeled this scenario is addressed using a distribution free approach based on scarf s rule the performance of the proposed methods and the significance of the modeling framework are finally corroborated through several simulations this analysis provides a sustainable environment production and retailing framework while still augmenting profitability using fundamental tools from revenue management

the effect of cognitive load on economic decision making a survey and new experiments abstract psychologists and economists have examined the effect of cognitive load in a variety of situations from risk taking to snack choice we review previous experiments that have directly manipulated cognitive load and summarize their findings we report the results of two new experiments where participants engage in a digit memorization task while simultaneously performing a variety of economic tasks including 1 choices involving risk 2 choices involving intertemporal substitution 3 choices with anchoring effects 4 choices over healthy and unhealthy snacks and 5 math problems we find that higher cognitive load reduces numeracy as measured by performance in math problems moreover within subject analysis indicates that cognitive load leads to more risk averse behavior more impatience over money and nominally more likelihood to anchor we do not find any evidence that cognitive load increases impatience over consumption goods or unhealthy snack choices exploiting the panel nature of our data set we find that those individuals who are most sensitive to cognitive load as measured by a large drop in their own math performance across 1 and 8 digit memorization treatments are driving much of the effect

group decision making theory and behavior under performance based water quality payments abstract two theoretical models explaining group allocation decisions under watershed level performance based payments are explored i reward and penalize individual contributors and ii reduce the problem with cost sharing and cooperative abatement under model i an optimal amount of pollution from individual contributors can be achieved with proper payment incentive and group allocation formula model ii represents a cost effective solution to pollution reduction where the group optimizes its return from group payments but does not necessarily achieve an optimal level of pollution field experiment observations support farmer behavior closer to model ii

an elasticity approach to the newsvendor with price sensitive demand we introduce a measure of elasticity of stochastic demand called the elasticity of the lost sales rate which offers a unifying perspective on the well known newsvendor with pricing problem this new concept provides a framework to characterize structural results for coordinated and uncoordinated pricing and inventory strategies concavity and submodularity of the profit function as well as sensitivity properties of the optimal inventory and price policies are characterized by monotonicity conditions or bounds on the elasticity of the lost sales rate these elasticity conditions are satisfied by most relevant demand models in the marketing and operations literature our results unify and complement previous work on price setting newsvendor models and provide a new tool for researchers modeling stochastic price sensitive demand in other contexts

ambient based pollution mechanisms a comparison of homogeneous and heterogeneous groups of emitters abstract over the last two decades ambient based tax mechanisms have been offered as a potential solution to the problem of nonpoint source water pollution previous theoretical analyses suggest that the performance of ambient based tax mechanisms does not depend on firm characteristics such as size whilst policy discussions advocate that such mechanisms are best suited for regulating relatively homogeneous firms using controlled laboratory experiments we provide empirical evidence that the distribution of firm sizes does have a significant impact on observed group decision making and further that heterogeneity has the potential to generate both some relatively desirable outcomes as well as some outcomes that are not attractive these results suggest that richer theoretical models that capture important strategic interactions and social preferences are needed to better describe laboratory behavior and by extension behavior in potential policy settings

dynamic and targeted bundle pricing of two independently valued products abstract bundling is when two or more products are offered as a single unit and at a price lower than the sum of the individual prices of the products we study a multi segment market in which a retailer aims to clear the inventory of an item by bundling it with a second product which is independently valued we investigate the question of how dynamic and segment specific bundle pricing impacts retailer s revenue we develop a revenue model that integrates the dynamic and segment specific aspects of the pricing decisions and present a computational study to analyze their revenue impact relative to a price promotion for the individual item only the computational results indicate that the bundle offers are most effective when the initial inventory of the item under consideration is high the results also demonstrate that dynamic pricing is beneficial when the initial inventory of the item is low an additional revenue improvement is observed when the price of the bundle is dynamically optimized in the computational study segment specific pricing is observed to have no direct impact on revenue when prices are static segment specific and dynamic pricing however can bring about substantial revenue improvements that are an increasing function of the initial inventory level of the item we consider the correlation in consumers valuations of the bundled products and show that dynamically priced and segment specific bundle offers yield a robust revenue performance mitigating the potentially revenue diminishing impact of positive correlation in consumers valuations of the products

