efficient and durable decision rules with incomplete information we compare six concepts of efficiency for economies with incomplete information depending on the stage at which individuals welfare is evaluated and on whether incentive constraints are recognized an example is shown in which an incentive efficient decision rule may be unanimously rejected by the individuals in the economy we define durable decision rules which can resist such unanimous rejection and show that efficient durable decision rules exist

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 growing supply of physicians has the market become more competitive the stock of u s physicians at any point in time is modeled as a weighted average of the supply that a perfect cartel would produce and that would prevail under perfect competition estimation of a system of stock and income equations over the post world war ii period shows that after holding constant demand and marginal cost conditions and accounting for gradual adjustment to changes in equilibrium the weighting parameter has moved toward the competitive extreme since 1965 this rise in the degree of competition is estimated to have increased physician stock by 6 20 and concomitantly decreased medical incomes by 19 45

grain transport and rural credit in mozambique solving the space time problem this paper shows how credit market failures can lead to large welfare losses in grain markets by inducing increased transport for seasonal storage in locations with low credit costs the burden of these welfare losses falls primarily on rural households these conclusions are obtained from a spatial temporal model solved using a mixed complementarity formulation that easily handles interest rate differentials across space efforts to address credit market failures and to improve the efficiency of rural storage should be given priority as opposed to the creation of large formal sector grain collection centers

robust trading mechanisms we consider the problem of designing a trading institution for a single buyer and seller when their valuation of the good is private information it is shown that posted price mechanisms are essentially the only mechanisms such that each trader has a dominant strategy a posted price mechanism is one where a price is posted in advance and trade occurs if and only if all traders agree to trade

spatial price discrimination in agricultural product procurement markets a computational economics approach significant transport costs and spatially distributed supply and processing create oligopsony power in agricultural markets price discrimination expressed in the form of partial or complete absorption of freight charges by processors is often observed in these environments but we understand little about how these pricing decisions are made analytical approaches are often intractable as an alternative we propose a computational economics approach to analyze a general spatial competition model and study firms choices of spatial pricing policy instead of the commonly presumed free on board pricing we find that buyers choose price discrimination either through uniform delivered pricing or through partial freight absorption

optimality versus practicality in market design a comparison of two double auctions we consider a market for indivisible items with m buyers and m sellers traders privately know their values costs which are statistically dependent two mechanisms are considered the buyer s bid double auction collects bids and asks from traders and determines the allocation by selecting a market clearing price it fails to achieve all possible gains from trade because of strategic bidding the designed mechanism is a revelation mechanism in which honest reporting of values costs is incentive compatible and all gains from trade are achieved this optimality however comes at the expense of plausibility i the monetary transfers among the traders are defined in terms of the traders beliefs about each other s value cost ii a trader may suffer a loss ex post iii the mechanism may run a surplus deficit ex post we compare the virtues of the simple yet mildly inefficient buyer s bid double auction to the flawed yet perfectly efficient designed mechanism

the impact of transport and transaction cost reductions on food markets in developing countries evidence for tempered expectations for burkina faso reductions in transport and transaction costs are expected to have a major effect on the functioning of food markets in developing countries for burkina faso this is a relevant issue as it may have important consequences for the food markets in urban and rural deficit areas a partial equilibrium model is presented to analyze the short term effects of reduced costs on price formation inter regional cereal trade and farmers and traders storage strategies our results show that the high expectations with regard to the direct effects of cost reductions on food prices and food availability require some nuance the effects of a reduction of transport costs will be small moreover also the unintended negative consequences on the competitive position of farmers and traders in other regions that do not profit from road construction should be taken into account finally it is concluded that only if transport and transaction costs are reduced simultaneously will both the consumers and farmers benefit significantly c 2004 elsevier b v all rights reserved

on the possibility of informationally efficient markets this paper presents conditions for a resolution of the grossman stiglitz paradox of informationally efficient markets we display a market with asymmetric information where a privately revealing equilibrium obtains in a competitive framework and where incentives to acquire information are preserved as long as the correlation in traders valuations is not too large the equilibrium is efficient and the problems associated with fully revealing rational expectations equilibria are precluded without resorting necessarily to noise traders the robustness of the results to general information structures is established and the effect of market power is examined in a large market approximation to the competitive economy the model is applied to explain changes in bidding behavior in central bank liquidity auctions in the crisis period jel d82 d84 g14 e59

