auctions of heterogeneous objects abstract simultaneous sealed bid auctions of heterogeneous objects are analyzed each bidder s reservation value for an object depends upon the other objects he obtains bidders reservation values are common knowledge in simultaneous first price auctions the set of walrasian equilibrium allocations contains the set of pure strategy nash equilibrium allocations which in turn contains the set of strict walrasian equilibrium allocations hence pure strategy nash equilibria when they exist are efficient mixed strategy nash equilibria may be inefficient in simultaneous second price auctions any efficient allocation can be implemented as a pure strategy nash equilibrium outcome if a walrasian equilibrium exists journal of economic literature classification numbers d44 d51

substitute goods auctions and equilibrium this paper identifies two notions of substitutes for auction and equilibrium analysis weak substitutes the usual price theory notion guarantees monotonicity of t tonnement processes and convergence of clock auctions to a pseudo equilibrium but only strong substitutes which treats each unit traded as a distinct good with its own price guarantees that every pseudo equilibrium is a walrasian equilibrium that the vickrey outcome is in the core and that the law of aggregate demand is satisfied when goods are divisible weak substitutes along with concavity guarantees all of the above properties except for the law of aggregate demand

walrasian equilibrium with gross substitutes in this paper we study the problem of efficient production and allocation of indivisible objects among a set of consumers we assume that the agents preferences depend on the bundle of objects and the quantity of money they consume furthermore we assume that preferences are quasilinear in money and that agents have a large endowment of money with indivisibilities it is well known that many familiar properties of the utility functions fail to ensure existence in their striking analysis of the matching problem kelso and crawford 5 introduce the gross substitutes gs condition which ensures the non emptiness of the core we propose two new conditions and show that with quasilinearity they are equivalent article id jeth 1999 2531 available online at http www idealibrary com on

informational limitations of ascending combinatorial auctions abstract we study the inherent limitations of natural widely used classes of ascending combinatorial auctions specifically we show that ascending combinatorial auctions that do not use both non linear prices and personalized prices cannot achieve social efficiency with general bidder valuations we also show that the loss of efficiency can be severe and that only a diminishing fraction of the social welfare may be captured this justifies the added complexity in the auctions suggested by e g parkes and ungar 2000 29 and ausubel and milgrom 2002 2

job matching under constraints studying job matching in a kelso crawford framework we consider arbitrary constraints imposed on sets of doctors that a hospital can hire we characterize all constraints that preserve the substitutes condition for all revenue functions that satisfy the substitutes condition a critical condition on hospitals revenue functions for well behaved competitive equilibria a constraint preserves the substitutes condition if and only if it is a generalized interval constraint which specifies the minimum and maximum numbers of hired doctors forces some hires and forbids others additionally generalized polyhedral constraints are precisely those that preserve the substitutes condition for all group separable revenue functions

a life cycle consumption model with liquidity constraints theory and empirical results a structural consumption model incorporating endogenous liquidity constraints is fit to a cross section of 798 u s families liquidity constrained families are estimated to constitute 19 4 percent of the population sampled a group that accounts for 16 7 percent of consumption in the population sampled in sample simulations of the model suggest that a temporary tax has three to four times more impact on aggregate consumption than it would if liquidity constraints were not in effect copyright 1987 by the econometric society

stability and auctions in labor markets with job security fu et al 2016 introduced a stability concept for labor markets with job security we show that their proposed outcomes form nash equilibria of an auction where firms compete for workers this parallels literature on stable outcomes and similar auctions and yields new price of anarchy bounds

multi item vickrey dutch auctions descending price auctions are adopted for goods that must be sold quickly and in private values environments for instance in flower fish and tobacco auctions in this paper we introduce ex post efficient descending auctions for two environments multiple non identical items and buyers with unit demand valuations and multiple identical items and buyers with non increasing marginal values our auctions are designed using the notion of universal competitive equilibrium uce prices and they terminate with uce prices from which the vickrey payments can be determined for the unit demand setting our auction maintains linear and anonymous prices for the homogeneous items setting our auction maintains a single price and adopts ausubel s notion of clinching to compute the final payments dynamically the auctions support truthful bidding in an ex post nash equilibrium and terminate with an ex post efficient allocation in simulation we illustrate the speed and elicitation advantages of these auctions over their ascending price counterparts

capital ideas from the past to the future modern finance theory modern portfolio theory neoclassical economics the ideas bestowed on us in 1952 1973 by the giants in our field are alive and well challenges to the efficient market theory the capital asset pricing model and mean variance efficiency have been raised but while recognizing that the assumptions of the theories do not hold up empirically we still lean on the ideas and develop them in new directions to say that this body of work is obsolete is to say that aristotle and euclid are obsolete

bundling equilibrium in combinatorial auctions this paper analyzes ex post equilibria in the vcg combinatorial auctions if is a family of bundles of goods the organizer may restrict the bundles on which the participants submit bids and the bundles allocated to them to be in t he vcg combinatorial auctions obtained in this way are known to be truth telling mechanisms in contrast this paper deals with non restricted vcg auctions in which the buyers choose strategies that involve bidding only on bundles in and these strategies form an equilibrium we fully characterize those that induce an equilibrium in every vcg auction and we refer to the associated equilibrium as a bundling equilibrium the main motivation for studying all these equilibria and not just the domination equilibrium is that they afford a reduction of the communication complexity we analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium

