In a simple market with incomplete information
01 Jan 1994-
TL;DR: In this paper, the authors show that in any equilibrium the amount by which a trader misreports is 0 (1/m) and the corresponding inefficiency is 0(1/mr2), and that the indeterminacy and the inefficiency that is caused by traders' bargaining behavior in small markets thus rapidly vanishes as the market increases in size.
Abstract: 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 0(1/m) and the corresponding inefficiency is 0(1/mr2). 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. A TRADER WHO PRIVATELY KNOWS his own preferences may demand more favorable terms than he is in truth willing to accept. Such behavior, which is the essence of bargaining, may lead to an impasse that delays or lessens the gains from trade. A trader who acts as a price-taker, by contrast, honestly responds to prices with his true demand. Price-taking behavior and market-clearing prices together guarantee efficient allocations. This behavior is plausible when there is a large number of traders, for competition then sharply constrains a trader's ability to affect price through bargaining. In this paper we model the incremen- tal progression from the indeterminacy and inefficiency that results from bar- gaining among a few traders to the determinacy and efficiency that results from price-taking by many traders. We show this convergence is fast. Our model thus supports the use of price theory, which posits efficient trade at a market-clear- ing price, even in moderately small markets in which a trader's preferences are private to himself. The trading mechanism we consider is a simple model of a call market. A call market collects bids and offers from traders, constructs supply and demand curves, fixes a market-clearing price, and executes the indicated trades. The daily opening price of each stock listed on the New York Stock Exchange is set by a call market that aggregates the bids and offers that have arrived overnight. Call markets twice a day fix copper and gold prices in London. The Wunsch system of, computerized trading conducts periodic call markets in each of the listed stocks of the New York Stock Exchange. Of all the institutions that
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TL;DR: An incentive compatible and budget balanced constant-factor approximation mechanism in a setting where buyers have XOS valuations and sellers' valuations are additive, the first such approximation mechanism for a two-sided market setting where the agents have combinatorial valuation functions.
Abstract: Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocation, require us to consider two-sided combinatorial auctions in which buyers have preferences on subsets of items, and sellers may offer multiple heterogeneous items. No efficient mechanism was known so far for such two-sided combinatorial markets. This work provides the first IR, IC and SBB mechanisms that provides an O(1)-approximation to the optimal social welfare for two-sided markets. An initial construction yields such a mechanism, but exposes a conceptual problem in the traditional SBB notion. This leads us to define the stronger notion of direct trade strong budget balance (DSBB). We then proceed to design mechanisms that are IR, IC, DSBB, and again provide an O(1)-approximation to the optimal social welfare. Our mechanisms work for any number of buyers with XOS valuations - a class in between submodular and subadditive functions - and any number of sellers. We provide a mechanism that is dominant strategy incentive compatible (DSIC) if the sellers each have one item for sale, and one that is bayesian incentive compatible (BIC) if sellers hold multiple items and have additive valuations over them. Finally, we present a DSIC mechanism for the case that the valuation functions of all buyers and sellers are additive.
25 citations
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TL;DR: In this paper, the authors examine the factors that lead liquidity-motivated investors to choose the type of market structure they prefer, and propose a new market structure that is more suitable for them.
Abstract: This paper examines the factors that lead liquidity-motivated investors to choose the type of market structure they prefer.
19 citations
Cites background or methods from "In a simple market with incomplete ..."
...An increase in the number of customers leads to an increase 11Vogler (1997) and Rustichini, Satterthwaite, and Williams (1994) show that, as the number of players increases, the double-auction outcome quickly converges to the standard Walrasian equilibrium (i.e., the competitive equilibrium), which…...
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...…the resultant macroeconomic outcomes, this approach can be used to analyze the aggregate dynamics of various economic systems, including the price dynamics typically observed 8SeeWerner (1997), and Rustichini, Satterthwaite, and Williams (1994) for examples of xed-order size double-auction models....
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...The standard set-up of k-DA is fairly restrictive, in the sense that the order size is exogenously xed (Werner 1997, Rustichini, Satterthwaite, and Williams 1994)....
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TL;DR: The trading mechanisms that maximize a broker's expected profit or expected total gains from trade are completely characterized by some modified monotonic virtual valuations and the bunching phenomenon will be a general feature in these mechanisms.