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

existence and convergence of equilibria in the buyer s bid double auction this paper concerns a bayesian game model of the buyer s bid double auction which is a procedure for organizing trade that selects a market clearing price from a list of offers bids strategic misrepresentation by traders may make the outcome of trade inefficient satterthwaite and williams 1989 showed that misrepresentation and inefficiency quickly converge to zero as the number of traders on each side of the market increases this is extended here to cases in which the number of buyers may differ from the number of sellers the existence of equilibria in a generic instance of the model is also proven this paper concerns a market in which each trader privately knows his own preferences such a trader may have an incentive to misrepresent his preferences in order to influence the market price in his favour a buyer for instance may bid less than his true evaluation of the good for sale in an attempt to drive the price down similarly a seller may ask for more than he is willing to accept with behaviour of this kind a seller s offer could exceed a buyer s bid even though a mutually profitable trade between them exists in the market as a whole a price may be determined at which all potential gains from trade are not achieved strategic misrepresentation may therefore cause inefficiency our confidence in markets rests upon the belief that this inefficiency is insignificant when there are a large number of small traders a small trader in a large market is unlikely to have much influence on the market price as a consequence he has little incentive to misrepresent and the market is therefore almost fully efficient this argument however is vague about a very important point when is a trader relatively small and how many traders constitute a large market the meaning of small and large in this context is critical to understanding when this intuitive argument applies this argument is investigated here by thoroughly analyzing a particular model of trade a market is considered in which money may be exchanged for indivisible units of a good for n m 1 there are n sellers each of whom has a unit to sell and m buyers each of whom wishes to buy a unit each trader is therefore small in that he trades at most one unit we shall consider arbitrary values of n and m however trade is organized with the following rules each seller submits an offer while each buyer submits a bid the n m offers bids are ordered in a list sl s2 sn m any

the rate of convergence to efficiency in the buyer s bid double auction as the market becomes large a trader who privately knows his preferences may misrepresent them in order to influence the market price this strategic behaviour may prevent realization of all gains from trade in this paper trade in a simple market with an explicit rule for price formation is modelled as a bayesian game we show that the difference between a trader s bid and his reservation value is maximally 0 1 m where m is the number of traders on each side of the market competitive pressure as m increases thus quickly overcomes the inefficiency private information causes and f ces the market towards an efficient allocation

existence of equilibrium in large double auctions abstract we show the existence of a pure strategy symmetric increasing equilibrium in double auction markets with correlated conditionally independent private values and many participants the equilibrium we find is arbitrarily close to fully revealing as the market size grows our results provide strategic foundations for price taking behavior in large markets

redistribution of social benefits from advances in extension and research in the tanzanian maize industry abstract this study determined consumer and producer welfare gains from advances in extension and research in the maize industry of tanzania to determine how a national taxing schedule should be determined it was found that for an off farm marketable surplus of 40 consumers and producers gain equally while for an off farm marketable surplus of 60 consumers realize 75 of the welfare benefits this suggests that consumers and producers should share equally in a revenue generating tax for funding maize research and extension programs however for large producers with a marketable surplus of 60 or more their tax should decrease proportionally to the amount sold alternatively if taxed equally large scale producers should receive some form of compensation through direct government payments

all stage strong correlated equilibrium abstract a strong correlated equilibrium is a strategy profile that is immune to joint deviations different notions of strong correlated equilibria were defined in the literature one major difference among those definitions is the stage in which coalitions can plan a joint deviation before ex ante or after ex post the deviating players receive their part of the correlated profile in this paper we show that an ex ante strong correlated equilibrium is immune to deviations at all stages thus the set of ex ante strong correlated equilibria of moreno wooders games econ behav 17 1996 80 113 is included in all other sets of strong correlated equilibria

the rate of convergence to perfect competition of matching and bargaining mechanisms abstract we study the steady state of a market with incoming cohorts of buyers and sellers who are matched pairwise and bargain under private information a friction parameter is the length of the time period until the next meeting we provide a necessary and sufficient condition for the convergence of mechanism outcomes to perfect competition at the linear rate in which is shown to be the fastest possible among all bargaining mechanisms the condition requires that buyers and sellers always retain some bargaining power the bargaining mechanisms that satisfy this condition are called nonvanishing bargaining power nbp mechanisms simple random proposer take it or leave it protocols are nbp while k double auctions k da are not we find that k das have equilibria that converge to perfect competition at a linear rate converge at a slower rate or even do not converge at all