simultaneous auctions without complements are almost efficient abstract a simultaneous item auction is a simple procedure for allocating multiple indivisible goods to a set of bidders in a simultaneous auction every bidder submits bids on all items simultaneously the allocation and prices are then resolved for each item separately based solely on the bids submitted on that item such procedures are similar to auctions used in practice e g ebay but are not incentive compatible we study the efficiency of bayesian nash equilibrium bne outcomes of simultaneous first and second price auctions when bidders have complement free a k a subadditive valuations we show that the expected social welfare of any bne is at least 1 2 of the optimal social welfare in the case of first price auctions and at least 1 4 in the case of second price auctions

substitutes and stability for matching with contracts we consider the matching problem with contracts of hatfield and milgrom 2005 and we introduce new concepts of bilateral and unilateral substitutes we show that bilateral substitutes is a sucient condition for the existence of a stable allocation in this framework however the set of stable allocations does not form a lattice under this condition and there does not necessarily exist a doctor optimal stable allocation under a slightly stronger condition unilateral substitutes the set of stable allocations still does not necessarily form a lattice with respect to doctors preferences but there does exist a doctor optimal stable allocation and other key results such as incentive compatibility and the rural hospitals theorem are recovered

competitive equilibrium with indivisibilities abstract this paper studies an exchange economy with a finite number of agents in which each agents is initially endowed with a finite number of personalized indivisible commodities we observe that the equivalence theorem of the core and the competitive equilibrium may not hold for this economy when the coalitional form game is generated in the standard manner we provide an alternative definition of the coalitional form game to resolve this problem so that the balancedness of the new defined game provides a useful necessary and sufficient condition for the existence of competitive equilibrium for the original economy journal of economic literature classification numbers c71 d41 d51

stability in large matching markets with complementarities labor markets can often be viewed as many to one matching markets it is well known that if complementarities are present in such markets a stable matching may not exist we study large random matching markets with couples we introduce a new matching algorithm and show that if the number of couples grows slower than the size of the market a stable matching will be found with high probability if however the number of couples grows at a linear rate with constant probability not depending on the market size no stable matching exists our results explain data from the market for psychology interns

a competitive market model for indivisible commodities abstract a general competitive market model for trading indivisible goods is introduced there are a group of traders and several indivisible goods each trader is initially endowed with several units of each indivisible good and some amount of money traders have preferences over the bundle of indivisible goods and the quantity of money they consume it is shown that the market has a walrasian equilibrium if and only if an associated linear program problem has an optimal solution with its value equal to the potential market value and that the equilibrium prices of the goods and the profits of the traders are the optimal solutions of the linear program problem

elicitation of honest preferences for the assignment of individuals to positions the problem of eliciting honest preferences from individuals who must be assigned to a set of positions is considered individuals know that they will be charged for the positions to which they are assigned a set of prices that provide no incentive for the individual to misrepresent his preferences is suggested it is shown that these prices constitute an element of the optimal solution to the dual of a linear programming assignment problem both the optimal allocation and the prices to be charged can be derived by solving two linear programming problems once preferences have been elicited the procedure can usefully be viewed as a simulation of a competitive market under conditions where such a market cannot be expected to function well it results in an efficient allocation where all resources are valued at their opportunity costs and consumer surplus is maximized its outcome thus has the desirable properties of competitive market equilibria

the average shadow price for milps with integral resource availability and its relationship to the marginal unit shadow price abstract the economic significance of the average shadow price for integer and mixed integer linear programming milp problems has been established by researchers kim and cho eur j operat res 37 1988 328 crema eur j operat res 85 1995 625 in this paper we introduce a valid shadow price aspira for integer programs where the right hand side resource availability can only be varied in discrete steps we also introduce the concept of marginal unit shadow price musp we show that for integer programs a sufficient condition for the marginal unit shadow price to equal the average shadow price is that the law of diminishing returns should hold the polyhedral structures that will guarantee this equivalence have been explored identification of the problem classes for which the equivalence holds complements the existing procedure for determining shadow price for such integer programs the concepts of aspira and musp introduced in this paper can play a vital role in resource acquisition plans and in defining efficient market clearing prices in the presence of indivisibilities

matching with couples stability and incentives in large markets accommodating couples has been a longstanding issue in the design of centralized labor market clearinghouses for doctors and psychologists because couples view pairs of jobs as complements a stable matching may not exist when couples are present this paper s main result is that a stable matching exists when there are relatively few couples and preference lists are suciently short relative to market size we also discuss incentives in markets with couples we relate these theoretical results to the job market for psychologists in which stable matchings exist for all years of the data despite the presence of couples

an efficient dynamic auction for heterogeneous commodities this paper proposes a new dynamic design for auctioning multiple heterogeneous commodities generalizing earlier work that treated identical objects an auctioneer wishes to allocate one or more units of each of k heterogeneous commodities to n bidders the auctioneer announces a vector of current prices bidders report back quantities demanded at these prices and the auctioneer adjusts the prices units are credited to bidders at the current prices as their opponents demands decline and the process continues until every commodity market clears bidders rather than being required to behave as price takers are permitted to strategically exercise their market power nevertheless with pure private values the proposed auction yields walrasian equilibrium prices an efficient outcome results as from a vickrey clarke groves mechanism but bidders are only required to evaluate their demands along a one dimensional path of prices rather than reporting their utilities over the entire k dimensional consumption set the auction is also more transparent and potentially simpler for bidders to understand and has the advantage of assuring the privacy of the upper portions of bidders demands theoretically the new auction provides a new foundation for convergence to walrasian equilibrium in an exchange economy practically it provides an efficient method for simultaneously auctioning two or more related types of securities for example three month and six month treasury bills it is also potentially useful for auctioning multiple types of communications spectrum for example licenses for paired and unpaired spectrum

