minimax regret and strategic uncertainty this paper introduces a new solution concept a minimax regret equilibrium which allows for the possibility that players are uncertain about the rationality and conjectures of their opponents we provide several applications of our concept in particular we consider pricesetting environments and show that optimal pricing policy follows a non degenerate distribution the induced price dispersion is consistent with experimental and empirical observations baye and morgan 2004

iterated regret minimization a new solution concept abstract for some well known games such as the traveler s dilemma or the centipede game traditional game theoretic solution concepts most notably nash equilibrium predict outcomes that are not consistent with empirical observations we introduce a new solution concept iterated regret minimization that exhibits the same qualitative behavior as that observed in experiments in many games of interest including traveler s dilemma the centipede game nash bargaining and bertrand competition as the name suggests iterated regret minimization involves the iterated deletion of strategies that do not minimize regret

efficient mechanisms for bilateral trading we consider bargaining problems between one buyer and one seller for a single object the seller s valuation and the buyer s valuation for the object are assumed to be independent random variables and each individual s valuation is unknown to the other we characterize the set of allocation mechanisms that are bayesian incentive compatible and individually rational and show the general impossibility of ex post efficient mechanisms without outside subsidies for a wide class of problems we show how to compute mechanisms that maximize expected total gains from trade and mechanisms that can maximize a broker s expected profit journal of economic literature classification number 026

the value of fast fashion quick response enhanced design and strategic consumer behavior a fast fashion system combines quick response production capabilities with enhanced product design capabilities to both design hot products that capture the latest consumer trends and exploit minimal production lead times to match supply with uncertain demand we develop a model of such a system and compare its performance to three alternative systems quick response only systems enhanced design only systems and traditional systems which lack both enhanced design and quick response capabilities in particular we focus on the impact of each of the four systems on strategic or forward looking consumer purchasing behavior i e the intentional delay in purchasing an item at the full price to obtain it during an end of season clearance we find that enhanced design helps to mitigate strategic behavior by offering consumers a product they value more making them less willing to risk waiting for a clearance sale and possibly experiencing a stockout quick response mitigates strategic behavior through a different mechanism by better matching supply to demand it reduces the chance of a clearance sale most importantly we find that although it is possible for quick response and enhanced design to be either complements or substitutes the complementarity effect tends to dominate hence when both quick response and enhanced design are combined in a fast fashion system the firm typically enjoys a greater incremental increase in profit than the sum of the increases resulting from employing either system in isolation furthermore complementarity is strongest when customers are very strategic we conclude that fast fashion systems can be of significant value particularly when consumers exhibit strategic behavior this paper was accepted by yossi aviv operations management

truthfulness with value maximizing bidders on the limits of approximation in combinatorial markets abstract in some markets bidders want to maximize value subject to a budget constraint rather than payoff this is different to the quasilinear utility functions typically assumed in auction theory and leads to different strategies and outcomes we refer to bidders who maximize value as value bidders while simple single object auction formats are truthful standard multi object auction formats allow for manipulation it is straightforward to show that there cannot be a truthful and revenue maximizing deterministic auction mechanism with value bidders and general valuations approximation has been used as remedy to achieve truthfulness on other mechanism design problems and we study which approximation ratios we can get from truthful mechanisms we show that the approximation ratio that can be achieved with a deterministic and truthful approximation mechanism with n bidders cannot be higher than 1 n for general valuations for randomized approximation mechanisms there is a framework with a ratio that is tight

technology investment under flexible capacity strategy with demand uncertainty abstract this paper investigates technology investment under flexible capacity strategy with demand uncertainty technology investment enables a firm to reduce its total production cost while flexible capacity strategy aims to reduce a firm s production waste by postponing production until demand is known adopting a general technology investment cost we examine how technology investment cost structure affects a firm s technology investment decisions we derive the conditions under which the firm will benefit from technology investment we show that the firm can increase its expected profit through technology investment only when the unit technology investment cost that varies inversely with the basic technology level is below a threshold however even though the technology investment cost is zero the benefit from the increase in technology level is limited furthermore we analytically determine the optimal technology levels and establish their relationships under different technology investment cost structures our findings will help firms evaluate various technology investment options and choose the most proper one

