On efficient trading mechanisms between one seller and n buyers

Myerson and Satterthwaite (1983) prove that if one seller and one buyer have independent private valuations for an indivisible object then no individually rational and incentive compatible trading mechanism can guarantee ex post efficiency when gains from trade are uncertain. Makowski and Mezzetti (1993) show that this is not the case when there are at least two buyers. In the latter context, if the highest possible seller's valuation is not too large, we provide an ex post efficient mechanism in which the mechanism designer and the agents are not required to know the probability distribution for the seller's valuation. Received: February 18, 1998 / Accepted: September 10, 1999     

Efficient trading with restriction

In a classical paper by Cramton, Gibbons, and Klemperer (CGK) (Econometrica 55:615–632, 1987), it is shown that an efficient trading mechanism exists if traders’ initial endowments are not too asymmetric. In this paper, we extend the CGK model by assuming that traders are not allowed to consume more than a given amount (upper bound) of the good. In the CGK model, instead the only restriction is that no agent can consume more than the entire endowment in the economy. By varying this upper bound, we characterize the set of endowments (efficient region) in which efficient trading mechanisms exist in terms of this upper bound. We show that the efficient region becomes smaller when the upper bound decreases. On the other hand, when this upper bound becomes the entire endowment of the economy, we obtain the result in CGK as a special case.     

Credit market segmentation,essentiality of commodities,and supermodularity

We consider incomplete market economies where agents are subject to price-dependent trading constraints compatible with credit market segmentation. Equilibrium existence is guaranteed when either commodities are essential, i.e, indifference curves through individuals’ endowments do not intersect the boundary of the consumption set, or utility functions are concave and supermodular. The smoothness of mappings representing preferences, financial promises, or trading constraints is not required. Hence, we may include in our framework economies where ambiguity is allowed and agents maximize the minimum expected utility over a set of priors, or where markets include non-recourse collateralized loans.     

Two-sided unobservable investment,bargaining, and efficiency

Asymmetric information can lead to inefficient outcomes in many bargaining contexts. It is sometimes natural to think of asymmetric information as emerging from imperfect observation of previously taken actions (e.g., obtaining compliments or substitutes for the item being bargained over). How do such strategic investment choices prior to bargaining interact with the strategic problem of bargaining under private information? We focus on bilateral bargaining when players can make unobserved investments in the value of the item prior to their interaction. With two-sided hidden investment, strategic uncertainty induces a post-investment problem analogous to that in Myerson and Satterthwaite (J Econ Theory 29(2):265–281, 1983), and inefficiencies might be expected to arise. But, there are strong incentives to avoid investment levels that do not lead to trade and this must be anticipated by the other trader. This effect is shown to drive a form of unraveling; as a result in every equilibrium to the larger game the good ends up in the hands of the agent with the higher valuation.     

On the structure of the set of fixed price equilibria

Working in the framework suggested by Drèze, this paper studies the number of fixed price equilibria and their continuity with respect to the price system. In an exchange economy, the concept of a rationing scheme is introduced, which specifies how shortages are shared among agents. For given utility functions and a given rationing scheme, under standard assumptions, an existence theorem is recalled, and it is shown that the graph of the equilibrium correspondence, when prices and initial endowments vary, is a piecewise continuously differentiable manifold. Moreover, generically, the number of equilibria for an economy, at given prices, is finite and the set of equilibria varies continuously with the price system and the initial endowments.     

Transaction costs and a redundant security: divergence of individual and social relevance

This paper shows that, in markets with transaction costs, even if a redundant security does not even save individual investors' total costs for their security trading, the prices of the other securities may well be different were it to not be available for trade, resulting in a different equilibrium consumption allocation. In this sense, a redundant security may give rise to the divergence of individual and social relevance in markets with transaction costs. We then show that this divergence may also be a robust phenomenon with respect to perturbations in utility functions, initial endowments, and transaction costs.     