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

matching with contracts comment the theory of two sided matching markets has interested researchers for its theoretical appeal and its relevance to the design of real world institutions the medical residency matching mecha nism in the united states the national resident matching program nrmp and student assign ment systems in new york city and boston are important mechanisms designed by economists using the theory 1 hatfield and paul r milgrom 2005 present a unified framework of matching with contracts which includes the two sided matching and package auction models as well as a simplified version of a labor market model of alexander kelso and vincent p crawford 1982 as special cases they introduce the substitutes condition of contracts which is an adaptation of the substitutability condition in the matching literature roth and marilda a oliveira sotomayor 1990 to matching with contracts they show that there exists a stable allocation if contracts are substitutes for hospitals and that a number of other results in matching generalize to problems with contracts they further claim that the substitutes condition on individual hospitals prefer ences is necessary to guarantee the existence of a stable allocation for all possible singleton preferences of others that is if contracts are not substitutes for a hospital then there exists a preference profile of other hospitals with single job openings and doctors such that there exists no stable allocation we show that this last claim of hatfield and milgrom 2005 does not hold in general the counterexample we present involves a hospital which has two different kinds of positions and the preferences of the hospital are a combination of preferences of these two positions while the substitutes condition does not hold for that hospital we adopt a technique developed by bettina klaus and flip klijn 2005 and show that there exists a stable allocation we then present the weak substitutes condition which we show is necessary to guarantee existence of stable allocations the modified result we present as well as the original contribu tion of hatfield and milgrom 2005 suggest a connection between the substitutes condition and stability 2

appropriation and efficiency a revision of the first theorem of welfare economics the first theorem of welfare economics rests on the assumption that individuals have neither price making nor market making capacities we offer a revision in which individuals have such capacities the revision emphasizes two keys for market efficiency i the need to align private rewards with social contributions called full appropriation and ii the need for an assumption to counter the possibility of coordination failures in the choice of produced commodities called noncomplementarity we also emphasize that information about prices of unmarketed commodities involves decentralized knowledge available only to product innovators and that pecuniary extemalities are important potential sources of market failure jel d51 d60 d62

joint bidding in the name your own price channel a strategic analysis in this paper we study the name your own price nyop channel we examine theoretically and empirically whether asking consumers to place a joint bid for multiple items rather than bid one item at a time as practiced today can increase nyop retailers profits relatedly we also examine whether allowing consumers to self select whether to place a joint bid or itemwise bids increases retailers profits and consumers surplus we construct a dynamic model that incorporates both demand uncertainty and supply uncertainty to address these issues our theoretical analysis identifies the conditions under which joint bidding can increase both nyop retailers profits and consumers surplus we find that some consumers might bid more for the very same items when they place joint bids the increase in bid amount is related to the fact that joint bidding reduces the chance of mismatch between nyop retailers costs and consumer bids we conducted a laboratory study to assess the descriptive validity of some of the

identifying combinatorial valuations from aggregate demand abstract we study identification of combinatorial valuations from aggregate demand each utility function takes as arguments subsets or alternatively quantities of the multiple goods we exploit mathematical insights from auction theory to generically identify the distribution of utility functions in our setting aggregate demand for each item is observable while demand for bundles is not nevertheless our identification result allows us to recover the latter

the effect of false name bids in combinatorial auctions new fraud in internet auctions we examine the effect of false name bids on combinatorial auction protocols false name bids are bids submitted by a single bidder using multiple identifiers such as multiple e mail addresses the obtained results are summarized as follows 1 the vickrey clarke groves vcg mechanism which is strategy proof and pareto efficient when there exists no false name bid is not falsename proof 2 there exists no false name proof combinatorial auction protocol that satisfies pareto efficiency 3 one sufficient condition where the vcg mechanism is false name proof is identified i e the concavity of a surplus function over bidders

explicit solution of a general consumption portfolio problem with subsistence consumption and bankruptcy this paper solves a general continuous time single agent consumption and portfolio decision problem with subsistence consumption in closed form the analysis allows for general continuously differentiable concave utility functions the model takes into consideration that consumption must be no smaller than a given subsistence rate and that bankruptcy can occur thus the paper generalizes the results of karatzas lehoczky sethi and shreve 1986

saving and liquidity constraints this paper is concerned with the theory of saving when consumers are not permitted to borrow and with the ability of such a theory to account for some of the stylized facts of saving behavior the models presented in the paper seem to account for important aspects of reality that are not explained by traditional life cycle models copyright 1991 by the econometric society

stability and competitive equilibrium in trading networks we introduce a model in which agents in a network can trade via bilateral contracts we find that when continuous transfers are allowed and utilities are quasi linear the full substitutability of preferences is sufficient to guarantee the existence of stable outcomes for any underlying network structure furthermore the set of stable outcomes is essentially equivalent to the set of competitive equilibria and all stable outcomes are in the core and are efficient by contrast for any domain of preferences strictly larger than that of full substitutability the existence of stable outcomes and competitive equilibria cannot be guaranteed

the package assignment model we study assignment problems where individuals trade packages consisting of several rather than single objects although buyers reservations values are non additive efficient assignments can be formulated as a linear programming problem in which the pricing functions expressing duality may be non linear in the objects constituting the packages the interconnections among the linear programming formulation walrasian equilibrium and the core are established in the single seller auction version a necessary and sufficient condition is given for the vickrey payoff point to be implementable by a pricing equilibrium journal of economic literature classification numbers c62 d44 d51