volume flexibility and capacity investment under demand uncertainty the paper considers optimal capacity investment decisions under uncertainty taking a real options approach concerning the production decision we study a flexible and an inflexible scenario the flexible firm can costlessly adjust production over time with the capacity level as the upper bound while the inflexible firm fixes production at capacity level from the moment of investment onwards we find that the flexible firm invests in higher capacity than the inflexible firm where the capacity difference increases with uncertainty for the flexible firm the initial capacity utilization rate can be quite low especially when investment costs are concave and the economic environment is uncertain as to the timing of the investment there are two contrary effects first the flexible firm has an incentive to invest earlier because flexibility raises the project value second the flexible firm has an incentive to invest later because costs are larger due to the higher capacity level the latter effect dominates in highly uncertain economic environments our model being dynamic enables us to derive the at first sight counterintuitive result that an increase in capacity holding cost raises the capacity level the firm invests in

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

cournot duopoly with two production periods and cost differentials abstract saloner 1987 analyzes a cournot model with two production periods before the market clears if costs do not vary across periods any point on the outer envelope of the reaction functions between the firms stackelberg outputs is attainable with a subgame perfect nash equilibrium spne saloner s analysis is generalized by allowing for cost differences across periods the continuum of equilibria vanishes for any cost differential if costs fall slightly over time there are multiple leader follower equilibria otherwise the model generates a unique spne where both firms produce their single period cournot outputs in the period when production is cheaper

inventory pooling under heavy tailed demand risk pooling has been studied extensively in the operations management literature as the basic driver behind strategies such as transshipment manufacturing flexibility component commonality and drop shipping this paper explores the benefit of risk pooling in the context of inventory management using the canonical model first studied in eppen eppen gd 1979 effects of centralization on expected costs in a multi location newsboy problem management sci 25 5 498 501 specifically we consider a single period multilocation newsvendor model where n different locations face independent and identically distributed demands and linear holding and backorder costs we show that eppen s celebrated result i e that the expected cost savings from centralized inventory management scale with the square root of the number of locations depends critically on the light tailed nature of the demand uncertainty in particular we establish that the benefit from pooling relative to the decentralized case in term

endogenous timing in duopoly games stackelberg or cournot equilibria abstract simultaneous versus sequential play is studied in an extended game in a preplay stage players decide whether to select actions in the basic game at the first opportunity or to wait until observing their rivals first period actions in one extended game players first decide when to select actions without committing to actions in the basic game the equilibrium has a simultaneous play subgame unless payoffs in a sequential play subgame pareto dominate those payoffs in another extended game deciding to select at the first turn requires committing to an action both sequential play outcomes are the equilibria only in undominated strategies

resource flexibility with responsive pricing this article studies two types of flexibility used by firms to better respond to uncertain market conditions resource flexibility and responsive pricing we consider a situation in which a single flexible resource can be used to satisfy two distinct demand classes while the resource capacity must be decided based on uncertain demand functions the resource allocation as well as the pricing decision are made based on the realized demand functions we characterize the effects of two key drivers of flexibility demand variability and demand correlation assuming normally distributed demand curve intercepts demand variability creates opportunity costs and with fixed prices decreases the firm s profit we show that with the additional flexibility gained from responsive pricing the firm can maximize the benefits of favorable demand conditions and mitigate the effects of poor demand conditions ultimately profiting from variability positive demand correlation on the other hand remains undesirable under responsive pricing the optimal capacity of the flexible resource is always increasing in both demand variability and demand correlation this contrasts with the scenarios based on fixed prices highlighting the crucial difference that responsive pricing makes in the management of flexible resources we further quantify the value of flexibility for the firm and its customers by considering as a benchmark a firm relying on two dedicated resources the value of flexibility is most significant if the demand levels are highly variable and negatively correlated in such cases the firm benefits from demand variability due to responsive pricing while facing limited demand risk due to resource flexibility finally we endogenize the input price of the flexible resource by considering the pricing decision of the resource supplier

