Efficiency of continuous double auctions under individual evolutionary learning with full or limited information

In this paper we explore how specific aspects of market transparency and agents’ behavior affect the efficiency of the market outcome. In particular, we are interested whether learning behavior with and without information about actions of other participants improves market efficiency. We consider a simple market for a homogeneous good populated by buyers and sellers. The valuations of the buyers and the costs of the sellers are given exogenously. Agents are involved in consecutive trading sessions, which are organized as a continuous double auction with order book. Using Individual Evolutionary Learning agents submit price bids and offers, trying to learn the most profitable strategy by looking at their realized and counterfactual or “foregone” payoffs. We find that learning outcomes heavily depend on information treatments. Under full information about actions of others, agents’ orders tend to be similar, while under limited information agents tend to submit their valuations/costs. This behavioral outcome results in higher price volatility for the latter treatment. We also find that learning improves allocative efficiency when compared to outcomes with Zero-Intelligent traders.     

The Second Welfare Theorem in Economies with Non‐Walrasian Markets

The standard version of the second welfare theorem assumes that market operations produce Walrasian outcomes. Therefore, if there are individuals who can manipulate prices, the conclusion of the second welfare theorem is questionable. In this paper, we address the decentralization of a Pareto‐optimal allocation, when markets are non‐Walrasian. Our objective in this paper is to develop a game which can implement Pareto‐optimal allocations as Nash equilibria of strategic exchange in markets. In this way, we develop a version of the second welfare theorem for economies where markets are strategic.     

Walrasian prices in markets with tradable rights

In this paper, we consider an exchange economy where there is an external restriction for the consumption of goods. This restriction is defined by both, a cap on consumption of certain commodities and the requirement of an amount of rights for the consumption of these commodities. The caps for consumption are imposed exogenously due to the negative effects that the consumption may produce. The consumption rights or licenses are distributed among the agents. This fact leads to the possibility of establishing license markets. These licenses do not participate in agents’ preferences, however, the individual’s budgetary constraint may be modified, leading to a reassignment of resources. Our aim is to show the existence of a Walrasian equilibrium price system linking tradable rights prices with commodity prices.     

Collusion-Proof Samuelson Conditions for Public Goods

We analyze a public good problem when agents form a grand coalition to promote their own collective goal instead of that of society as a whole. When collusion takes place under symmetric information , the collusion-proof Samuelson rule takes a simple form that is close to an ex ante cost-benefit analysis . Then, we analyze the case where agents collude under asymmetric information . First, we describe the set of collusion-proof allocations. Second, we establish the collusion-proof Samuelson rule that highlights the role of coalitional virtual valuations . Asymmetric information within the coalition allows the principal to recover some flexibility in the design of the optimal policy. We finally discuss the nature of the inefficiency created by the agents' collusive behavior and the scope of their ex ante gain in forming a coalition.     

MONEY HOLDINGS,INFLATION, AND WELFARE IN A COMPETITIVE MARKET*

This article examines an environment where money is essential and agents exchange in perfectly competitive, Walrasian markets. Agents consume and produce a homogeneous good, but hold money to purchase consumption in the event of a relatively low productivity shock. A Walrasian market delivers a nondegenerate distribution of money holdings across agents and avoids some of the computational difficulties associated with the market assumption of bilateral bargaining common to search‐theoretic environments. The model is calibrated to long‐run U.S. velocity, and the welfare costs of inflation are assessed for variable buyer–seller ratios and persistent states of buying and selling.     

Sequential bargaining and competition

Summary This paper studies a sequential bargaining model of a decentralised market. A main objective is to explore the conditions under which the unique subgame perfect equilibrium outcome of the market game approximates the Walrasian outcome of the market. The three main messages that emerge from our results are as follows. First, contrary to conventional wisdom, frictionless markets need not be Walrasian. Second, the relative magnitudes of frictions can have a profound impact on the market outcome even in the limit as the absolute magnitudes of the frictions become negligible. And third, the relative magnitudes of certain types of frictions may have to be significantly large in order for markets to be Walrasian, reflecting that certain types of frictions are needed in the market in order to induce the Walrasian outcome.This paper is based on a chapter of my Ph.D. thesis. I would like to thank Ken Binmore, David Canning, Partha Dasgupta and Frank Hahn for their helpful comments. I owe special thanks to Ariel Rubinstein for his comments, remarks and encouragement. The comments and suggestions of an anonymous referee have significantly improved the exposition at several places.     

