CK-Equilibria and Informational Efficiency in a Competitive Economy

We consider a very simple competitive economy with infinitesimal agents and asymmetric information. We define a Common Knowledge (CK hereafter) Equilibrium as a price distribution compatible with CK of market clearing and rationality. At equilibrium, expectational mistakes and incorrect information revelation by price are possible. But, whenever unique, the CK equilibrium is a fully revealing Rational Expectations Equilibrium. Hence uniqueness of equilibrium means market informational efficiency. We give different conditions of uniqueness of equilibrium bearing on the information structure. The first ones emphasize that many informed agents are required for market efficiency. Agents need not be perfectly informed, but each "piece" of information has to be known by a large enough proportion of the population. The main result is a characterization of the information structures allowing for local uniqueness: multiplicity of equilibria obtains when all the agents have to extract information from the price to obtain information about the same event. We show that this result holds in an exchange economy with finitely many goods and generic preferences. Finally, we provide a simple market game in which the CK-equilibria obtain through infinitely repeated elimination of weakly dominated strategies.

Reputation-based pricing and price improvements in dealership markets

In many security markets, dealers trade with their regular clients at a discount relative to prevailing bid and ask quotes. In this article we provide an explanation to this phenomenon. We consider a dealer and an investor engaged in a long-term relationship. The dealer assigns a reputational index to his client. This index increases (reputation decreases) when the client conducts trades which results in a loss for the regular dealer. The dealer grants a price improvement if and only if the client's index is smaller than a threshold and suspends price improvements otherwise. We show that this pricing strategy induces the investor to refrain from exploiting private information against her regular dealer. We also find that it worsens the quotes posted by other dealers. For this reason, there are cases in which the investor is better off if long-term relationships are impossible (for instance, if trading is anonymous). Our model predicts that a dealer's decision to grant a price improvement depends on his past trading profits with the trader requesting the improvement.Market microstructure; Reputation and Implicit contracts; Non-Anonymous trading

Privileged information exacerbates market volatility

We study how asymmetric information affects market volatility in a linear setup where the outcome is determined by forecasts about this same outcome. The unique rational expectations equilibrium will be stable when it is the only rationalizable solution. It has been established in the literature that stability is obtained when the sensitivity of the outcome to agents' forecasts is less than 1, provided that this sensitivity is common knowledge. Relaxing this common knowledge assumption, instability is obtained when the proportion of agents who a priori know the sensitivity is large, and the uninformed agents believe it is possible that the sensitivity is greater than 1.Asymmetric information, common knowledge, eductive learning, rational expectations, rationalizability, volatility.

Strongly rational expectations equilibria with endogenous acquisition of information

This paper analyzes conditions for existence of a strongly rational expectations equilibrium (SREE) in models with private information, where the amount of private information is endogenously determined. It is shown that the conditions for existence of a SREE known from models with exogenously given private information do not change as long as it is impossible to use the information transmitted through market prices. In contrast, these conditions are too weak, when there is such learning from prices. It turns out that the properties of the function which describes the costs that are associated with the individual acquisition of information are important in this respect. In case of constant marginal costs, prices must be half as informative than private signals in order for a SREE to exist. An interpretation of this result that falls back on the famous Grossman– Stiglitz–Paradox is also given.Eductive Learning, Private Information, Rational Expectations, Strongly Rational Expectations Equilibrium

Stabilizing through Poor Information

This paper studies the effect of asymmetric information on equilibrium stability in a class of linear models where the actual state depends on the forecasts about it. Stability is deffined by the so-called eductive criterion which relies on common knowledge of rationality. The main result is that stability obtains when the proportion of uninformed agents is high enough. The expectational behavior of these agents indeed displays more inertia. This behavior, and then the actual outcome, are therefore easier to predict. This result is linked to the issue of informational efficiency. Extensions to cases with higher order uncertainty, additional agents heterogeneity, and sunspots are also considered.Asymmetric information, eductive stability, rational expecta- tions, stabilization.

Strongly rational expectations equilibria with endogenous acquisition of information

This paper analyzes conditions for existence of a strongly rational expectations equilibrium (SREE) in models with private information, where the amount of private information is endogenously determined. It is shown that the conditions for existence of a SREE known from models with exogenously given private information do not change as long as it is impossible to use the information transmitted through market prices. In contrast, these conditions are too weak, when there is such learning from prices. It turns out that the properties of the function which describes the costs that are associated with the individual acquisition of information are important in this respect. In case of constant marginal costs, prices must be half as informative than private signals in order for a SREE to exist. An interpretation of this result that falls back on the famous Grossman–Stiglitz–Paradox is also given

Appariements sur le Marché du Logement.

Cette publication n'a pas de résumé

Appariements sur le Marché du Logement

Cet article souhaite contribuer à une théorie du marché du logement locatif où les frictions de recherche sont rendues endogènes par une fonction d’appariement entre propriétaires et locataires potentiels. Le loyer est déterminé par une négociation à la Nash entre propriétaires et locataires ou choisi par le propriétaire ex ante. L’introduction de frictions de recherche modifie largement les résultats traditionnels et la statique comparative de l’état stationnaire est menée dans cette perspective. On étudie, notamment, un équilibre de court terme (le cas d’une ville fermée) et un autre de moyen terme (le cas d’une ville ouverte où l’offre de logements est fixe et les travailleurs libres d’entrer, ou non, sur le marché). Dans les deux cas, on discute les conséquences d’une taxation des appartements vacants. On retrouve un résultat relativement général en présence de frictions importantes : les mesures qui tendent à protéger les agents d’un certain type (employés, locataires) le font au détriment de ceux qui aspirent à accéder à ce statut (chômeurs, personnes ayant des difficultés à se loger)

Stabilizing through Poor Information *

Abstract This paper studies the effect of asymmetric information on equilibrium stability in a class of linear models where the actual state depends on the forecasts about it. Stability is defined by the so-called eductive criterion which relies on common knowledge of rationality. The main result is that stability obtains when the proportion of uninformed agents is high enough. The expectational behavior of these agents indeed displays more inertia. This behavior, and then the actual outcome, are therefore easier to predict. This result is linked to the issue of informational efficiency. Extensions to cases with higher order uncertainty, additional agents' heterogeneity, and sunspots are also considered