Regular economies and sets of measure zero in Banach spaces

Using concepts of measure zero in Banach spaces, Debreu result guaranteeing full measure for the economies with stable and finite number of equilibria is generalized. Here, we include utility functions as well as initial endowments in the definition of an economy.     

Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

Equilibrium price dynamics in an overlapping-generations exchange economy

An extension to the Yaari (1965)–Blanchard (1985) continuous time overlapping generations model for an endowment Arrow–Debreu economy with an age-structured population is presented. It is proved that Arrow–Debreu equilibrium prices are represented by a double linear integral equation, and depend on the age-distributions of population and endowments. For an economy with a balanced growth, and logarithmic utility, we prove that bubbles may exist if endowments are distributed earlier than some critical age.     

A note on the equilibrium theory of economies with asymmetric information

In this note, we give an equilibrium existence theorem for exchange economies with asymmetric information and with an infinite dimensional commodity space. In our model, we assume that preferences are represented by well behaved utility functions, the positive cone has a non empty interior and the individual rational utility set is compact. Our result complements the corresponding one in Podczeck and Yannelis (2008), in the sense that is applicable to commodity spaces in which the order intervals are (possibly) not compact with respect to any Hausdorff linear topology.     

Equilibrium and arbitrage in incomplete asset markets with fixed prices

At arbitrary prices of commodities and assets, fix-price equilibria exist under weak assumptions: endowments need not satisfy an interiority condition, utility functions need only satisfy a very weak monotonicity requirement, and the asset return matrix allows for redundant assets. Prices of assets may permit arbitrage. At equilibrium, though restricted through endogenously determined trading constraints, arbitrage possibilities may persist; in an example, an individual holds an arbitrage portfolio.     

Inefficiency of equilibria with incomplete markets

As is well known, equilibria with incomplete markets are generically Pareto inefficient. In this paper, we demonstrate the leading role of a budget constraint in the occurrence of Pareto inefficiency of equilibria with incomplete markets. Specifically, on the basis of the classical two-period one-good pure exchange model we prove that so long as a budget constraint is met for all agents, equilibria with incomplete markets are generically Pareto inefficient in initial endowments and utility functions regardless of the optimization behavior of each agent. All we require of utility functions is a very weak hypothesis called current monotonicity. A simple unified method applicable to both a real asset case and a nominal asset case is presented, so that our claim is proved in both cases.     

Piecewise linear exchange equilibrium

It is known that if a pure exchange model in which all consumers have linear utility functions has an equilibrium it has one which is rational in the initial data. Examples show on the other hand that this is no longer true in general if utility functions are merely piecewise linear. In this note we observe that for the case of two traders the rationality result carries over and we sketch a finite procedure for calculating the equilibrium.     

Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

Asset price and wealth dynamics in a financial market with heterogeneous agents

This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each period each group allocates its wealth between the risky asset and the safe asset according to myopic expected utility maximization, but the two groups have heterogeneous beliefs about the price change over the next period: the chartists are trend extrapolators, while the fundamentalists expect that the price will return to the fundamental. We assume that investors’ optimal demand for the risky asset depends on wealth, as a result of CRRA utility. A market maker is assumed to adjust the market price at the end of each trading period, based on excess demand and on changes of the underlying reference price. The model results in a nonlinear discrete-time dynamical system, with growing price and wealth processes, but it is reduced to a stationary system in terms of asset returns and wealth shares of the two groups. It is shown that the long-run market dynamics are highly dependent on the parameters which characterize agents’ behaviour as well as on the initial condition. Moreover, for wide ranges of the parameters a (locally) stable fundamental steady state coexists with a stable ‘non-fundamental’ steady state, or with a stable closed orbit, where only chartists survive in the long run: such cases require the numerical and graphical investigation of the basins of attraction. Other dynamic scenarios include periodic orbits and more complex attractors, where in general both types of agents survive in the long run, with time-varying wealth fractions.     