Walras' Law and Keynesian Macroeconomics

This paper examines the claim that Keynesian models violate Walras' law. Walras' law is founded in the logic of exchange. Standard statements misrepresent it, as it pertains to a monetary economy. Keynesian models are consistent with Walras' law once this misrepresentation is corrected. The law holds for both notional and effective demands. It also holds in unconstrained Walrasian equilibria, constrained Walrasian equilibria, and constrained non-Walrasian equilibria. The latter corresponds to a Keynesian conception of equilibrium: markets need not clear, but agents expectations must be fulfilled.     

Evolution of Walrasian equilibrium in an exchange economy

We study the stochastic stability of a dynamic trading process in an exchange economy. We use a simplified version of a trading model à la Shapley and Shubik (J Polit Econ 85:937–968, 1977). Two types of agents equipped with Leontief preferences trade goods in markets by offering endowments, and actual trades occur at market clearing prices. Better behavior tends to spread through the same type of agents by imitation, and agents also make mistakes occasionally. We provide a sufficient condition for the perturbed dynamic process to have a unique stochastically stable state that is a Walrasian equilibrium allocation. In this sense, we give a rationale for Walrasian behavior.     

Allocating multiple units

Summary. This paper studies the allocation and rent distribution in multi-unit, combinatorial-bid auctions under complete information. We focus on the natural multi-unit analogue of the first-price auction, where buyers bid total payments, pay their bids, and where the seller allocates goods to maximize his revenue. While there are many equilibria in this auction, only efficient equilibria remain when the truthful equilibrium restriction of the menu-auction literature is used. Focusing on these equilibria we first show that the first-price auction just described is revenue and outcome equivalent to a Vickrey auction, which is the multi unit analogue of a second-price auction. Furthermore, we characterize these equilibria when valuations take a number of different forms: diminishing marginal valuations, increasing average valuations, and marginal valuations with single turning points. Received: December 23, 1999; revised version: December 10, 2001     

A note on Walrasian equilibria in non-Walrasian models

We demonstrate that equilibria termed ‘Walrasian’ in non-Walrasian models are generally not, but rather Hicksian Temporary Competitive Equilibria in expected virtual prices. They are only Walrasian when the expected virtual prices would clear all markets.     

INTERTEMPORAL COURNOT AND WALRAS EQUILIBRIA: AN ILLUSTRATION*

In an intertemporal general equilibrium framework, we compare a Cournot equilibrium to the Walras equilibrium. The Cournot agents trade and invest less than the Walras agents. This generates an inefficiency that does not vanish as the number of Cournot agents tends to infinity. A larger number of strategic Cournot agents implies that the amount of trade (relative to their aggregate consumption) increases (i.e., it moves towards the Walrasian amount), but their investment (relative to the stock) decreases (i.e., it moves away from the Walrasian amount). "S'il y avait 3, 4, ...n producteurs en concurrence [...] la valeur de p, qui en résulte, diminuerait indéfiniment par l'accroissement indéfini du nombre n,”A. A. Cournot (1838, p. 63)."     

About market structure

I study an economy where sellers choose locations, and buyers choose which location to visit. All sellers in one location correspond to the Walrasian market while each seller in a separate location corresponds to the standard random matching model. Trades are consummated in auctions, and it turns out that the Walrasian market is not an equilibrium market structure. Rather, the sellers choose to distribute themselves in several locations endogenously creating the imperfectness of markets. I determine the number of sellers per location in equilibrium as a function of the ratio of buyers to sellers.     

信息不对称资本市场的实验研究

我们采用经济学实验研究方法构建了信息不对称的实验室资本市场,研究信息是否可以通过市场迅速传递。实验结果表明,在信息不对称的情况下,资本市场是非有效的;市场对信息的传递和价格反应是有条件的而且也是需要时间的;资本市场中的投资者并非完全理性,而是具有认知和行为偏差的普通人,存在过度自信和过度交易的情况;信息不对称还可能引起市场操纵行为,从而导致价格泡沫的形成。     

Selective Acceptance and Inefficiency in a Two-Issue Complete Information Bargaining Game

This paper explores the effects of a “selective acceptance” rule on the outcome of two-issue negotiations. The alternating-offer game introduced here allows for the possibility that settlement may be reached on one issue while negotiation continues about the other. This model captures features of laws that are generally believed to increase efficiency. The analysis shows that if one issue is indivisible, there are inefficient subgame perfect equilibria with no Pareto-improving alternative equilibria. With opposing valuations, rapid communication guarantees inefficiency. These are unique examples of this strong form of inefficiency in an alternating-offer bargaining game with complete (and perfect) information. Journal of Economic Literature Classification Numbers: C72, J30.     