Abstract: We analyze optimal trading mechanisms in environments where each trader owns some units of a good to be traded and may be either a seller or a buyer, depending on the realization of privately observed valuations. First, the concept of virtual valuation is extended to ex ante unidentified traders; contrary to the case with identified traders, the traders' virtual valuations now depend on the trading mechanisms and are generally not monotonic even if the distribution of valuations is regular. We show that the trading mechanisms that maximize a broker's expected profit or expected total gains from trade are completely characterized by some modified monotonic virtual valuations. Here, the bunching phenomenon, which is specific to ex ante unidentified traders, will be a general feature in these mechanisms. We also show that the randomization rule by which ties are broken is now an important instrument in the design of the optimal mechanisms. Nous analysons les mecanismes optimaux d'echange dans un contexte ou chaque participant possede quelques unites d'un bien a etre echange et pourrait etre soit un acheteur, soit un vendeur, dependant de la realisation des valorisations qui sont de l'information privee des participants. D'abord, le concept de valeur virtuelle est generalise aux agents qui ne sont pas ex ante identifies comme acheteurs ou vendeurs; contrairement au cas ou les agents sont bien identifies, les valeurs virtuelles des agents dependent0501ntenant du mecanisme d'echange et ne sont generalement pas monotones meme si la distribution des valorisations est reguliere. Nous montrons que les mecanismes optimaux d'echange, qui maximisent l'esperance de profit ou de gains d'echange d'un intermediaire, sont completement caraterises par ces valeurs virtuelles. Le phenomene de discrimination incomplete (bunching), qui est ici specifique aux agents non identifies ex ante, va etre une caracteristique generale dans les mecanismes optimaux. Nous montrons aussi que la regle de repartition aleatoire par laquelle les egalites sont brisees est0501ntenant un instrument important dans le design de ces mecanismes.
18 citations
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TL;DR: In this paper, the authors examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types, and they show that there is no "free lunch", i.e., there exists no clearing schedule that is simultaneously optimal along both objectives.
Abstract: We examine two-sided markets where players arrive stochastically over time and are drawn from a continuum of types. The cost of matching a client and provider varies, so a social planner is faced with two contending objectives: a) to reduce players' waiting time before getting matched; and b) to form efficient pairs in order to reduce matching costs. We show that such markets are characterized by a quick-or-cheap dilemma: Under a large class of distributional assumptions, there is no 'free lunch', i.e., there exists no clearing schedule that is simultaneously optimal along both objectives. We further identify a unique breaking point signifying a stark reduction in matching cost contrasted by an increase in waiting time. Generalizing this model, we identify two regimes: one, where no free lunch exists; the other, where a window of opportunity opens to achieve a free lunch. Remarkably, greedy scheduling is never optimal in this setting.
5 citations
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TL;DR: In this paper, the authors present a struggling attempt to give structure to the statement: "Business in under-developed countries is difficult"; in particular, a structure is given for determining the economic costs of dishonesty.
Abstract: This paper relates quality and uncertainty. The existence of goods of many grades poses interesting and important problems for the theory of markets. On the one hand, the interaction of quality differences and uncertainty may explain important institutions of the labor market. On the other hand, this paper presents a struggling attempt to give structure to the statement: “Business in under-developed countries is difficult”; in particular, a structure is given for determining the economic costs of dishonesty. Additional applications of the theory include comments on the structure of money markets, on the notion of “insurability,” on the liquidity of durables, and on brand-name goods.
17,764 citations
TL;DR: In this article, a new general auction model was proposed, and the properties of affiliated random variables were investigated, and various theorems were presented in Section 4-8 and Section 9.
Abstract: : In Section 2, we review some important results of the received auction theory, introduce a new general auction model, and summarize the results of our analysis. Section 3 contains a formal statement of our model, and develops the properties of affiliated random variables. The various theorems are presented in Sections 4-8. In Section 9, we offer our views on the current state of auction theory. Following Section 9 is a technical appendix dealing with affiliated random variables.
3,857 citations
TL;DR: The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc.
Abstract: (This article originally appeared in Management Science, November 1967, Volume 14, Number 3, pp. 159-182, published by The Institute of Management Sciences.)
The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities.
In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent," in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players. But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption.
In cases where the consistency assumption holds, the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution, and the outcome of this lottery will decide which particular subgame will be played, i.e., what the actual values of the relevant parameters will be in the game. Yet, each player will receive only partial information about the outcome of the lottery, and about the values of these parameters. However, every player will know the "basic probability distribution" governing the lottery. Thus, technically, the resulting game will be a game with complete information. It is called the Bayes-equivalent of the original game. Part I of the paper describes the basic model and discusses various intuitive interpretations for the latter. Part II shows that the Nash equilibrium points of the Bayes-equivalent game yield "Bayesian equilibrium points" for the original game. Finally, Part III considers the main properties of the "basic probability distribution."
2,710 citations
TL;DR: In this paper, it was shown that risk-averse traders can still never agree to any non-null trade when they receive private information, and that an equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.
1,662 citations
TL;DR: In this article, the authors 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.
Abstract: 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.
675 citations