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

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

taxing variable cost environmental regulation as industrial policy abstract conventional wisdom has it that a country that enacts strict environmental regulations will place its firms at a competitive disadvantage this view has been challenged recently some commentators argue that stricter regulation will enhance domestic competitiveness strict regulations induce innovation we evaluate this argument in a strategic trade model in very special cases a strengthening of regulation may result in a shift of profits from foreign to domestic firms this is not a general result however environmental regulation should of course be imposed to control externalities but it is unlikely that it will serve to generate industrial advantage

rethinking the optimal level of environmental quality justifications for strict environmental policy abstract traditional environmental theory suggests that the optimal level of a pollution emission occurs when the marginal damage created by the emissions is equal to the marginal cost of reducing the emissions we argue that the benefits from reducing pollution should be much more broadly defined to include at least three other sources of benefits first we develop a game theoretic model in which firms may under invest in cost saving green technologies second we demonstrate that consideration of future damages and abatement costs leads to a lower current optimal pollution level than that obtained in traditional models finally we show that ecological complexity creates indirect pathways by which greater pollution increases the likelihood of generating irreversible environmental damage this broader definition of the benefits of pollution abatement yields an optimal level of pollution that may actually be less than the level at which conventionally measured marginal damages are equal to marginal abatement costs thus environmental policy should be stricter

effectivity and constructivity in economic theory the implicit nonconstructive and noneffective contents of some aspects of general equilibrium theory are formally investigated in particular the claims of some applied computable general equilibrium cge theorists regarding the constructivity and effectivity of cge models are rigorously analyzed and shown to be unsubstantiated an attempt is also made to extract some general methodological guidelines for the meaningful mathematization of economic theory

a primer on mathematical modelling in economics the commission on graduate education in economics had raised several concerns regarding the role of mathematics in graduate training in economics krueger 1991 colander 1998 2005 this paper undertakes a detailed scrutiny of the notion of a utility function to motivate and describe the common patterns across mathematical concepts and results that are used by economists in the process one arrives at a classification of mathematical terms which is used to state mathematical results in economics the usefulness of the classification scheme is illustrated with the help of a discussion of arrow s impossibility theorem common knowledge of the patterns in mathematical concepts and results could be effective in enhancing communication between students teachers and researchers specializing in different sub fields of economics

fleetwood on causal holism clarification and critique fleetwood 2002 cambridge journal of economics vol 26 no 1 27 45 provided a critical evaluation of causal holism boylan and o gorman 1995 ekonomia vol 1 no 2 9 21 from the perspective of critical realism for fleetwood there are three fundamental areas of disagreement namely the differential approaches to unobservable entities description and explanation in this paper the authors dispute fleetwood s analysis of causal holism in all these areas to contextualise and clarify their disagreements with fleetwood the authors examine the most significant differences between the two methodological frameworks they argue that notwithstanding their shared criticism of mainstream economics critical realism and causal holism remain methodologically incompatible copyright 2006 oxford university press

the double dividend second best worlds and real world environmental policy abstract the recent series of papers by bovemberg goulder parry and others argue that the double dividend is unlikely to exist because of second best problems they argue that the imposition of environmental tax in an economy already distorted by income taxes will further distort the economy by reducing incentives to supply labor our paper argues that this is not likely to be the case because of the restrictive assumptions made by these models and because of the role of the environment as a factor of production

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 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 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

economic theory in the mathematical mode iif a symbolic date were to be chosen for the birth of mathematical economics our profession in rare unanimous agreement would select 1838 the year in which augustin cournot published his recherches sur les principes mathematiques de la thetorie des richesses students of the history of economic analysis could point out contributions made to mathematical economics as early as the beginning of the eighteenth century they could also point out johann heinrich von thunen s der isolierte staat 1826 a prototypical example of the use of mathematical reasoning in economic theory with little mathematical formalism but cournot stands out as the first great builder of mathematical models explaining economic phenomena among his successors in the nineteenth century and the early twentieth century the highest prominence will be given in this lecture to leon walras 1834 1910 the founder of the mathematical theory of general economic equilibrium to francis y edgeworth 1845 1926 and to vilfredo pareto 1848 1923 all three lived long enough into the twentieth century to have increased for all nobel laureates the value of the economics prize had it like the other prizes been initiated in 1901 if 1838 is the symbolic birthdate of mathematical economics 1944 is the symbolic beginning of its contemporary period in that year john von neumann and oskar morgenstern published the first edition of the theory of games and economic behavior an event that announced a profound and extensive transformation of economic theory in the following decade powerful intellectual stimuli also came from many other directions in addition to von neumann and morgenstern s book wassily leontiefs input output analysis paul samuelson s foundations of economic analysis tjalling koopmans activity analysis of production and george dant