The revelation of information in strategic market games: A critique of rational expectations equilibrium

We criticize the R.E.E. approach to asymmetric information general equilibrium because it does not explain how information gets ‘into’ the prices. This leads to well-known paradoxes. We suggest a multiperiod game instead, where the flow of information into and out of prices is explicitly modeled. In our game Nash equilibria (N.E.) (1) generalize Walrasian equilibria to asymmetric information, (2) exist generically, (3) eliminate pure speculation, (4) allow prices to reveal information and markets to become more efficient over time, (5) are consistent with the weak efficient markets hypothesis that tracking past prices is not profitable, (6) yet always lead to higher utility for better informed agents (such as experts). Throughout the paper we use one concrete game. In the last section we prove that there is a broad range of games that would have the same properties.     

Competitive market equilibrium under asymmetric information

This paper studies the existence of a competitive market equilibrium under asymmetric information. There are two agents involved in the trading of the risky assets: an “informed” trader and an “ordinary” trader. The market is competitive and the ordinary agent can infer the insider information from the price dynamics of the risky assets. The insider information is considered to be the total supply of the risky assets. The definition of market equilibrium is based on the law of supply-demand as described by a rational expectations equilibrium of the Grossman and Stiglitz (Am Econ Rev 70:393–408, 1980) model. We show that equilibrium can be attained by linear dynamics of an admissible price process of the risky assets for a given linear supply dynamics.      

An equilibrium model of insider trading in continuous time

We study a Bayesian–Nash equilibrium model of insider trading in continuous time. The supply of the risky asset is assumed to be stochastic. This supply can be interpreted as noise from nonrational traders (noise traders). A rational informed investor (the insider) has private information on the growth rate of the dividend flow rewarded by the risky asset. She is risk averse and maximizes her inter-temporal utility rate over an infinite time-horizon. The market is cleared by a risk neutral market maker who sets the price of the risky asset competitively as the conditional present value of future dividends, given the information supplied by the dividend history and the cumulative order flow. Due to the presence of noise traders, the market demand does not fully reveal the insider’s private information, which slowly becomes incorporated in prices. An interesting result of the paper is that a nonstandard linear filtering procedure gives an a priori form for the equilibrium strategy to be postulated. We show the existence of a stationary linear equilibrium where the insider acts strategically by taking advantage of the camouflage provided by the noise which affects the market maker’s estimates on private information. In this equilibrium, we find that the insider’s returns on the stock are uncorrelated over long periods of time. Finally, we show that the instantaneous variance of the price under asymmetric information lies between the instantaneous variance of the price under complete and incomplete information. The converse inequalities hold true for the unconditional variance of the price.     

Financial Markets, Development and Economic Growth: Tales of Informational Asymmetries

Abstract.  The development of financial systems is very often characterised by the development of innovative financial contracts which allow a more efficient allocation of resources and a higher level of capital productivity and economic growth. By exploiting the microeconomic theory of the optimal financial contract under asymmetric information, economists have recently managed to shed new light on the well studied issue of the relationship between financial market development and economic growth. This paper reviews the most recent progress of this literature which shows that the amount of information asymmetry in the credit market and the degree of heterogeneity between borrowers (typically firms) and lenders (typically workers or savers) determine the nature of the financial system. Differences in endowments and in the level of information distribution can give rise to very different financial contracts which affect, and in turn are affected, by capital accumulation and growth.     

Indescribability and its irrelevance for contractual incompleteness

The incomplete contracts literature often cites indescribable contingencies as a major obstacle to the creation of complete contracts. Using agents’ minimum foresight concerning possible future payoffs, Maskin and Tirole (Rev Econ Stud 66:83–114, 1999) show that indescribability does not matter for contractual incompleteness as long as there is symmetric information at both the contracting stage and the trading stage. This is called the irrelevance theorem. The following generalization of the irrelevance theorem is shown here: indescribability does not matter even in the presence of asymmetric information at the trading stage, as long as there is symmetric information at the contracting stage. This is an important clarification because Kunimoto (Econ Lett 99:367–370, 2008) shows that indescribability can matter if there is asymmetric information at both stages. It is thus argued that asymmetric information at the contracting stage is necessary for indescribability to be important in the rational agents contracting model.