contracts versus salaries in matching a general result abstract it is shown that a matching market with contracts can be embedded into a matching market with salaries under weaker conditions than substitutability of contracts in particular the result applies to the recently studied problem of cadet to branch matching as an application of the embedding result a new class of mechanisms for matching markets with contracts is defined that generalize the firm proposing deferred acceptance algorithm to the case where contracts are unilateral substitutes for firms

on ascending vickrey auctions for heterogeneous objects abstract we construct an ascending auction for heterogeneous objects by applying a primal dual algorithm to a linear program that represents the efficient allocation problem for this setting the auction assigns personalized prices to bundles and asks bidders to report their preferred bundles in each round a bidder s prices are increased when he belongs to a minimally undersupplied set of bidders this concept generalizes the notion of overdemanded sets of objects introduced by demange gale and sotomayor for the one to one assignment problem under a submodularity condition the auction implements the vickrey clarke groves outcome we show that this type of condition is somewhat necessary to do so when classifying the ascending auction literature in terms of their underlying algorithms our auction fills a gap in that literature we relate our results to various ascending auctions in the literature

equilibria existence and characterization in auctions achievements and open questions establishing existence and characterizing equilibria is a fundamental step in the study of auctions theoretical characterizations and empirical predictions are well accepted only to the extent that they are based on equilibria however despite the fact that auctions have been extensively studied there are still many problems regarding equilibrium existence and characterization waiting for resolution in this survey we review the landmark results and highlight open questions in addition we review the standard assumptions underlying these results and discuss the suitability of the nash equilibrium solution concept we focus our review on single object auctions but also review results in multi unit divisible combinatorial and double auctions

auction protocols for decentralized scheduling decentralized scheduling is the problem of allocating resources to alternative possible uses over time where competing uses are represented by autonomous agents market mechanisms use prices derived through distributing bidding protocols to determine schedules we investigate the existence of equilibrium prices for some general classes of scheduling problems the quality of equilibrium solutions and the behavior of an ascending auction mechanism and bidding protocol to remedy the potential nonexistence of price equilibria due to complementarities in preference we introduce additional markets in combinations of basic goods finally we consider direct revelation mechanisms and compare to the market based approach journal of economic literature classification numbers c62 c70 d44

ascending price vickrey auctions for general valuations ascending price auctions typically involve a single price path with buyers paying their final bid price using this traditional definition no ascending price auction can achieve the vickrey clarke groves vcg outcome for general private valuations in the combinatorial auction setting we relax this definition by allowing discounts to buyers from the final price of the auction or alternatively calculating the discounts dynamically during the auction while still maintaining a single price path using a notion called universal competitive equilibrium prices shown to be necessary and sufficient to achieve the vcg outcome using ascending price auctions we define a broad class of ascending price combinatorial auctions in which truthful bidding by buyers is an ex post nash equilibrium any auction in this class achieves the vcg outcome and ex post efficiency for general valuations we define two specific auctions in this class by generalizing two known auctions in the literature 11 24

an economic perspective on auctions the recent spectrum auctions in europe have shown that serious problems can wise in auctions where multiple complementary objects are being sold such as blocks of radio spectrum that will subsequently be used by the wining bidders to compete against each other in downstream markets other important instances of such situations include take off and landing slots at airports and rights for electricity and gas transmission t i first review some of the theory describing multi object auctions i i next outline the importance of strategic effects arising in auctions that are followed by competition between the bidders and the tension arising between various goals such as efficiency and revenue maximization although more flexible auction formats can have virtues particularly in taking into account complementarities they can also be manipulated by bidders to build market power to the detriment of consumers we next apply these insights to the recent european umts licence auctions finally we draw the main conclusions and policy implications

an efficient ascending bid auction for multiple objects when bidders exhibit multi unit demands standard auction methods generally yield inefficient outcomes this article proposes a new ascending bid auction for homogeneous goods such as treasury bills or telecommunications spectrum the auctioneer announces a price and bidders respond with quantities items are awarded at the current price whenever they are clinched and the price is incremented until the market clears with private values this dynamic auction yields the same outcome as the sealed bid vickrey auction but has advantages of simplicity and privacy preservation with interdependent values this auction may retain efficiency whereas the vickrey auction suffers from a generalized winner s curse

why we need a pension revolution a broad consensus exists that workplace pension arrangements around the world are sick and in need of strong medicine rather than resurrect the traditional defined benefit db plan or broaden defined contribution dc plan coverage this article argues that we move from an either or to an and and mindset to improve global workplace pension coverage adequacy and certainty pension arrangements can combine the best of db and dc plans and minimize the impact of their less attractive features however we must also redesign the institutions through which workplace pensions are delivered the ideal pension delivery institution is expert has scale and acts solely in the best interests of plan participants

beyond portfolio theory the next frontier logically investment theory s next frontier is to put into practice the rich set of tools that academia has bestowed on the investment community starting with harry markowitz s seminal article on portfolio selection in 1952 or is it in fact the next frontier lies beyond simply engineering the implementation of new investment decision tools the time has come to integrate the powerful insights offered by information theory and principal agent theory into a holistic comprehensive theory of investing only such an expanded theory offers any material hope of improving the economic prospects of the millions of clients beneficiaries of today s mutual funds pension funds endowments and foundations

thoughts on the future theory and practice in investment management existing finance theory can be put into practice in ways that will greatly benefit clients from individuals to pension funds to endowments