minimax regret strategies for bargaining over several variables for the sealed bid mechanism for bilateral bargaining we explore models in which each player bids so as to minimize his maximum regret here regret is defined as the difference between the profit the player could have made with the wisdom of hindsight and the profit he actually made we study bargaining over both price and quantity as well as over more general sets of bargaining alternatives with complete and incomplete information in each case there is a minimax regret strategy that is linear in the true value or cost and the minimax regret is not unacceptably large journal qf economic literature classification numbers 022 026

non cooperative bargaining theory an introduction the paper provides an informal introduction to some of the main themes of the recent literature on non cooperative or sequential bargaining models it focuses in particular on the relationship between the new approach and the traditional axiomatic approach exemplified by nash bargaining theory it illustrates the new insights offered by the non cooperative approach by reference to a detailed analysis of the manner in which the presence of an outside option available to one of the parties will affect the negotiated outcome finally the difficulties which arise in extending this analysis to two person bargaining with incomplete information and to n person bargaining are discussed this is a revised version of the fourth review of economic studies lecture presented in april 1985 at the joint meeting of the association of university teachers of economics and the royal economic society held in oxford the choice of lecturer is made by a panel whose members are currently professors hahn mirrlees and nobay and the paper is refereed in the usual way this paper aims to provide an informal and elementary introduction to an approach to bargaining which has received a great deal of attention over the past few years the approach involves writing down some particular sequence of moves offers and replies to be made over time in the course of negotiations and then looking for a non cooperative equilibrium in the game thus specified in practice a perfect equilibrium or in games of incomplete information a sequential equilibrium while the approach appears at first sight to be very different in spirit from the traditional axiomatic approach in which a bargaining solution is specified by appealing to a number of general requirements which are deemed appropriate on the basis of some a priori considerations the two approaches are in fact complementary while the

robust monopoly pricing we consider a robust version of the classic problem of optimal monopoly pricing with incomplete information in the robust version the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution we characterize the pricing policies under two distinct decision criteria with multiple priors i maximin utility and ii minimax regret the equilibrium price under either criterion is lower then in the absence of uncertainty the concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty

design for postponement a comprehensive characterization of its benefits under unknown demand distributions recent papers have developed analytical models to explain and quantify the benefits of delayed differentiation and quick response programs these models assume that while demands in each period are random they are independent across time and their distribution is perfectly known i e sales forecasts do not need to be updated as time progresses in this paper we characterize these benefits in more general settings where parameters of the demand distributions fail to be known with accuracy or where consecutive demands are correlated here it is necessary to revise estimates of the parameters of the demand distributions on the basis of observed demand data we analyze these systems in a bayesian framework assuming that our initial information about the parameters of the demand distributions is characterized via prior distributions we also characterize the structure of close to optimal ordering rules in these systems for a variety of types of order cost functions

approximations of dynamic multilocation production and inventory problems consider a central depot or plant which supplies several locations experiencing random demands orders are placed or production is initiated periodically by the depot the order arrives after a fixed lead time and is then allocated among the several locations the depot itself does not hold inventory the allocations are finally received at the demand points after another lag unfilled demand at each location is backordered linear costs are incurred at each location for holding inventory and for backorders also costs are assessed for orders placed by the depot the object is to minimize the expected total cost of the system over a finite number of time periods this system gives rise to a dynamic program with a state space of very large dimension we show that this model can be systematically approximated by a single location inventory problem all the qualitative and quantitative results for such problems can then be applied

