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

comparing alternative models of heterogeneity in consumer choice behavior summary when modeling demand for differentiated products it is vital to adequately capture consumer taste heterogeneity but there is no clearly preferred approach here we compare the performance of six alternative models currently the most popular are mixed logit mixl particularly the version with normal mixing n mixl and latent class lc which assumes discrete consumer types recently several alternative models have been developed the generalized multinomial logit g mnl extends n mixl by allowing for heterogeneity in the logit scale coefficient scale heterogeneity logit s mnl is a special case of g mnl with scale heterogeneity only the mixed mixed logit mm mnl assumes a discrete mixture of normals heterogeneity distribution finally one can modify n mixl by imposing theoretical sign constraints on vertical attributes we call this t mixl we find that none of these models dominates the others but g mnl mm mnl and t mixl typically outperform the popular n mixl and lc models copyright 2012 john wiley sons ltd

limits of exact equilibria for capacity constrained sellers with costly search abstract this paper studies finite versions of competitive matching models in which sellers announce prices and buyers understand the relationship between price and probability of trade two equilibrium concepts are studied for finite games subgame perfect equilibrium and rational expectations equilibrium it is shown that the distribution of prices offered by sellers under both equilibrium concepts converges weakly to the same competitive equilibrium distribution of prices furthermore the payoffs that sellers face in both kinds of equilibrium have the market utility property in the limit journal of economic literature classification numbers c78 d41 d45

convergence to efficiency in a simple market with incomplete information a model of trade with m buyers and m sellers is considered in which price is set to equate revealed demand and supply in a bayesian nash equilibrium each trader acts not as a price taker but instead misrepresents his true demand supply to influence price in his favor this causes inefficiency we show that in any equilibrium the amount by which a trader misreports is o 1 m and the corresponding inefficiency is o 1 m2 the indeterminacy and the inefficiency that is caused by the traders bargaining behavior in small markets thus rapidly vanishes as the market increases in size

individually rational budget balanced mechanisms and allocation of surplus abstract we investigate the issue of implementation via individually rational ex post budget balanced bayesian mechanisms we show that all decision rules generating a nonnegative expected social surplus are implementable via such mechanisms if and only if the probability distribution of the agents type profiles satisfies two conditions the well known condition of cremer and mclean 1988 full extraction of the surplus in bayesian and dominant strategy auctions econometrica 56 1247 1257 and the identifiability condition introduced in this paper we also show that these conditions are necessary for ex post efficiency to be attainable with budget balance and individual rationality and that the expected social surplus in these mechanisms can be distributed in any desirable way lastly we demonstrate that like cremer mclean condition the identifiability condition is generic if there are at least three agents

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

continuity in auction design abstract j cremer and r p mclean econometrica56 1988 1247 1257 have shown that the auctioneer can extract all the surplus when the private valuations of bidders are not statistically independent the paper shows that this result does not necessarily arise under limited liability or risk aversion under limited liability and or risk aversion we prove that the functions corresponding to the auctionner s optimal expected gain and to the maximum total surplus are continuous in the space of possible information distributions thus by continuity the auctioneer wil not be able to extract all the rents when bidders private valuations are approximately independent

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

the optimality of a simple market mechanism strategic behavior in a finite market can cause inefficiency in the allocation and market mechanisms differ in how successfully they limit this inefficiency a method for ranking algorithms in computer science is adapted here to rank market mechanisms according to how quickly inefficiency diminishes as the size of the market increases it is shown that trade at a single market clearing price in the k double auction is worst case asymptotic optimal among all plausible mechanisms evaluating mechanisms in their least favorable trading environments for each possible size of the market the k double auction is shown to force the worst case inefficiency to zero at the fastest possible rate

modelling heterogeneity in patients preferences for the attributes of a general practitioner appointment this paper examines the distribution of preferences among respondents to a discrete choice experiment on the choice of general practitioner appointments in addition to standard logit mixed and latent class logit models are used to analyse the data from the choice experiment it is found that there is significant preference heterogeneity for all the attributes in the experiment and that both the mixed and latent class models lead to significant improvements in fit compared to the standard logit model moreover the distribution of preferences implied by the preferred mixed and latent class models is similar for many attributes