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

the psychological lives of the poor abstract all individuals rely on a fundamental set of mental capacities and functions or bandwidth in their economic and non economic lives yet many factors associated with poverty such as mal

ambient taxes when polluters have multiple choices economic research on environmental policy design has largely been concerned with the merits of emissions based economic incentives e g emissions charges emissions reduction subsidies transferable discharge permits ambient based tax subsidy schemes have drawn considerable interest in nonpoint pollution literature as alternatives to emissions based instruments expanding especially on segerson s seminal article this article examines the optimal design and budget balancing properties of ambient tax subsidy schemes under more realistic assumptions about the dimensions of firms choice sets than prior research

a risk averse competitive newsvendor problem under the cvar criterion abstract we study a risk averse newsvendor problem with quantity competition and price competition under the conditional value at risk cvar criterion we characterize the optimal quantity and pricing decisions under both quantity and price competition for quantity competition we consider two demand splitting rules namely proportional demand allocation and demand reallocation although competition always leads to overstocking interestingly it does not necessarily lead to a profit loss in certain competitive environments such as demand reallocation by avoiding reducing overstocking that results from competition under the risk neutral criterion for price competition we consider both additive and multiplicative demand we find that the order quantity sale price and the expected profit decrease in the degree of risk aversion further both high price sensitivity and competition intensity force decision makers to lower their prices however high price sensitivity always reduces the order quantity while competition can have the opposite effect

monopoly pricing in the presence of social learning a monopolist offers a product to a market of consumers with heterogeneous quality preferences although initially uninformed about the product quality they learn by observing past purchase decisions and reviews of other consumers our goal is to analyze the social learning mechanism and its effect on the seller s pricing decision consumers follow an intuitive non bayesian decision rule under conditions that we identify we show that consumers eventually learn the product s quality we show how the learning trajectory can be approximated in settings with high demand intensity via a mean field approximation that highlights the dynamics of this learning process its dependence on the price and the market heterogeneity with respect to quality preferences two pricing policies are studied a static price and one with a single price change finally numerical experiments suggest that pricing policies that account for social learning may increase revenues considerably relative to policies that do not this

technical note optimal dynamic joint inventory pricing control for multiplicative demand with fixed order costs and lost sales this note studies the optimal dynamic decision making problem for a retailer in a price sensitive multiplicative demand framework our model incorporates lost sales holding cost fixed and variable procurement costs as well as salvage value we characterize the structure of the retailer s discounted expected profit maximizing dynamic inventory policy for both finite and infinite selling horizon problems

a note on probability distributions with increasing generalized failure rates distributions with an increasing generalized failure rate igfr have useful applications in pricing and supply chain contracting problems we provide alternative characterizations of the igfr property that lead to simplify verifying whether the igfr condition holds we also relate the limit of the generalized failure rate and the moments of a distribution

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

repeated auctions with budgets in ad exchanges approximations and design ad exchanges are emerging internet markets where advertisers may purchase display ad placements in real time and based on specific viewer information directly from publishers via a simple auction mechanism advertisers join these markets with a prespecified budget and participate in multiple second price auctions over the length of a campaign this paper studies the competitive landscape that arises in ad exchanges and the implications for publishers decisions the presence of budgets introduces dynamic interactions among advertisers that need to be taken into account when attempting to characterize the bidding landscape or the impact of changes in the auction design to this end we introduce the notion of a fluid mean field equilibrium fmfe that is behaviorally appealing and computationally tractable and in some important cases it yields a closed form characterization we establish that an fmfe approximates well the rational behavior of advertisers in these markets we then show how this framework may be used to provide sharp prescriptions for key auction design decisions that publishers face in these markets in particular we show that ignoring budgets a common practice in this literature can result in significant profit losses for the publisher when setting the reserve price this paper was accepted by dimitris bertsimas optimization