Search, money, and inflation under private information

I study monetary exchange and inflation when buyers have private information about their willingness to pay for certain goods. Introducing imperfect information in the Lagos-Wright [A unified framework for monetary theory and policy analysis, J. Polit. Economy 113(3) (2005) 463-484] economy shows that the existence of monetary equilibrium is a more robust feature of the environment. In general, my model has a monetary steady state in which only a proportion of the agents hold money. Agents who do not hold money cannot participate in trade in the decentralized market. The proportion of agents holding money is endogenous and depends (negatively) on the level of expected inflation. As in Lagos and Wright's model, in equilibrium there is a positive welfare cost of expected inflation, but the origins of this cost are very different.     

Auctions with private uncertainty and resale opportunities

When an auction is followed by an opportunity for resale, bidder valuations are endogenously determined, reflecting anticipated profit from buying/selling in the resale market. These valuations vary with the resale market structure, can differ across auction types, and may be lower or higher than if resale were impossible. Although resale introduces a common value element to the model, revenue equivalence can hold; when it fails, this is due not to affiliation but to differences in information conveyed to the secondary market. Information linkages between markets can also lead to signaling and, in some cases, preclude separation in the auction.     

A MIXED NASH–WALRASIAN EQUILIBRIUM MODEL WITH ENDOGENOUS STEALING AND ENDOGENOUS SPECIALIZATION

Abstract. Using a price vector and a conjecture about a population's activities, this paper suggests that a mixed Nash–Walrasian equilibrium (NWE) occurs if, when every individual maximizes her utility under her conjecture, the trading markets and the theft ‘markets’ are all cleared. Thus, in our model the property rights system, instead of giving protection directly to producers, is aimed mainly at discouraging illegal behaviour. As a result, the equilibrium of the economy is seen to depend not only on self‐protection and/or the legal system itself, but also on the transportation efficiency of the economy.     

The Marshallian Market and the Walrasian Economy. Two Incompatible Bedfellows

The aim of this paper is to question a view which is usually taken for granted, namely that the Marshallian partial equilibrium and Walrasian general equilibrium analysis stand in a relationship of continuity. It will be claimed that the contrary is true: the generalisation of the Marshallian market does not lead to a Walrasian economy or, conversely, the Walrasian economy is not composed of Marshallian markets. To bring this point home, the basic methodological choices underpinning the analysis of the Marshallian market and of the Walrasian economy will be compared. The issue of why no full-fledged Marshallian representation of the economy has arisen which might stand as an alternative to the Walrasian account will also be investigated and a series of reasons for this lack of generalisation of the Marshallian market will be considered. Finally, it will be claimed that if the Marshallian economy concept has no explicit existence, it has nonetheless an implicit one. It forms the background against which a series of reasoning about the working of the economy as a whole, which cannot fit the Walrasian economy framework, are developed. No less prestigious names than those of Keynes, Hicks, Patinkin, Friedman, Clower and Leijonhufvud will be adduced as witnesses.     

MARRIAGE,DIVORCE, AND ASYMMETRIC INFORMATION

We use data on people's valuations of options outside marriage and beliefs about spouses' options. The data demonstrate that, in some couples, one spouse would be happier and the other spouse unhappier outside of some marriages, suggesting that bargaining takes place and that spouses have private information. We estimate a bargaining model with interdependent utility that quantifies the resulting inefficiencies. Our results show that people forgo some utility in order to make their spouses better off and, in doing so, offset much of the inefficiency generated by their imperfect knowledge. Thus, we find evidence of asymmetric information and interdependent utility in marriage.     

Optimal asset taxes in financial markets with aggregate uncertainty

This paper studies Pareto-optimal risk-sharing arrangements in a private information economy with aggregate uncertainty and ex ante heterogeneous agents. I show how to implement Pareto optima as equilibria when agents can trade claims to consumption contingent on aggregate shocks in financial markets. The first result is that if aggregate and idiosyncratic shocks are independent, the implementation of optimal allocations does not require any interventions in financial markets. This result can be extended to dynamic settings in the sense that, in this case, only savings need to be distorted, but not trades in financial markets. Second, I characterize optimal trading distortions in financial markets when aggregate and idiosyncratic shocks are not independent. In this case, optimal asset taxes must be higher for those securities that pay out in aggregate states in which consumption is more volatile. For instance, this can provide an efficiency justification for the frequently observed differential tax treatment of different asset classes, such as debt and equity claims.