optimal selling strategies when to haggle when to hold firm a seller encountering risk neutral buyers one at a time should if commitments are feasible quote a single take it or leave it price to each this strategy is superior to any other for finite or infinite buyer populations whether there is learning or the distribution of buyer prices is known at the outset with one object for sale or many although haggling may offer advantages in terms of price discrimination these gains are more than offset by the losses it generates by encouraging buyers to refuse purchases at high prices

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

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

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

controlling stock externalities flexible versus inflexible pigovian corrections abstract this paper examines the use of inflexible pigovian taxes subsidies to correct a stock externality an optimal control framework is first used to characterize the first best path for a pigovian correction that varies continuously this first best path is then contrasted with inflexible second best paths in which the level of the correction can be set only once or twice the optimal timing of a fixed one time correction is also studied a deferment of this correction is desirable when the initial state of the environmental stock is less deteriorated than the first best steady state or the adjustment costs are sufficiently great

a game theory framework for cooperative management of refillable and disposable bottle lifecycles abstract firms engaged in industrial ecology hope to reduce environmental impacts and costs improve resource efficiency and create symbiotic relationships that reduce transaction costs and enhance information flow however current lca tools do not explain firms incentives to implement the principles of industrial ecology or how an individual or firm can affect the products and processes at other firms game theory on the other hand allows investigation of the willingness of producers and consumers to seek strategies that promote the common interest of the system while not harming their own interests this paper applies game theory to the lifecycle of bottle packaging and presents a framework for analysis of the choice between refillable and disposable bottles although refillable bottles may be more cost effective in the long run bottlers only have incentive to use refillable bottles when they are sure that consumer return rates will be reasonably high it has been found that consumers who keep or dispose of refillable bottles or respond to deposit refund return incentives by reducing their demand may drive costs up and encourage adoption of disposables a simple model is provided which finds the optimal bottler strategy as a function of the bottler s expectations for consumer cooperation

stock externalities pigovian taxation and dynamic stability abstract stock externalities represent a type of consumption externality in which individual consumption of a particular good leads to production of a public bad such as in the arms race and in the greenhouse effect certain of these stock externalities can be regulated by pigovian taxation of the good that produces the externality for others however depending on an ordinal property of preferences the equilibrium becomes dynamically unstable so it is necessary to use direct regulation to support an optimal equilibrium

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

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

information revelation in a market with pairwise meetings the paper presents a simple pairwise meetings model of trade the new feature is that agents have asymmetric information about the true state of the world the focus is on the transmission of the information through the process of trade the qualitative question is to what extent is the information revealed to uninformed agents through the trading process when the market is in some sense frictionless in particular does the decentralized process give rise to full revelation results as derived by the literature on rational expectations for centralized and competitive environments in the context of the model of this paper it turns out that the information is not fully revealed to uninformed agents even when the market is in some sense approximately frictionless

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 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

axiomatization and formalism in economics in this paper we address a number of issues in the historiography and methodology of the formalization of economics in the twentieth century we argue that debreu s approach to formalism pursuing his bourbakist programme was based on hilbert s version of finitism the latter project attempted to retain its place in cantor s paradise and in so doing bequeathed serious methodological consequences there was however at the turn of the twentieth century an alternative version of finitism available that provided by poincare which if adopted by economics would have led to a radically different approach to economic theorizing and modelling we argue that these reflections must be embedded in an alternative larger methodological framework copyright 2007 the authors journal compilation 2007 blackwell publishing ltd