the english auction with differentiated commodities abstract we study economies with indivisibilities that satisfy the gross substitutes gs condition we define an excess demand set with the property that increasing the prices of all goods in excess demand eventually leads to the smallest walrasian prices this procedure is a generalization of the auction studied by g demange d gale and m j sotomayor polit econ 94 1986 863 872 in our auction truthful revelation of demand is a perfect bayesian equilibrium if the smallest walrasian prices correspond to the vickrey clarke groves payments however no dynamic auction can reveal sufficient information to implement the vickrey mechanism if all gs preferences are allowed journal of economic literature classification numbers d4 d44 d5 d51

optimal mean variance portfolio selection using cauchy schwarz maximization fund managers highly prioritize selecting portfolios with a high sharpe ratio traditionally this task can be achieved by revising the objective function of the markowitz mean variance portfolio model and then resolving quadratic programming problems to obtain the maximum sharpe ratio portfolio this study presents a closed form solution for the optimal sharpe ratio portfolio by applying cauchy schwarz maximization and the concept of kuhn tucker conditions an empirical example is used to demonstrate the efficiency and effectiveness of the proposed algorithms moreover the proposed algorithms can also be used to obtain the optimal portfolio containing large numbers of securities which is not possible or at least is complicated via traditional quadratic programming approaches

bayesian incentive compatibility via matchings abstract optimally allocating cellphone spectrum advertisements on the internet and landing slots at airports is computationally intractable when the participants may strategize not only must the optimizer deal with complex feasibility constraints but also with complex incentive constraints we give a very simple method for constructing a bayesian incentive compatible mechanism from any potentially non optimal algorithm that maps agents reports to an allocation the expected welfare of the mechanism is approximately at least that of the algorithm on the agents true preferences the construction is based on a maximum weight matching in the type space of each agent that be calculated quickly when the type spaces are reasonably sized furthermore the computation can be performed independently for each agent and therefore scales well with the number of agents a similar construction was previously given by hartline and lucier 2010 for agents with single dimensional types ours allows multi dimensional types

contracts versus salaries in matching workers and firms may bargain over general multidimensional contracts they may negotiate over health benefits housing retirement plans etc substitutes on the other hand is the assumption commonly placed on firms preferences to guarantee the existence of stable matchings of workers and firms in this paper i show that when firms regard contracts as substitutes bargaining over contracts can be embedded into a model of bargaining over wages the economics of the embedding is straightforward except for a small twist when a firm and a worker negotiate over a contract they may bargain over many dimensions however the pareto frontier of contracts is in a sense one dimensional what is better for the worker is worse for the firm so pareto optimal contracts may be viewed as salaries with the better contracts for the firm meaning lower salaries and the better contracts for the worker meaning higher salaries the twist is that a firm s ranking over contracts might be affected by the firm s other hires for example health plan a may be better than b for a firm if it has many employees but b beats a if it has few when contracts are substitutes it turns out that the ranking is not affected in this way hatfield and milgrom 2005 present a model of two sided worker firm matching with contracts a firm will hire a collection of workers and will negotiate a contract with each one of them the model is a generalization of kelso and crawford 1982 where each firm and each worker negotiate a wage 1 kelso and crawford show that when firms demands satisfy gross substitutes the core of the matching market is nonempty hatfield and milgrom show that when the firms preferences over contracts satisfy their notion of substitutes the core of the market is nonempty i show that hatfield and milgrom s model can be embedded into the model of kelso and crawford hatfield and milgrom s assumption of substitutability enables an embedding where firms demands for workers satisfy kelso and crawford s notion of gross substitutes as a result the nonemptiness of the core follows from the argument in kelso and crawford and their salary adjustment algorithm finds a stable matching of workers to firms and a vector of supporting salaries hatfield and milgrom s paper is an elegant analysis of two sided matching it simplifies matching models and makes their relationship to auction models more transpar ent their paper contributes much more than showing the nonemptiness of the core when firms and workers can sign general contracts and my result does not diminish

competitive equilibria in two sided matching markets with general utility functions we present an exact characterization of utilities in competitive equilibria of two sided matching markets in which the utility of each agent depends on the choice of partner and the terms of the partnership potentially including monetary transfer examples of such markets include sellers and buyers or jobs and workers demange and gale showed that the set of competitive equilibria in this type of market forms a complete lattice with each extreme point of the lattice representing an equilibrium with the highest utilities for the agents on one side and the lowest utilities for the agents on the opposite side our characterization is based on establishing a connection between the competitive equilibria of a market and the competitive equilibria of certain strict subsets of that market each obtained by removing exactly one agent this characterization captures the effect of competition when agents are added to the market or removed from the market it gives a precise procedure for constructing competitive eq

job matching and coalition formation with utility or disutility of co workers abstract this paper studies the job matching market in kelso and crawford 1982 econometrica50 1483 1504 with one exception that co workers may generate utility or disutility in the workplace we provide a simple idea to show how a great number of sufficient conditions for a nonempty core in the literature can be extended to this labor market a generalized competitive equilibrium with a tax subsidy system is also discussed journal of economic literature classification number d71

an equilibrium analysis of the simultaneous ascending auction we provide a bayes nash equilibrium analysis of the simultaneous ascending auction saa when local bidders interested in a single item compete against global bidders interested in aggregating many items we first assume that each local bidder values only a specific item e g the license for the region where it has monopoly power and that global bidders valuation functions are convex for this environment we show that a global bidder faces an exposure problem with adverse consequences for revenue and efficiency in the limit when the number of items grows large the saa is revenue and efficiency equivalent to the vickrey clarke groves vcg mechanism we extend our analysis to include the case where items are substitutes for local bidders so that price arbitrage will occur as observed in many spectrum auctions this environment which combines substitutes and complements results in an aggravated exposure problem consequently the saa is no longer efficient and may yield dramatically lower revenues than the vcg mechanism finally we relax the assumption that global bidders valuation functions are convex by considering an environment with medium sized global bidders who demand fewer than all items we show that global bidders divide the market at low prices when market sharing is feasible while they engage in mutually destructive bidding when there is a fitting problem in both cases the saa again underperforms relative to the vcg mechanism