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 risk tolerance analysis for a joint price differentiation and inventory decisions problem with demand leakage effect abstract price differentiation is a commonly used practice in revenue management rm to improve a firm s profitability however most studies in the literature have considered a risk neutral firm to demonstrate the benefits of price differentiation the main contribution of this paper is in considering several important objectives while determining the optimal product prices and order production quantities for a risk adjusted firm with demand leakage effects in the presence of a price dependent stochastic demand the objectives considered include the maximization of a firm s expected profit and maximizing the probability of exceeding the risk adjusted expected revenue closed form expressions for optimal product prices and production quantities are derived for several of these objectives a numerical study is also presented to calibrate the impact of a firm s risk tolerance and other factors such as demand leakage market demand variability on the firm s profitability and its optimal decision

team approaches in reducing nonpoint source pollution abstract it is technically difficult and costly to monitor nonpoint source pollution consequently most economic instruments directed towards reducing this type of pollution have focused on circumventing the monitoring problem by focusing on readily observable factors such instruments include taxes or tradable permits on inputs or other incentives to induce changes in farming practices one difficulty with such approaches is that the incentives may not be consistent with the primary objectives of the policies to reduce nutrient runoffs this paper seeks to identify under what conditions it would be beneficial to apply more direct incentives for reduced nutrient runoffs monitoring and enforcement are core issues in this connection it is still difficult to monitor individual farm field runoffs hence the incentive problems associated with multiple agents emitting to the same recipient need to be resolved

stocking and pricing decisions under endogenous demand and reference point effects abstract in this paper we study the newsvendor s pricing and stocking decisions under reference point effects the demand faced by the newsvendor is endogenous and the customers may also decide to procure the product from an outside option we characterize the firm s optimal pricing and stocking decisions our analysis reveals a threshold policy on the firm s ordering and pricing decisions while considering the impact of reference point effects we also find that as the level of optimism increases the firm s optimal ordering level decreases and optimal price increases we further study the impact of loss aversion on the firm s ordering and pricing decisions

price versus production postponement capacity and competition this article presents a comparative analysis of possible postponement strategies in a two stage decision model where firms make three decisions capacity investment production inventory quantity and price typically investments are made while the demand curve is uncertain the strategies differ in the timing of the operational decisions relative to the realization of uncertainty we show how competition uncertainty and the timing of operational decisions influence the strategic investment decision of the firm and its value in contrast to production postponement price postponement makes the investment and production inventory decisions relatively insensitive to uncertainty this suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility under price postponement additional postponement of production has relatively small incremental value therefore it may be worthwhile to consider flexible ex post pricing before production postponement reengineering while more postponement increases firm value it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty we highlight the different impact of more timely information which leads to higher investment and inventories and of reduced demand uncertainty which decreases investment and inventories our analysis suggests appropriateness conditions for simple make to stock and make to order strategies we also present technical sufficiency and uniqueness conditions under price postponement these results extend to oligopolistic and perfect competition for which pure equilibria are derived interestingly the relative value of operational postponement techniques seems to increase as the industry becomes more competitive

a risk averse newsvendor model under marketing dependency and price dependency abstract in this paper we analyze a single period inventory model where a risk averse newsvendor makes a joint decision on ordering pricing and marketing under the cvar risk measure criterion the newsvendor can exert marketing effort to enhance market demand we assume that the newsvendor s marketing effort affects the scale of the demand distribution and hence to model the marketing dependent demand as a multiplicative form we characterize sufficient conditions that guarantee existence and uniqueness of the optimal solutions under some mild assumptions on demand distribution expected demand function and marketing effort cost which are widely used in the related literature we show that the optimal order quantity increases in the newsvendor s marketing effort but the optimal price remains unchanged whether the demand is marketing dependent or not additionally we explore impact of exogenous parameters such as unit order cost salvage value and the newsvendor s risk aversion coefficient on the optimal decision variables and find that the optimal marketing effort always keeps the same changing direction with the optimal marketing independent order quantity as the exogenous parameters change this suggests that impact of the parameters on the optimal order quantity gets strengthened in the case of marketing dependent demand