dynamic matching two sided incomplete information and participation costs existence and convergence to perfect competition consider a decentralized dynamic market with an infinite horizon and participation costs in which both buyers and sellers have private information concerning their values for the indivisible traded good time is discrete each period has length and each unit of time continuums of new buyers and sellers consider entry traders whose expected utility is negative choose not to enter within a period each buyer is matched anonymously with a seller and each seller is matched with zero one or more buyers every seller runs a first price auction with a reservation price and if trade occurs both the seller and the winning buyer exit the market with their realized utility traders who fail to trade continue in the market to be rematched we characterize the steady state equilibria that are perfect bayesian we show that as converges to zero equilibrium prices at which trades occur converge to the walrasian price and the realized allocations converge to the competitive allocation we also show the existence of equilibria for sufficiently small provided the discount rate is small relative to the participation

monotonicity and rationalizability in a large first price auction this paper proves that the monotonicity of bidding strategies together with the rationality of bidders implies that the winning bid in a first price auction converges to the competitive equilibrium price as the number of bidders increases wilson 1977 instead of analysing the symmetric nash equilibrium we examine rationalizable strategies bernheim 1984 pearce 1984 among the set of monotonic bidding strategies to prove that any monotonic rationalizable bidding strategy must be within a small neighbourhood of the truthful valuation of the object conditioned on the signal received by the bidder we obtain an information aggregation result similar to that of wilson 1977 while dispensing with almost all symmetric assumptions and using a milder solution concept than the nash equilibrium in particular if every bidder is ex ante identical then any rationalizable bidding strategy must be within a small neighbourhood of the symmetric nash equilibrium in a symmetric first price auction the symmetry of outcomes is implied rather than assumed copyright 2005 wiley blackwell

bargaining with incomplete information an infinite horizon model with two sided uncertainty the resolution of any bargaining conflict depends crucially on the relative urgency of the agents to reach agreement and the information each agent has about the others preferences this paper explores within the context of an infinite horizon bargaining model with two sided uncertainty how timing and information affect the rational behaviour of agents when commitment is not possible since the bargainers are uncertain about whether trade is desirable they must communicate some of their private information before an agreement can be reached this need for learning due to incomplete information about preferences results in bargaining inefficiencies trade often occurs after costly delay thus the model provides an explanation for the inefficient bargaining behaviour that appears to occur often in practice

bargaining under incomplete information this paper presents and analyzes a bargaining model of bilateral monopoly under uncertainty under the bargaining rule proposed the buyer and the seller each submit sealed offers that determine whether the good in question is sold and the transfer price the nash equilibrium solution of this bargaining game implies an offer strategy of each party that is monotonic in its own reservation price and depends on its assessment of the opponent s reservation price issues of relative bargaining advantage and efficiency are examined for a number of special cases finally we discuss the appropriateness of the nash solution concept

toward a strategic foundation for rational expectations equilibrium a step toward a strategic foundation for rational expectations equilibrium is taken by considering a double auction with n buyers and m sellers with interdependent values and affiliated private information if there are sufficiently many buyers and sellers and their bids are restricted to a sufficiently fine discrete set of prices then generically there is an equilibrium in nondecreasing bidding functions that is arbitrarily close to the unique fully revealing rational expectations equilibrium of the limit market with unrestricted bids and a continuum of agents in particular the large double auction equilibrium is almost efficient and almost fully aggregates the agents information

price formation in single call markets this paper reports a laboratory experiment designed to examine the price formation process in a simple market institution the single call market the experiment features random values and costs each period so each period generates a new price formation observation other design features are intended to enhance the predictive power of the bayesian nash equilibrium bne theory developed recently for this trading institution we find that the data support several qualitative implications of the bne but that subjects bid and ask behavior is not as responsive to changes in the pricing rule as the bne predictions bids and asks tend to reveal more of the underlying values and costs than predicted particularly when subjects are experienced nevertheless observed trading efficiency falls below the bne prediction the results offer more support for the bne when subjects compete against nash robot opponents a simple learning model accounts for several of the deviations from bne

opening and closing the market evidence from the london stock exchange we investigate the performance of call markets at the open and close using a unique natural experiment provided by the london stock exchange where traders can choose between a call and an off exchange dealership system although the call market dominates dealers in terms of price discovery it suffers from a high failure rate to open and close trading especially when trading conditions are difficult the call s trading costs increase with asymmetric information slow trading order flow imbalances and uncertainty traders resort to use of call auctions is negatively correlated with firm size implying that the call may not be the optimal method for opening and closing trading of medium and small sized stocks