existence and welfare properties of equilibrium in an exchange economy with multiple divisible indivisible commodities and linear production technologies abstract in this paper we consider a class of economies with a finite number of divisible commodities linear production technologies and indivisible goods and a finite number of agents this class contains several well known economies with indivisible goods and money as special cases it is shown that if the utility functions are continuous on the divisible commodities and are weakly monotonic both on one of the divisible commodities and on all the indivisible commodities if each agent initially owns a sufficient amount of one of the divisible commodities and if a no production without input like assumption on the production sector holds then there exists a competitive equilibrium for any economy in this class the usual convexity assumption is not needed here furthermore by imposing strong monotonicity on one of the divisible commodities we show that any competitive equilibrium is in the core of the economy and therefore the first theorem of welfare also holds we further obtain a second welfare theorem stating that under some conditions a pareto efficient allocation can be sustained by a competitive equilibrium allocation for some well chosen redistribution of the total initial endowments journal of economic literature classification numbers d4 d46 d5 d51 d6 d61

the communication requirements of social choice rules and supporting budget sets the paper examines the communication requirements of social choice rules when the sincere agents privately know their preferences it shows that for a large class of choice rules any minimally informative way to verify that a given alternative is in the choice rule is by verifying a budget equilibrium i e that the alternative is optimal to each agent within a budget set given to him therefore any communication mechanism realizing the choice rule must find a supporting budget equilibrium we characterize the class of choice rules that have this property furthermore for any rule from the class we characterize the minimally informative messages budget equilibria verifying it this characterization is used to identify the amount of communication needed to realize a choice rule measured with the number of transmitted bits or real variables applications include efficiency in convex economies exact or approximate surplus maximization in combinatorial auctions the core in indivisible good economies and stable many to one matchings

the existence and computation of competitive equilibria in markets with an indivisible commodity abstract this paper considers an exchange economy called a generalized assignment market in which sellers and buyers trade one indivisible commodity possibly with product differentiation for a perfectly divisible commodity the existence of a competitive equilibrium in this economy is proved using kakutani s fixed point theorem this existence theorem is applied to a production economy in which sellers are formulated as producers with convex cost functions two examples of housing markets are provided and their competitive equilibria are numerically calculated

the vulnerability of price stabilization schemes to speculative attack this paper examines the effects of government attempts to stabilize the prices of commodities by use of buffer stocks agricultural goods subject to supply uncertainty as well as depletable resources are considered in each case it is shown that the resulting rational expectations competitive equilibrium contains a speculative attack a situation where the entire government stock is suddenly purchased by previously inactive speculators the analysis is applied to the historical attempt to peg the gold price which caused the attack of 1968 the insights gained and the methodology developed also apply to the various international agreements to impose bans on commodity prices which have been proposed by the united nations conference on trade and development

matching with contracts we develop a model of matching with contracts which incorporates as special cases the college admissions problem the kelso crawford labor market matching model and ascending package auctions we introduce a new law of aggregate demand for the case of discrete heterogeneous workers and show that when workers are substitutes this law is satisfied by profit maximizing firms when workers are substitutes and the law is satisfied truthful reporting is a dominant strategy for workers in a worker offering auction matching algorithm we also parameterize a large class of preferences satisfying the two conditions

the pension problem on demographic time bombs and odious debt much has been written recently particularly after 2000 2002 left pensions in tatters about the challenge of meeting pension obligations the challenge discussed here is interesting and multifaceted embracing issues of demographics reasonable expectations business ethics stakeholder interests the social compact and intergenerational equity the first step is to acknowledge the reality that assuming investments will earn a risk premium without acknowledging the risk that they will not deliver a premium disguises the real size of pension liabilities

consumption and investment under constraints abstract we study the problem of an investor who is endowed with a deterministic level of initial capital and must use this endowment to consume and invest in a financial market the investor is constrained to consume at a minimum rate throughout the period and has to maintain his wealth over a lower bound at all times both these minimal requirements may be stochastic an example of such an investor would be an investment firm with cash flow commitments and subject to regulatory capital constraints in addition the investor s portfolio choices are limited to a convex constraint set this accounts for prohibitions on short selling and incompleteness of the market using the space of associated risk neutral measures we construct portfolio policies to support target consumption investment plans we also consider a utility maximization problem for the investor and provide a related dual minimization problem over the space of measures the solution of this dual problem provides a price system under which the investor can solve for his optimal consumption investment policy in general however we are not assured of existence due to the fact that the investor s minimal requirements may themselves be beyond the span of the constrained portfolios

competitive equilibrium in an exchange economy with indivisibilities abstract we analyze an exchange economy in which i all commodities except money are indivisible ii agents preferences can be described by a reservation value for each bundle of indivisible objects and iii all agents are price takers we obtain a necessary and sufficient condition under which market clearing prices exist implications for market mechanisms are discussed journal of economic literatureclassification numbers d51 c78

