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142
The market game: existence and structure of equilibrium
 Journal of Mathematical Economics
, 1992
"... We analyze the canonical market game. There are e commodities, a single inside money, L markets in which commodities are exchanged for inside money, and n consumers. Each consumer’s trategy is the nonnegative vector of his commodity offers and his money bids. Given endowments and sufftciently large ..."
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Cited by 37 (5 self)
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We analyze the canonical market game. There are e commodities, a single inside money, L markets in which commodities are exchanged for inside money, and n consumers. Each consumer’s trategy is the nonnegative vector of his commodity offers and his money bids. Given endowments and sufftciently large offers, the set of interior Nash equilibrium strategies is finite and nonempty. Hence the set of interior Nash ~uiljbria in strategy space is paramet~~d by the endimensional vector of offers. In allocation space the manifold of Nash equilibrium allocations has generic dimension ene, which is also the dimension of the set of feasible allocations. 1. Intr~u~tion and summary For models of perfect competition, there are extensive and systematic studies of the existence of equilibrium and of the structure of the equiIibrium set. See the references in Debreu (1959), Arrow and Hahn (1971), MasCole11 (1985), and Balasko (1987). For models of imperfect competition, analyses of the existence and the structure of equilibrium are less extensive and less
Market uncertainty: correlated and sunspot equilibria in imperfectly competitive economies
 Rev. Econ. Studies
, 1991
"... An imperfectly competitive economy is very prone to market uncertainty, including uncertainty about the liquidity (or "thickness") of markets. We show, in particular, that there exist stochastic equilibrium outcomes in nonstochastic market games if (and only if) the endowments are not Pare ..."
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Cited by 31 (8 self)
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An imperfectly competitive economy is very prone to market uncertainty, including uncertainty about the liquidity (or "thickness") of markets. We show, in particular, that there exist stochastic equilibrium outcomes in nonstochastic market games if (and only if) the endowments are not Pareto optimal. We also provide a link between extrinsic uncertainty arising in games (e.g. correlated equilibria) and extrinsic uncertainty in market economies (e.g. sunspot equilibria). A correlated equilibria to the market game is either a sunspot equilibrium or a nonsunspot equilibrium to the related securities games, but the converse is not true in general. 1.
Efficiency of ScalarParameterized Mechanisms
"... We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communica ..."
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Cited by 23 (2 self)
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We consider the problem of allocating a fixed amount of an infinitely divisible resource among multiple competing, fully rational users. We study the efficiency guarantees that are possible when we restrict to mechanisms that satisfy certain scalability constraints motivated by large scale communication networks; in particular, we restrict attention to mechanisms where users are restricted to onedimensional strategy spaces. We first study the efficiency guarantees possible when the mechanism is not allowed to price differentiate. We study the worstcase efficiency loss (ratio of the utility associated with a Nash equilibrium to the maximum possible utility), and show that the proportional allocation mechanism of Kelly (1997) minimizes the efficiency loss when users are price anticipating. We then turn our attention to mechanisms where price differentiation is permitted; using an adaptation of the VickreyClarkeGroves class of mechanisms, we construct a class of mechanisms with onedimensional strategy spaces where Nash equilibria are fully efficient. These mechanisms are shown to be fully efficient even in general convex environments, under reasonable assumptions. Our results highlight a fundamental insight in mechanism design: when the pricing flexibility available to the mechanism designer is limited, restricting the strategic flexibility of bidders may actually improve the efficiency guarantee.
Computation in a Distributed Information Market
, 2003
"... According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where informatio ..."
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Cited by 22 (4 self)
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According to economic theory, supported by empirical and laboratory evidence, the equilibrium price of a financial security reflects all of the information regarding the security's value. We investigate the dynamics of the computational process on the path toward equilibrium, where information distributed among traders is revealed stepby step over time and incorporated into the market price. We develop a simplified model of an information market, along with trading strategies, in order to formalize the computational properties of the process. We show that securities whose payoffs cannot be expressed as a weighted threshold function of distributed input bits are not guaranteed to converge to the proper equilibrium predicted by economic theory. On the other hand, securities whose payoffs are threshold functions are guaranteed to converge, for all prior probability distributions. Moreover, these threshold securities converge in at most n rounds, where n is the number of bits of distributed information. We also prove a lower bound, showing a type of threshold security that requires at least n/2 rounds to converge in the worst case.
Beyond Search: Fiat Money in Organized Exchange
 International Economic Review
, 2000
"... Abstract: A model of fiat money is constructed in which spatial separation and the logistics of communication are made explicit as in search theory, but in which exchange is organized by profitseeking business enterprises as in all market economies. Firms mitigate search costs by opening shops that ..."