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

a framework for electricity price spike analysis with advanced data mining methods there are many techniques for electricity market price forecasting however most of them are designed for expected price analysis rather than price spike forecasting an effective method of predicting the occurrence of spikes has not yet been observed in the literature so far in this paper a data mining based approach is presented to give a reliable forecast of the occurrence of price spikes combined with the spike value prediction techniques developed by the same authors the proposed approach aims at providing a comprehensive tool for price spike forecasting in this paper feature selection techniques are first described to identify the attributes relevant to the occurrence of spikes a simple introduction to the classification techniques is given for completeness two algorithms support vector machine and probability classifier are chosen to be the spike occurrence predictors and are discussed in detail realistic market data are used to test the proposed model with promising results

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

taste variation in discrete choice models this paper develops an extension of the classical multinomial logit model which approximates a class of models obtained when there is uncontrolled taste variation across agents and choices in addition to the stochastic noise inherent in the logit model unlike semiparametric and parametric alternatives the extended logit model is easy to estimate even when there are many potential choices unlike parametric alternatives it does not require the specification of a distribution of varying tastes the extended logit model can give a quick indication of the impact of taste variation on estimates and it generates estimates of the covariances of the taste shifters it can be used as an exploratory device en route to the construction of a model incorporating a particular form of random taste variation and it can be used to determine whether such effort is required at all when the amount of taste variation is not excessive the approximate model can be adequate itself the model nests the conventional logit model which leads to a misspecification diagnostic a method for estimating the model using conventional logit model software is proposed asymptotic properties of estimators are derived and an application is presented

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

correlated information and mechanism design in models of asymmetric information possession of private information leads to rents for the possessors this induces mechanism designers to distort away from efficiency the authors show that this is an artifact of the presumption that information is independently distributed rent extraction in a large class of mechanism design games is analyzed and a necessary and sufficient condition for arbitrarily small rents to private information is provided additionally the two person bargaining game is shown to have an efficient solution under first order stochastic dominance and a hazard rate condition similar conditions allow full rent extraction in milgrom weber auctions

profit or patients health benefit exploring the heterogeneity in physician altruism abstract this paper investigates physician altruism toward patients health benefit using behavioral data from hennig schmidt et al s 2011 laboratory experiment in the experiment medical students in the role of physicians decide on the provision of medical services the experimental setup allows us to identify the influence of profits and patients health benefit on the choice of medical treatment we estimate physician altruism the weight individuals attach to patients health benefit by fitting mixed logit and multinomial logit regression models to the experimental data estimation results provide evidence for physician altruism we find however substantial variation in the degree of physician altruism we also discuss some implications of our results for the design of physician payment schemes in the light of the theoretical literature

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

walras retrouve decentralized trading mechanisms and the competitive price we extend the standard analysis of decentralized markets to allow for the possibility that traders interact simultaneously with more than one trader on the opposite side of the market in contrast with the literature we reconcile the walrasian equilibrium with the outcome of decentralized strategic trade we show that there exist generic matching technologies that determine local market conditions such that as market frictions vanish the equilibrium price is the one that would result in the static walrasian market our analysis highlights the importance of local market conditions for the determination of equilibrium prices

does organizational ownership matter objectives of employees in public nonprofit and for profit nursing homes does organizational ownership matter for employees we conducted a discrete choice experiment to reveal employees objectives in for profit nonprofit and governmental nursing homes the results indicate that differences in objectives among nursing home staff are at least partially related to differences in ownership type more specifically we find that employees of public nursing homes are less extrinsically motivated than their for profit and nonprofit counterparts however the results also show that employees of for profit nonprofit and governmental nursing homes are trading off output quality and output quantity differently in line with the view that public providers of elderly care are pursuing a supplier of last resort objective function

identification and inference in ascending auctions with correlated private values we introduce and apply a new nonparametric approach to identification and inference on data from ascending auctions we exploit variation in the number of bidders across auctions to nonparametrically identify useful bounds on seller profit and bidder surplus using a general model of correlated private values that nests the standard independent private values ipv model we also translate our identified bounds into closed form and asymptotically valid confidence intervals for several economic measures of interest applying our methods to much studied u s forest service timber auctions we find evidence of correlation among values after controlling for a rich vector of relevant auction covariates this correlation causes expected profit the profit maximizing reserve price and bidder surplus to be substantially lower than conventional ipv analysis of the data would suggest