mechanisms for a spatially distributed market abstract we consider the problem of a spatially distributed market with strategic agents a single good is traded in a set of independent markets where shipment between markets is possible but costly the problem has previously been studied in the non strategic case in which it can be analyzed and solved as a min cost flow problem we consider the case where buyers and sellers are strategic our first result gives a double characterization of the vcg prices first as distances in a certain residue graph and second as the minimal for buyers and maximal for sellers equilibrium prices this provides a computationally efficient individually rational and incentive compatible welfare maximizing mechanism this mechanism is necessarily not budget balanced and we also provide a budget balanced mechanism which is also computationally efficient incentive compatible and individually rational that achieves high welfare finally we present results for some extensions of the model

understanding preferences demand types and the existence of equilibrium with indivisibilities we propose new techniques for understanding agents valuations our classification into demand types incorporates existing definitions substitutes complements strong substitutes etc and permits new ones our unimodularity theorem generalises previous results about when competitive equilibrium exists for any set of agents whose valuations are all of a demand type for indivisible goods contrary to popular belief equilibrium is guaranteed for more classes of purely complements than of purely substitutes preferences our intersection count theorem checks equilibrium existence for combinations of agents with specific valuations by counting the intersection points of geometric objects applications include matching and coalition formation and the product mix auction introduced by the bank of england in response to the financial crisis

iterative auction design for tree valuations we study a special class of multi item valuations tree valuations that exhibit both value complementarity and substitutability we provide a linear programming formulation of the efficient allocation problem that is of polynomial size in the number of agents and items this reveals a new class of valuations for which a walrasian equilibrium exists in the presence of value complementarities an iterative algorithm for this linear program in conjunction with an appropriate payment rule yields an iterative auction that implements the efficient outcome at an ex post perfect equilibrium this auction relies on a simple pricing rule compact demand reports and uses a novel interleaved price update structure to assign final payments to bidders that guarantee truthful bidding

consumption liquidity constraints and asset accumulation in the presence of random income fluctuations recent empirical research flavin 1981 hagashi 1982 has rejected the certainty equivalent formulation of permanent income hypothesis hall 1978 these findings are often attributed to households inability to borrow completely against expected future labor income this paper is a theoretical investigation of optimal consumption behavior under risk aversion random income fluctuations and borrowing restrictions our principle objective is to establish the existence and to investigate the properties of the stationary probability distribution which characterizes the asymptotic behavior of consumption under these conditions this abstract was borrowed from another version of this item

a new and improved design for multiobject iterative auctions in this paper we present a new improved design for multiobject auctions and report on the results of experimental tests of that design we merge the better features of two extant but very different auction processes the simultaneous multiple round smr design used by the fcc to auction the electromagnetic spectrum and the adaptive user selection mechanism ausm of banks et al 1989 allocating uncertain and unresponsive resources an experimental approach rand journal of economics vol 20 no 1 pp 1 25 then by adding one crucial new feature we are able to create a new design the resource allocation design rad auction process which performs better than both our experiments demonstrate that the rad auction achieves higher efficiencies lower bidder losses higher net revenues and faster times to completion without increasing the complexity of a bidder s problem

an alternative proof of an equilibrium existence theorem in exchange economies with indivisibilities abstract bikhchandani and mamer 1997 j econom theory 74 385 413 studied an exchange economy with multiple indivisible objects and established a necessary and sufficient condition for the existence of competitive equilibrium by a linear programming approach this paper provides an alternative proof of their theorem by the core of a coalitional form game journal of economic literature classification number c71

multi item auctions a collection of items is to be distributed among several bidders and each bidder is to receive at most one item assuming that the bidders place some monetary value on each of the items it has been shown that there is a unique vector of equilibrium prices that is optimal in a suitable sense for the bidders in this paper we describe two dynamic auction mechanisms one achieves this equilibrium and the other approximates it to any desired degree of accuracy

bundling decisions by a multiproduct monopolist with incomplete information this paper analyzes bundling decisions of a rnultiproduct monopolist facing uncertain demand the monopolist sells his products using an auction mechanism and the market is analyzed as a game with incomplete information in which the buyers as well as the seller are strategic agents with a small number of buyers a profit maximizing seller will bundle all his output this makes buyers uniformly worse off compared to the case where the same monopolist does not bundle in the sense that any buyer is worse off regardless of his demand for the monopolist s outputs with a larger number of buyers the seller will have a tendency to unbundle his output and high demand buyers are worse off than they would be if the monopolist bundled his output low demand buyers on the other hand are always better off when the monopolist unbundles his output regardless of the number of competing buyers despite the fact that high demand buyers are the typical purchasers of the monopolist s output the net effect of increasing the number of buyers is greater market efficiency since bundling creates market inefficiencies both ex post and ex ante

package auctions and exchanges we report recent advances concerning the package allocation problem in which traders seek to buy or sell combinations of goods the problems are most difficult when some goods are not substitutes in that case competitive equilibrium typically fail to exist but the core is non empty and comprises the competitive solutions also in that case the vickrey auction fails to select core allocations and yield revenues that are less than competitive the ausubel milgrom auction generally selects core allocations and when goods are substitutes prescribes the vickrey allocation we also evaluate the problems and promise of mechanisms for the package exchange problem

a double sided multiunit combinatorial auction for substitutes theory and algorithms combinatorial exchanges have existed for a long time in securities markets in these auctions buyers and sellers can place orders on combinations or bundles of different securities these orders are conjunctive they are matched only if the full bundle is available on business to business b2b exchanges buyers have the choice to receive the same product with different attributes for instance the same product can be produced by different sellers a buyer indicates his preference by submitting a disjunctive order where he specifies the quantity he wants of each particular good and what limit price he is willing to pay for each good thus providing a subjective valuation of each attribute only the goods with the best prices will be traded this article considers a doubled sided multiunit combinatorial auction for substitutes that is a uniform price auction where buyers and sellers place both types of orders conjunctive and orders and disjunctive xor orders we show that linear competitive prices exist we also propose an algorithm to clear the market which is particularly efficient when the number of traders is large and the goods are divisible