selling to conspicuous consumers pricing production and sourcing decisions consumers often purchase goods that are hard to find to conspicuously display their exclusivity and social status firms that produce such conspicuously consumed goods such as designer apparel fashion goods jewelry etc often face challenges in making optimal pricing and production decisions such firms are confronted with precipitous trade off between high sales volume and high margins because of the highly uncertain market demand strategic consumer behavior and the display of conspicuous consumption in this paper we propose a model that addresses pricing and production decisions for a firm using the rational expectations framework we show that in equilibrium firms may offer high availability of goods despite the presence of conspicuous consumption we show that scarcity strategies are harder to adopt as demand variability increases and we provide conditions under which scarcity strategies could be successfully adopted to improve profits finally to credibly commit to scarcity strategy we show that firms can adopt sourcing strategies such as sourcing from an expensive production location supplier or using expensive raw materials this paper was accepted by preyas desai and pradeep chintagunta marketing

optimal reserve prices in sealed bid auctions with reference effects abstract the reference effect and loss aversion are incorporated into the buyer s utility in the symmetric independent private value models of sealed bid auctions the buyer s equilibrium bidding strategy and the seller s optimal reserve price are derived for the first price and second price sealed bid auctions in both auction mechanisms the seller s optimal reserve price and expected revenue are increasing in the reference point we compare the seller s expected revenues as well as the optimal reserve prices in the two auctions the results show that the seller will set a higher optimal reserve price but obtain lower optimal expected revenue in the second price auction compared to the first price auction further we extend the model to the gain seeking case and endogenize the reference point as the ex ante expected price of the item in equilibrium in contrast to the loss averse case the seller will set a lower optimal reserve price but obtain higher optimal expected revenue in the second price auction compared to the first price auction if the buyers are gain seeking with an endogenous reference point similar results are obtained in terms of revenue comparison between the two auctions

an integrated approach to price differentiation and inventory decisions with demand leakage abstract price differentiation is among widely practiced tools in revenue management rm in which a seller offers same or slightly different products or services at different prices to its customers earlier research studies have shown that the benefits from price differentiation are evident when the market segmentation is assumed to be perfect in a perfect market segmentation customers associated with a market segment do not move between market segments however it is not uncommon to observe that a market segmentation a firm operates in is seldom prefect and due to imperfect segmentation customers move between market segments which is also referred to as demand leakage in addition the firms predominantly experience stochastic demand and thus a firm experiences both the short sales and leftovers due to demand uncertainty this research proposes a model to address the issue of an optimal market segmentation using price differentiation as a tool we also establish an integrated framework for pricing order and production quantity allocation decisions in each market segment when a firm experiences demand leakage from one market segment to another and faces price dependent stochastic demand the model is analyzed to determine an optimal decision framework on pricing order quantity allocation and market segmentation using the proposed price differentiation due to the complexity of the problem both the hierarchical and joint optimization approaches are developed a simplified closed form optimal solution to the problem is outlined in the case of hierarchical approach the model is also analyzed for a situation in which the distribution of the price dependent stochastic demand is unknown and a distribution free approach is utilized to address the problem it is identified that the use of distribution free approach also results in a closed form optimal solution to the problem a numerical study is presented to demonstrate the performance of the model and solution approaches the benefits of the optimal market segmentation using a differentiation price are also highlighted along with the proposed integrated optimal decision framework when a firm experiences demand leakage

non point source regulation a self reporting mechanism abstract information feasible regulatory mechanisms that do not require the regulator to acquire firm level information have been proposed long ago for stochastic non point emission problems these mechanisms do not take polluter cooperation and firm entry exit incentives simultaneously into account nor are these issues addressed in an informationally efficient way in this paper we propose an informationally feasible self reporting mechanism that is robust to cooperation among polluters while giving participating firms correct abatement incentives as well as giving entry exit incentives that are correct to a first order approximation