eliciting gps preferences for pecuniary and non pecuniary job characteristics abstract this study examines general practitioners preferences for pecuniary and non pecuniary job characteristics in the context of choosing a general practice in which to work a discrete choice experiment is used to test hypotheses about the nature of the utility function marginal rates of substitution between income and non pecuniary characteristics are calculated the results suggest that policies aimed at influencing general practitioners location choices should take account of both non pecuniary and pecuniary factors particularly out of hours work commitments

competitive pricing and efficiency in search equilibrium we consolidate and generalize some results on price determination and efficiency in search equilibrium extending models by rubinstein and wolinsky and by gale heterogeneous buyers and sellers meet according to a general matching technology and prices are determined by a general bargaining condition when the discount rate r and search costs converge to 0 we show that prices in all exchanges are the same and equal the competitive market clearing price given positive search costs efficiency obtains iff bargaining satisfies hosios condition and r 0 when prices are set by third party market makers however we show that search equilibrium is necessarily efficient

dynamic markets with competitive bidding the model features a dynamic market in steady state in which prices are determined in first price auctions it combines competition over time familiar from the pairwise meeting models with instantaneous bidding competition it inquires how different properties of the model determine the relative importance of these two aspects of the competition and in particular how the non market clearing price result of the matching and bargaining models is affected by the

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

identification and estimation of auction models with unobserved heterogeneity in many procurement auctions the bidders unobserved costs depend both on a common shock and on idiosyncratic private information assuming a multiplicative structure i derive sufficient conditions under which the model is identified and propose a non parametric estimation procedure that results in uniformly consistent estimators of the cost components distributions the estimation procedure is applied to data from michigan highway procurement auctions private information is estimated to account for 34 of the variation in bidders costs it is shown that accounting for unobserved auction heterogeneity has important implications for the evaluation of the distribution of rents efficiency and optimal auction design

probabilistic optimal power flow in electricity markets based on a two point estimate method this paper presents an application of a two point estimate method 2pem to account for uncertainties in the optimal power flow opf problem in the context of competitive electricity markets these uncertainties can be seen as a by product of the economic pressure that forces market participants to behave in an unpredictable manner hence probability distributions of locational marginal prices are calculated as a result instead of using computationally demanding methods the proposed approach needs 2n runs of the deterministic opf for n uncertain variables to get the result in terms of the first three moments of the corresponding probability density functions another advantage of the 2pem is that it does not require derivatives of the nonlinear function used in the computation of the probability distributions the proposed method is tested on a simple three bus test system and on a more realistic 129 bus test system results are compared against more accurate results obtained from mcs the proposed method demonstrates a high level of accuracy for mean values when compared to the mcs for standard deviations the results are better in those cases when the number of uncertain variables is relatively low or when their dispersion is not large

heterogeneous effect of coinsurance rate on healthcare expenditure generalized finite mixtures and matching estimators the article proposes a combination of finite mixture models and matching estimators to account for heterogeneous and nonlinear effects of the coinsurance rate on healthcare expenditure the analysis with panel data for adult japanese consumers in 2008 2010 and for female consumers in 2000 2010 demonstrates the presence of subpopulations with high medium and low healthcare expenditure and subpopulation membership is explained by lifestyle variables generalized finite mixtures provide adequate fit compared to loglinear model conditional average treatment effect estimations reveal the existence of nonlinear effects of the coinsurance rate in the subpopulation with high expenditure

a decentralized market with common values uncertainty non steady states we analyse a market where i trade proceeds by random and anonymous pairwise meetings with bargaining ii agents are asymmetrically informed about the value of the traded good and iii no new entrants are allowed once the market is open we show that information revelation and efficiency never obtain in equilibrium even as discounting is removed this holds whether the asymmetry is two sided or one sided in some cases there exist equilibria where a substantial amount goes untraded this contrasts with the earlier literature which was based on the steadystate equilibria of a model where agents enter the market every period

recreation demand models with taste differences over people we estimate random parameter logit models of anglers choice of fishing site the models generalize logit by allowing coefficients to vary randomly over anglers rather than being fixed the models do not exhibit the restrictive independence from irrelevant alternatives property of logit and can represent any substitution pattern estimation explicitly accounts for the fact that the variation in coefficients over anglers induces correlation in unobserved utility over trips by the same angler willingness to pay for improved fish stock and the value to anglers of specific sites are calculated from the models and compared with the estimates obtained from a standard logit model