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Cited by 22 (0 self)
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Abstract: A model of fiat money is constructed in which spatial separation and the logistics of communication are made explicit as in search theory, but in which exchange is organized by profitseeking business enterprises as in all market economies. Firms mitigate search costs by opening shops that are easily located. Equilibria may exist in which fiat money is used as a universal medium of exchange. When a monetary equilibrium exists, fiat money is essential. The model provides a foundation to cashinadvance theory, without specifying in advance that one object will be used as the universal medium of exchange JEL Classification: E40
Proportional response dynamics leads to market equilibrium
 In STOC ’07: Proceedings of the thirtyninth annual ACM symposium on Theory of computing
, 2007
"... One of the main reasons of the recent success of peer to peer (P2P) file sharing systems such as BitTorrent is its builtin titfortat mechanism. In this paper, we model the bandwidth allocation in a P2P system as an exchange economy and study a titfortat dynamics, namely the proportional respons ..."
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Cited by 20 (1 self)
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One of the main reasons of the recent success of peer to peer (P2P) file sharing systems such as BitTorrent is its builtin titfortat mechanism. In this paper, we model the bandwidth allocation in a P2P system as an exchange economy and study a titfortat dynamics, namely the proportional response dynamics, in this economy. In a proportional response dynamics each player distributes its good to its neighbors proportional to the utility it received from them in the last period. We show that this dynamics not only converges but converges to a market equilibrium, a standard economic characterization of efficient exchanges in a competitive market. In addition, for some classes of utility functions we consider, it converges much faster than the classical tâtonnement process and any existing algorithms for computing market equilibria. As a part of our proof we study the double normalization of a matrix, an operation that linearly scales the rows of a matrix so that each row sums to a prescribed positive number, followed by a similar scaling of the columns. We show that the double normalization process of any nonnegative matrix always converges. This complements the previous studies in matrix scaling that has focused on the convergence condition of the process when the row and column normalizations are considered as separate steps. 1
Money as a mechanism in a Bewley economy
 International Economic Review
, 2005
"... We study what features an economic environment might possess, such that it would be Pareto efficient for the exchange of goods in that environment to be conducted on spot markets where those goods trade for money. We prove a conjecture that is essentially due to Bewley [1980, 1983]. Monetary spot t ..."
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Cited by 16 (0 self)
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We study what features an economic environment might possess, such that it would be Pareto efficient for the exchange of goods in that environment to be conducted on spot markets where those goods trade for money. We prove a conjecture that is essentially due to Bewley [1980, 1983]. Monetary spot trading is nearly efficient when there is only a single perishable good (or a composite commodity) at each date and state of the world; random shocks are idiosyncratic, privately observed, and temporary; markets are competitive; and the agents are very patient. This result is a fairly close analogue, for trade using outside, fiat money, of a recent characterization by Levine and Zame [2002] of environments in which spot trade using inside money, in the form of oneperiod debt payable in a commodity, is nearly Pareto efficient. We also study examples where nonmonetary and expansionary monetary mechanism Pareto dominates laissezfaire or contractionary monetary mechanism in an environment with impatient agents. J.E.L. Classification: E31, E42
Comparing the robustness of trading systems to higherorder uncertainty
 Review of Economic Studies
, 1996
"... Abstract: This paper compares the performance of a decentralized market with that of a dealership market when traders have differential information. Trade occurs as a result of equilibrium actions in a Bayesian game, where uncertainty is captured by a finite state space and information is represente ..."
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Cited by 16 (3 self)
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Abstract: This paper compares the performance of a decentralized market with that of a dealership market when traders have differential information. Trade occurs as a result of equilibrium actions in a Bayesian game, where uncertainty is captured by a finite state space and information is represented by partitions on this space. In the benchmark case of trade with common knowledge of endowments, the two mechanisms deliver virtually identical outcomes. However, with differential information, the dealership market has strictly higher trading volume, and yields an efficient posttrade allocation in most states. In contrast, the decentralized market suffers from suboptimal trading volume. The reason for this poor performance is the vulnerability of the decentralized market to higher order uncertainty concerning the fundamentals of the market. Traders may know that mutually beneficial trade is feasible, and perhaps know that they know, and yet a failure of common knowledge that this is so precludes efficient trade. The dealership market is robust to this type of uncertainty. * I would like to record my debt to Stephen Morris for shaping my views on the issues raised here. Ian Jewitt, as managing editor, and three referees guided this paper through several revisions, and I am grateful to them for their perseverance. I am especially grateful to one of the referees for pointing to the importance of limit orders in modifying the results reported here. I have gained from the comments of Helmut Bester, Katie