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

the 2007 nobel memorial prize in mechanism design theory this paper provides an overview of mechanism design theory and explains the roles played by leonid hurwicz eric maskin and roger myerson in the development of this field

internet auctions with many traders abstract we study a multi unit auction environment similar to ebay sellers each with a single unit of a homogeneous good set reserve prices at their own second price auctions each buyer has private value for the good and wishes to acquire a single unit buyers can bid as often as they like and move between auctions we characterize a perfect bayesian equilibrium for this decentralized dynamic mechanism in which conditional on reserve prices an efficient set of trades occurs at a uniform price in a large but finite market the sellers set reserve prices equal to their true costs under a very mild distributional assumption so ex post efficiency is achieved buyers strategies in this equilibrium are simple and do not depend on their beliefs about other buyers valuations or the number of buyers and sellers

a dominant strategy double auction a double auction mechanism that provides dominant strategies for both buyers and sellers is analyzed this mechanism satisfies the 1n convergence to efficiency of the buyer s bid double auction in addition the mechanism always produces full information first best prices the inefficiency arises because the least valuable profitable trade may be prohibited by the mechanism the mechanism has an oral implementation utilizing bid and asked prices

a spatial analysis of maize marketing policy reforms in zambia in this study we analyze recent and proposed maize marketing reforms in zambia to capture the effects of changing transport systems we use a continuous space model in place of the traditional point representation model of takayama and judge this method permits us to use prereform data on supply demand and transport costs to infer both intra and interregional effects of liberalization and shows that the welfare gains from liberalization are larger than commonly thought these results provide policy makers with estimates of the magnitude of change associated with alternative reform programs beyond what would be available from a conventional approach

general economic equilibrium as a unifying concept in energy economic modeling in the pristine model of general economic equilibrium producers and consumers are assumed to take prices for their inputs and outputs as given a market equilibrium solution is obtained when the prices of all products lead to equal amounts of supply and demand for each the mathematical properties of this model provide a rich and powerful unifying foundation for much of modern microeconomic theory however in many practical applications it is difficult or impossible to develop the data and formulate and solve the equations required to implement the model of general economic equilibrium in its most general form in practice generality of formulation is often sacrificed for ease of computation and interpretation these tradeoffs allow the latest breakthroughs in optimization algorithms and computer technology to be applied in the analysis of important societal problems a potential drawback associated with this otherwise desirable trend is that the analysis could become infatuated with the use of particular algorithms and lose sight of the restrictive simplifying assumptions they imply the present paper includes a comparison of the simplifying assumptions required in four of the most popular types of energy economic models with respect to the model of general economic equilibrium this comparison helps sharpen our appreciation for the tradeoffs between generalization of formulation and ease of computation and interpretation that are available the concept of general economic equilibrium is employed to provide a common framework for four ostensibly different approaches to large scale modeling 1 variable coefficient input output theory 2 process network methodology 3 linear programming and 4 general nonlinear optimization the similarities and the differences of the four approaches are isolated within this framework this comparison makes both the absolute and the relative strengths and weaknesses of the models more transparent

convergence to perfect competition of a dynamic matching and bargaining market with two sided incomplete information and exogenous exit rate abstract consider a decentralized dynamic market with an infinite horizon and incomplete information in which buyers and sellers values for the traded good are private and independently drawn time is discrete each period has length and each unit of time a large number of new buyers and sellers enter the market within a period each buyer is matched with a seller and each seller is matched with zero one or more buyers every seller runs a first price auction with a reservation price and if trade occurs the seller and winning buyer exit with their realized utility traders who fail to trade either continue in the market to be rematched or exit at an exogenous rate we show that in all steady state perfect bayesian equilibria as approaches zero equilibrium prices converge to the walrasian price and realized allocations converge to the competitive allocation