yield optimization of display advertising with ad exchange it is clear from the growing role of ad exchanges in the real time sale of advertising slots that web publishers are considering a new alternative to their more traditional reservation based ad contracts to make this choice the publisher must trade off in real time the short term revenue from ad exchange with the long term benefits of delivering good spots to the reservation ads in this paper we formalize this combined optimization problem as a multiobjective stochastic control problem and derive an efficient policy for online ad allocation in settings with general joint distribution over placement quality and exchange prices we prove the asymptotic optimality of this policy in terms of any arbitrary trade off between the quality of delivered reservation ads and revenue from the exchange and we show that our policy approximates any pareto optimal point on the quality versus revenue curve experimental results on data derived from real publisher inventory confirm that there are significant benefits

optimal quality and quantity provisions for centralized vs decentralized distribution market size uncertainty effects abstract we provide insights on how market size uncertainty affects the optimal quality quantity provision in distribution channels when consumers are heterogeneous in their willingness to pay for product quality in this context we denote the difference between the manufacturer s optimal quality quantity provision for a centralized channel and its optimal analog for a decentralized channel as the quality quantity differential we find that market size uncertainty creates or increases the quantity differential but it does not affect the differential s polarity in contrast market size uncertainty decreases the quality differential and it does so to the extent that depending on the level of consumer heterogeneity it reverses the differential s polarity moreover we find that the higher the inherent uncertainty level the more pronounced are the effects we likewise find that the effects of market size uncertainty are amplified if the notion of consumer heterogeneity is replaced with retail level competition

the setting of profit targets for target oriented divisions abstract setting profit targets and striving to achieve them is fundamental to business survival and success however there has been little research on modeling profit target setting in this paper we study analytic target setting under a common business scenario where a firm is in control of multiple divisions both the firm and the divisions maximize the profit probability i e the probability of achieving some given profit target the firm sets a profit target for each division which then acts as a price setting newsvendor we first obtain the optimal order quantity the optimal retail price and the maximal profit probability of a single division given its assigned target we then derive the firm s profit probability and focus on two specific cases to gain more managerial insights in the first case of fair target setting we show that when each division s demand distribution has an increasing failure rate if a division has a relatively high low production cost its assigned profit target decreases increases with regard to its price elasticity in the second case if the firm is in control of two identical divisions each division s optimal profit target is just half of the firm s profit target when the price elasticity is two or more regardless of production cost and demand distribution

purchasing pricing and quick response in the presence of strategic consumers we consider a retailer that sells a product with uncertain demand over a finite selling season the retailer sets an initial stocking quantity and at some predetermined point in the season optimally marks down remaining inventory we modify this classic setting by introducing three types of consumers myopic consumers who always purchase at the initial full price bargain hunting consumers who purchase only if the discounted price is sufficiently low and strategic consumers who strategically choose when to make their purchase a strategic consumer chooses between a purchase at the initial full price and a later purchase at an uncertain markdown price in equilibrium strategic consumers and the retailer make optimal decisions given their rational expectations regarding future prices availability of inventory and the behavior of other consumers we find that the retailer stocks less takes smaller price discounts and earns lower profit if strategic consumers are present than if there are no strategic consumers we find that a retailer should generally avoid committing to a price path over the season assuming such commitment is feasible committing to a markdown price or to not mark down at all is often too costly inventory may remain unsold even in the presence of strategic consumers the better approach is to be cautious with the initial quantity and then mark down optimally furthermore we discuss the value of quick response the ability to procure additional inventory after obtaining updated demand information albeit at a higher unit cost than the initial order we find that the value of quick response to a retailer is generally much greater in the presence of strategic consumers than without them on average 67 more valuable and as much as 558 more valuable in our sample in other words although it is well established in the literature that quick response provides value by allowing better matching of supply with demand it provides more value often substantially more value by allowing a retailer to control the negative consequences of strategic consumer behavior