option exercise games an application to the equilibrium investment strategies of firms under the standard real options approach to investment under uncertainty agents formulate optimal exercise strategies in isolation and ignore competitive interactions however in many real world asset markets exercise strategies cannot be determined separately but must be formed as part of a strategic equilibrium this article provides a tractable approach for deriving equilibrium investment strategies in a continuous time cournot nash framework the impact of competition on exercise strategies is dramatic for example while standard real options models emphasize that a valuable option to wait leads firms to invest only at large positive net present values the impact of competition drastically erodes the value of the option to wait and leads to investment at very near the zero net present value threshold copyright 2002 oxford university press

the strategic perils of delayed differentiation the value of delayed differentiation also known as postponement for a monopolist has been extensively studied in the operations literature we analyze the case of imperfectly competitive markets with demand uncertainty wherein the choice of supply chain configuration i e early or delayed differentiation is endogenous to the competing firms we characterize firms choices in equilibrium and analyze the effects of these choices on quantities sold profits consumer surplus and welfare we demonstrate that purely strategic considerations not previously identified in the literature play a pivotal role in determining the value of delayed differentiation in the face of either entry threats or competition these strategic effects can significantly diminish the value of delayed differentiation in fact under plausible conditions these effects dominate the traditional risk pooling benefits associated with delayed differentiation in which case early differentiation is the dominant strategy for firms even under cost parity with delayed differentiation we extend the main model to study the effects of alternate market structures asymmetric markets and inventory holdback our results in particular that for a broad range of parameter values early differentiation is a dominant strategy even under cost parity with delayed differentiation are robust to these relaxations

demand uncertainty and price maintenance markdowns as destructive competition this paper offers a new theory of destructive competition the authors compare minimum resale price maintenance to retail market clearing in a model with a monopolistic manufacturer selling to competitive retailers in both the resale price maintenance and flexible price games retailers must order inventories before the realization of demand uncertainty the authors find that manufacturer profits and equilibrium inventories are higher under resale price maintenance than under market clearing surprisingly consumer surplus can also be higher in which case unfettered retail competition can legitimately be called destructive copyright 1997 by american economic association

competition and investment in flexible technologies this paper examines the implications of market structure on investment in flexible manufacturing systems fms we analyze a two stage game in which firms choose between a flexible and a less flexible technology in the first stage then choose production quantities in the second stage in equilibrium a large proportion of fms firms is associated with more concentrated markets our model predicts that a larger market and or a more differentiated product results in a higher proportion of fms firms being sustained these predictions are empirically supported using cross section industry level data from both the us and japan

strategic technology choice and capacity investment under demand uncertainty this paper studies the impact of competition on a firm s choice of technology product flexible or product dedicated and capacity investment decisions specifically we model two firms competing with each other in two markets characterized by price dependent and uncertain demand the firms make three decisions in the following sequence choice of technology technology game capacity investment capacity game and production quantities production game the technology and capacity games occur while the demand curve is still uncertain and the production game is postponed until after the demand curve is revealed we develop best response functions for each firm in the technology game and compare how a monopolist and a duopolist respond to a given flexibility premium we show that the firms may respond to competition by adopting a technology which is the same as or different from what the competitor adopts we conclude that contrary to popular belief flexibility is not always the best response to competition flexible and dedicated technologies may coexist in equilibrium we demonstrate that as the difference between the two market sizes increases a duopolist is willing to pay less for flexible technology whereas the decision of a monopolist is not affected further we find that a firm that invests in flexibility benefits from a low correlation between demands for two products but the extent of this benefit differs depending on the competitor s technology choice our results indicate that higher demand substitution may or may not promote the adoption of flexibility under competition whereas it always facilitates the adoption of flexibility without competition finally we show that contrary to intuition as the competitor s cost of capacity increases the premium a flexible firm is willing to pay for flexibility decreases

equilibria of the sealed bid mechanism for bargaining with incomplete information we study the nash equilibria of the sealed bid bargaining mechanism with incomplete information a nonzero sum game for the case of uniform priors we describe two uncountably numerous families of equilibria the first has differentiable strategies in the second the strategies are step functions the efficiencies of these equilibria range from second best to zero for independent nonuniform priors we show that a similar situation obtains these results seem discouraging with regard to using the sealed bid mechanism in practice the mechanism might be salvaged however if bargainers turn out to confine themselves to linear strategy equilibria