the effects of population aging on the physician services market a computable equilibrium analysis this paper formulates a computable equilibrium model cem of the market for physician services the simulation results based upon the cem are consistent with widely held beliefs about the effects of aging on the health care sector for example that aggregate expenditures will increase as the population ages in addition however the simulations suggest differential effects on prices and expenditures for various types of services and on expenditures by different types of consumers for example prices and aggregate expenditures for services typically used by the elderly are found to increase under older age distributions whereas prices and aggregate expenditures for other services are found to decrease elderly women are found to be unequivocally worse off under older as opposed to younger age structures they spend more yet consume fewer services

a simple analysis of the us emission permits auctions we examine a stylized version of epa auctions when agents know the list of values of sellers and buyers there are inefficient equilibria where no goods are traded and efficient equilibria where all exchange occurs at a uniform price we also provide examples under incomplete information when the uniform price equilibrium holds and when it does not hold c 1999 elsevier science s a all rights reserved jel classification d44 q29

modularity and greed in double auctions abstract designing double auctions is a complex problem especially when there are restrictions on the sets of buyers and sellers that may trade with one another the goal of this paper is to develop a modular approach to the design of double auctions by relating it to the exhaustively studied problem of designing one sided mechanisms with a single seller or alternatively a single buyer we consider several desirable properties of a double auction feasibility dominant strategy incentive compatibility the still stronger incentive constraints offered by a deferred acceptance implementation exact and approximate welfare maximization and budget balance for each of these properties we identify sufficient conditions on two one sided algorithms one for ranking the buyers one for ranking the sellers and on a method for their composition into trading pairs which guarantee the desired property of the double auction our framework also offers new insights into classic double auction designs such as the vcg and mcafee auctions with unit demand buyers and unit supply sellers

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

truthful double auction mechanisms following the multistage design approach we propose two asymptotically efficient truthful double auction mechanisms the bc lp mechanism and the mbc mechanism for an exchange market with many buyers and sellers in this market each buyer wants to procure a bundle of commodities and each seller supplies one unit of a commodity furthermore various transaction related costs will be incurred when a buyer trades with a seller we prove that under both mechanisms truthful bidding is a dominant strategy for all buyers and sellers when the buyers bundle information and the transaction cost information are common knowledge the bc lp mechanism can be implemented by just solving two linear programs whereas the mbc mechanism has a higher complexity the empirical study shows that the mbc mechanism achieves higher efficiency over the bc lp mechanism and that both outperform the ksm tr mechanism the only known truthful mechanism for a more restrictive exchange market

modeling spatial price transmission in the grain markets of ethiopia with an application of ardl approach to white teff following the agricultural market liberalization policy there is an emerging grain market structure in ethiopia in which the central wholesale market exhibits concentration of power and spatial integration with the local markets due to this it is hypothesized that the central wholesale market influences the long run price movements in the local markets the relationship can be modeled as spatial price equilibrium with the aim to guide subsequent policy decisions with regard to public intervention in the post liberalization period in this study we modeled the spatial equilibrium relationship between the producer and the wholesale prices of white teff a major staple in ethiopia using the autoregressive distributed lag modeling approach to cointegration analysis first the existence of a nonspurious long run relationship in levels between the producer prices in the local market and the wholesale prices in the central market is confirmed second the long run relationship and the error correction model for the producer price are estimated the results reveal that the wholesale price of white teff in the central consumer market is a major short and long run determinant of the producer price in the local supply markets therefore the institutional role of the government with the aim of improving producers marketing margin and the overall performance of the grain markets in the post liberalization period can be influenced through targeted interventions at the central wholesale market

bilateral matching and bargaining with private information we study equilibria of a dynamic matching and bargaining game dmbg with two sided private information bilateral bargaining the model is a private information replica of mortensen and wright 2002 there are two kinds of frictions time

using markets to allocate pollution permits and other scarce resource rights under limited information abstract we consider the design of government policy to ration such scarce resources as water or pollution permits in the presence of limited information when government policy is formulated some informed agents e g established public utilities know how highly they value the resource other uninformed agents e g potential independent power producers only learn their valuations at some later date the government allows uninformed agents to trade the resource rights they receive on a competitive market informed agents may or may not have the same privilege the optimal initial distribution of resource rights differs significantly according to whether informed agents can trade the rights they receive