optimal investment with minimum performance constraints abstract we consider the portfolio problem of an investor whose wealth is constrained to be at least as large as that generated by investment in a stochastic benchmark portfolio using standard option pricing results the optimal portfolio policy of a hara utility investor is derived explicitly this policy is shown to be equivalent at any point in time to the investor s optimal unconstrained policy when he has contracted to paying out a proportion of the value of the benchmark portfolio at the terminal date this proportion which lies between zero and one is smaller the more likely it is that the investor will strictly outperform the benchmark over the investment horizon

combinatorial auction design combinatorial auctions have two features that greatly affect their design computational complexity of winner determination and opportunities for cooperation among competitors dealing with these forces trade offs between desirable auction properties such as allocative efficiency revenue maximization low transaction costs fairness failure freeness and scalability computational complexity can be dealt with algorithmically by relegating the computational burden to bidders by maintaining fairness in the face of computational limitations by limiting biddable combinations and by limiting the use of combinatorial bids combinatorial auction designs include single round first price sealed bidding vickrey clarke groves vcg mechanisms uniform and market clearing price auctions and iterative combinatorial auctions combinatorial auction designs must deal with exposure problems threshold problems ways to keep the bidding moving at a reasonable pace avoiding and resolving ties and controlling complexity

side communication yields efficiency of ascending auctions the two items case we analyze an ascending auction with anonymous item prices when there are two items that are substitutes this popular auction format entails increased opportunities for bidders to coordinate bids as the bidding process is longer and since bidders see the other bids and can respond to various signaling this has happened in many real auctions e g in the netherlands 3g telecom auction and in the fcc auctions in the us

consumption and portfolio policies with incomplete markets and short sale constraints the infinite dimensional case abstract we employ a martingale approach to study a dynamic consumption portfolio problem in continuous time with incomplete markets and short sale constraints we introduce a notion of minimax local martingale and transform the dynamic problem into a static problem of maximizing expected utility over the consumption bundles that satisfy a single budget constraint formed using that measure we establish the existence of and characterize the minimax local measure provide sufficient conditions for the dynamic consumption portfolio problem to have a solution and relate the optimal policies to the solution of quasi linear partial differential equation

equilibria and indivisibilities gross substitutes and complements this paper examines an exchange economy with heterogeneous indivisible objects that can be substitutable or complementary we show that a competitive equilibrium exists in such economies provided that all the objects can be partitioned into two groups and from the viewpoint of each agent objects in the same group are substitutes and objects across the two groups are complements this condition generalizes the well known kelso crawford gross substitutes condition and is called gross substitutes and complements we also provide practical and typical examples from which substitutes and complements are both jointly observed

price controls non price quality competition and the nonexistence of competitive equilibrium we investigate how price ceilings and floors affect outcomes in continuous time double auction markets with discrete goods and multiple qualities when price controls exist the existence of competitive equilibria is no longer guaranteed hence we investigate the nature of non price competition and how markets might evolve in its presence we develop a quality competition model based on matching theory equilibria of the quality competition model always exist in such price constrained markets moreover they naturally correspond to competitive equilibria when competitive equilibria exist additionally we characterize the set of equilibria of the quality competition model in the presence of price restrictions in a series of experiments we find that market outcomes closely conform to the predictions of the model in particular price controls induce non price competition between agents both in theory and in the experimental environment market behaviors result in allocations close to the predictions of the model

on auction protocols for decentralized scheduling abstract this note shows that for the combinatorial market goods defined by wellman et al 2001 there may not exist an optimal allocation that is in equilibrium moreover this result holds even if the value of each processed job is independent of its completion time the proposed algorithm for finding an equilibrium allocation using an assignment model fails due to complementarity even for instances that admit an optimal allocation which is in equilibrium

pricing and allocation for quality differentiated online services we explore the problem of pricing and allocation of unique one time digital products in the form of data streams we look at the short term problem where the firm has a capacitated shared resource and multiple products or service levels we formulate the allocatively efficient generalized vickrey auction gva for our setting and point out the computational challenges in determining the individual discriminatory transfer payments we propose an alternative uniform price computationally efficient revenue maximizing knapsack formulation called the multiple vickrey auction mva while not incentive compatible the mva mechanism achieves bounded posterior regret and can be solved in real time it has the added benefit of realizing imputed commodity prices for the various services a feature lacking in the discriminatory gva approach for service providers that are concerned about the incentive compatibility but want imputed service prices we suggest a maximal mva mmva uniform pricing scheme that trades off revenue maximization for allocative efficiency for sake of completeness we discuss the properties of a first price pay your bid scheme while np hard and not incentive compatible this formulation has the perceived benefit of cognitive simplicity on the parts of sellers and bidders

connecting the cooperative and competitive structures of the multiple partners assignment game multiple partners assignment game is the name used by sotomayor the multiple partners game in m majumdar ed equilibrium and dynamics essays in honor of david gale the macmillan press ltd new york 1992 the lattice structure of the set of stable outcomes of the multiple partners assignment game int j game theory 28 1999 567 583 to describe the cooperative structure of the many to many matching market with additively separable utilities stability concept is proved to be different from the core concept an economic structure is proposed where the concept of competitive equilibrium payoff is introduced in connection to the equilibrium concept from standard microeconomic theory the paper examines how this equilibrium concept compares with the cooperative equilibrium concept properties of interest to the cooperative and competitive markets are derived