regret aversion and opportunity dependence this paper provides an axiomatic model of decision making under uncertainty in which the decision maker is driven by anticipated ex post regrets our model allows both regret aversion and likelihood judgement over states to coexist also we characterize two special cases minimax regret with multiple priors that generalizes savage s minimax regret and a smooth model of regret aversion

global facility network design in the presence of competition abstract we study the facility network design problem for a global firm that is a monopolist seller in its domestic market but faces local competition in its foreign market the global firm produces in the face of demand and exchange rate uncertainty but can postpone localization and distribution of the output until after uncertainties are resolved the competitor in the foreign market however enjoys the flexibility of postponing all production activities until after uncertainties are resolved the two firms engage in an ex post cournot competition in the foreign market we consider three potential network configurations for the global firm under a linear demand function we provide the necessary and sufficient condition that one of the three networks is the global firm s optimal choice and explore how the presence of foreign competition affects the sensitivity of the global firm s design to various cost parameters and market uncertainties

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

the value of flexibility in make to order systems the effect of demand correlation we consider a manufacturer of mass customized modular products who orders components under demand uncertainty and sets prices produces to order and trades excess components in a secondary market after this uncertainty is resolved the sequence of events reflects in a parsimonious fashion the considerable reduction in demand uncertainty between the procurement stage and the selling season typical of industries with long supply lead times and short product life cycles we prove that in contrast to conventional wisdom the value of production flexibility and expected profit increase with demand correlation if and only if commonality between the corresponding products does not exceed a threshold we also prove that the value of flexibility and expected profit may each increase or decrease with demand variability depending on demand correlations and component commonalities across the entire product line finally we prove that when demand shocks are independent the optimal product prices are positively correlated if and only if the degree of commonality between the corresponding products exceeds a threshold

bilateral trade with the sealed bid k double auction existence and efficiency for k in the unit interval the k double auction determines the terms of trade when a buyer and a seller negotiate transfer of an item the buyer submits a bid b and the seller submits an offer s trade occurs if b exceeds s at price kb 1 k s we model trade as a bayesian game in which each trader privately knows his reservation value but only has beliefs about the other trader s value existence of a multiplicity of equilibria is proven for a class of trader s beliefs for generic beliefs however these equilibria are shown to be ex ante inefficient

capacity optimization under uncertainty the impact of operational time lags time lags in switching operational modes are typical in the manufacturing and power sectors but are not treated in most real options models in this paper we consider a firm that has the opportunity to suspend and to resume production infinitely many times subject to a time lag after each startup decision we contribute to the literature by allowing the firm to determine its level of installed capacity in conjunction with its optimal investment timing we find that an increase in the length of the time lag results in an increase in the optimal capacity level capacity optimization also interacts with the length of the time lag to affect investment timing and the triggers to suspend and resume production thereby weakening the result about hysteresis from a standard real options model under the assumption of a fixed level of capacity a longer lag speeds up the decision to resume operations due to a positive upside to the revenue but delays the suspension of operations by contrast with capacity optimization a longer time lag results in a larger capacity choice which can indirectly delay the investment decision and the timing to resume operations this indirect effect dominates when the level of market uncertainty is low and the time lag is initially small

endogenous leadership in a new market in this article i analyze strategic investment under uncertainty in a new market where firms face a tradeoff between commitment and flexibility the model predicts asymmetric equilibria under fairly general conditions even though firms are ex ante identical and have symmetric opportunities to enter the market in equilibrium one firm commits to early investment and the other firm follows a wait and see strategy in the ex post outcome firms end up with asymmetric sizes if the market profitability turns out close to or lower than expected firms end up in symmetric position if the market turns out highly profitable if uncertainty is small the model yields approximately stackelberg outcomes