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

the modified vickrey double auction abstract we modify w vickrey s 1961 j finance 16 8 37 mechanism for call markets by introducing the participation stage and study the efficiency properties of the modified mechanism we provide sufficient conditions under which the modified vickrey double auction achieves full efficiency in addition we prove that the modified vickrey double auction achieves asymptotic efficiency even when full efficiency cannot be achieved journal of economic literature classification numbers c72 d44 d82

three minimal market institutions with human and algorithmic agents theory and experimental evidence we define and examine the performance of three minimal strategic market games sell all buy sell and double auction in laboratory relative to the predictions of theory unlike open or partial equilibrium settings of most other experiments these closed exchange economies have limited amounts of cash to facilitate transactions and include feedback general equilibrium theory since it abstracts away from market mechanisms and has no role for money or credit makes no predictions about how the paths of convergence to the competitive equilibrium may differ across alternative mechanisms

a competitive distribution of auctions in this paper a competitive distribution of auctions is described for an economy consisting of an infinite number of buyers and sellers all of whom differ according to their valuation for the single indivisible object being traded a competitive distribution of auctions is such that no seller can improve his profits by deviating to any alternative direct mechanism it is shown that the competitive distribution of auctions will have the property that each buyer and seller s best reply is independent of his beliefs about the tastes of other buyers and sellers on the market the purpose of this paper is to provide an equilibrium for an economy in which sellers compete by offering different direct mechanisms to buyers no attempt is made to give a complete characterization of all possible equilibria rather we focus on one equilibrium in which the contracts that are offered by sellers in equilibrium and buyer s behaviour under these contracts are both independent of traders beliefs about one another the equilibrium illustrates one of the reasons why contracts that are employed in practice may not be as finely tuned to beliefs as the theory of mechanism design says that they should be the answer is simply that contracts are not offered in a vacuum sellers in the model studied in this paper need to compete with one another in order to attract buyers highly tuned mechanisms tend to extract buyer surplus in such an environment sellers are able to attract many buyers by offering to use cruder mechanisms that leave some surplus for buyers in this paper sellers are allowed to have different costs for the commodity that is being traded nonetheless the equilibrium for the limit economy in which there are infinitely many buyers and sellers is such that every seller offers a second price auction and publicizes a reserve price equal to his cost in a standard monopoly auction the optimal reserve price for the seller exceeds his cost by an amount that depends on his beliefs about buyers valuations myerson 1981 a seller who raises his reserve price has his profits affected in two distinct ways by raising his reserve price the seller makes it unprofitable for some buyer types to participate in his auction the seller therefore loses any surplus that he might have earned by trading with these buyers the buyers who still find it profitable to participate in the seller s auction will end up having to pay a higher price when they win because of this increase in the seller s reserve price this means that the seller will be able to extract a bit more surplus from buyers who continue to participate the seller raises the reserve price until the marginal cost associated with raising the reserve price is just equal to the marginal gain associated with the ability to extract more surplus from remaining buyers competition mitigates this argument since there is a limit to the amount of surplus that the seller can extract from remaining buyers before they decide that they should instead choose one of the alternative auctions that are being held on the market with

virtual utility and the core for games with incomplete information abstract the core is extended to games with incomplete information the feasible set is characterized by incentive compatible mechanisms blocking is organized at the interim stage by an incentive compatible mediation plan membership of the blocking coalition itself may be determined randomly by the blocking mediator nonemptiness of an interim fine core is proven for games with a balanced structure independent types and sidepayments an offer of severance payments may be needed to inhibit blocking core allocations are characterized in terms of virtual utility scales that generalize the weighted utility scales of the inner core mechanisms that achieve core allocations are coalitionally durable

the rate at which a simple market converges to efficiency as the number of traders increases an asymptotic result for optimal trading mechanisms private information in an independent private values market provides incentives to traders to manipulate equilibrium prices strategically this strategic behavior precludes ex post efficient market performance increasing the number of traders improves the efficiency of some trading mechanisms by enabling them to better utilize the private information traders bids and offers reveal this paper shows that the expected inefficiency of optimally designed mechanisms relative to ex post efficient allocations decreases almost quadratically as the number of traders increases

efficiency of large double auctions we consider large double auctions with private values values need be neither symmetric nor independent multiple units may be owned or desired participation may be stochastic we introduce a very mild notion of a little independence we prove that all nontrivial equilibria of auctions that satisfy this notion are asymptotically efficient for any alpha 0 inefficiency disappears at rate 1 n 2 alpha