full extraction of the surplus in bayesian and dominant strategy auctions we consider auctions for a single indivisible object in the case where the bidders have information about each other which is not available to the seller we show that the seller can use this information to his own benefit and we completely characterize the environ ments in which a well chosen auction gives him the same expected payoff as that obtainable were he able to sell the object with full information about each bidder s willingness to pay we provide this characterization for auctions in which the bidders have dominant strate gies and for those where the relevant equilibrium concept is bayesian nash in both set ups the existence of these auctions hinges on the possibility of constructing lotteries with the correct properties we consider the situation in which an agent the seller possesses one indivisible unit of a good to which he attaches no value but the good has value to a number of potential buyers and its transfer to one of them would increase social welfare in particular the transfer to the buyer with the highest valuation maximizes social welfare in this paper we completely characterize environments in which the seller can design an auction that will enable him to capture for himself the full increase in social welfare induced by the transfer of the good to the bidder with the highest willingness to pay if the seller had full information about the reservation prices of potential buyers his optimal selling strategy would be very simple he would announce a price equal or very close to the highest reservation value the optimal strategy for the bidder with the highest evaluation would be to accept the offer note that we are treating a situation in which the seller can commit himself to a price as a result of the exchange the utility of the seller increases by the full amount of the increase in social welfare and he has been able to fully extract the surplus in many circumstances however a seller has only imperfect knowledge of the buyers willingnesses to pay in this case he must find some mechanism or auction which will enable him to maximize his benefit from the sale of the object the auction literature starts with this observation and shows how the seller can by an astute choice of auction extract the largest possible fraction of the surplus in general the literature has shown that this proportion is strictly less than one in some circumstances the bidders will have information about each other which is not available to the seller for instance in auctions for petroleum drilling rights bidders know the results of geological tests which they have

on the trade off between deficit and inefficiency and the double auction with a fixed transaction fee in many trading environments any incentive compatible and individually rational market mechanism will be either inefficient or will run a deficit we prove that as the market size m gets large for any fixed surplus or deficit x m times the minimal absolute inefficiency converges to c x where c is essentially a quadratic function of textitx we introduce a new mechanism the double auction with a fixed transaction fee by choosing the size of the fee appropriately any level of deficit or surplus can be implemented and the resulting mechanisms achieve the above bound corollaries include an asymptotic version of the myerson satterthwaite impossibility theorem a description of the minimal subsidy required to implement the efficient trading rule a characterization of the minimal inefficiency obtainable with budget balanced market mechanisms recommendations on the optimal organization of trade and insights on the effects of taxation

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

multi stage flexible expansion co planning under uncertainties in a combined electricity and gas market natural gas is an important fuel source in the power industry electricity and natural gas are both energy that can be directly consumed to improve the overall efficiency of the energy infrastructure it is imperative that the expansion of gas power plants electricity transmission lines and gas pipelines can be co planned the co planning process is modeled as a mixed integer nonlinear programming problem to handle conflicting objectives simultaneously we propose a novel model to identify the optimal co expansion plan in terms of social welfare to evaluate the robustness of plans under different scenarios the flexibility criterion is used to identify each plan s adaptation cost to uncertainties such as demand growth fuel cost and financial constraints etc we developed a systematic and comprehensive planning model to understand develop and optimize energy grids in order to reach higher social welfare and is therefore of great importance in terms of supporting and guiding investment decisions for the power and gas industry meanwhile we use the sequential importance sampling sis to perform scenario reduction for achieving a higher computational efficiency a comprehensive case study on the integrated ieee 14 bus and a test gas system is conducted to validate our approach

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

an efficient probabilistic assessment method for electricity market risk management managing electricity market risks is crucial for market participants for electricity price risk management expectation and standard deviation of price along with possible occurrence of price spike need to be assessed in order to support further risk control in this paper a hybrid probabilistic assessment method based on adaptive importance sampling ais and sequential importance sampling sis is developed improvements on ais and sis make the method better suit electricity market problems case studies are conducted on an equivalent australian national electricity market nem system uncertainties considered include system load renewable energy output generator bidding strategy and outage rate the proposed method provides much faster estimation of both normal price and price spike probability meanwhile achieving comparable accuracy as monte carlo mc simulation results sensitivity of its estimation efficiency against different load level is also analyzed which shows the robustness of the proposed method

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