An admissible set occurring in various bargaining situations

Given a set of alternatives S and a binary relation M on S the admissible set of the pair (S, M) is defined to be the set of maximal elements with respect to the transitive closure of M. It is shown that existing solutions in game theory and mathematical economics are special cases of this concept (they are admissible sets of a natural S and M). These include the core of an n-person cooperative game, Nash equilibria of a noncooperative game, and the max-min solution of a two-person zero sum game. The competitive equilibrium prices of a finite exchange economy are always contained in its admissible set. Special general properties of the admissible set are discussed. These include existence, stability, and a stochastic dynamic process which leads to outcomes in the admissible set with high probability.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

The genesis of expectations and of sunspot equilibria

The existence—under certain conditions—of sunspot equilibria in overlapping generations models is a well-known theoretical result, but a lot of research has still to be made to understand whether and how such equilibria may occur as a consequence of a dynamic process. In this paper, we explore a model with individuals having simple utility functions and discover situations in which the dynamic processes of expectations and observed prices do not converge in spite of the existence of static equilibria. In other words, unfounded beliefs do still have a permanent influence on the real economy but induce erratic evolutions.     

A dynamic model of expectations equilibrium

This paper describes a dynamic information adjustment process which achieves (rational) expectations equilibria for stochastic exchange environments. An informational temporary equilibrium is an exchange equilibrium in which agents' expectations are conditioned on their initial information and market data generated in previous informational temporary equilibria. An equilibrium is a temporary equilibrium which reveals no further information. This process leads to an equilibrium even when the data observed by agents is insufficient to permit the existence of an expectations equilibrium.     

Rational expectations in microeconomic models: An overview

This paper is an expository introduction to several topics of current research in the general equilibrium theory of rational expectations. More specifically, we discuss the existence of exact and approximate rational expectations equilibria, the implementation of equilibria, the behavior of learning and smoothing processes by which traders construct expectations from repeated observations of the market, and the lagged use of the information revealed by prices in an intertemporal sequence of markets. The purpose of this discussion is to introduce papers on these topics appearing in the Journal of Economic Theory Symposium on Rational Expectations in Microeconomic Models.     

Essential equilibria of large generalized games

We characterize the essential stability of games with a continuum of players, where strategy profiles may affect objective functions and admissible strategies. Taking into account the perturbations defined by a continuous mapping from a complete metric space of parameters to the space of continuous games, we prove that essential stability is a generic property and every game has a stable subset of equilibria. These results are extended to discontinuous large generalized games assuming that only payoff functions are subject to perturbations. We apply our results in an electoral game with a continuum of Cournot-Nash equilibria, where the unique essential equilibrium is that only politically engaged players participate in the electoral process. In addition, employing our results for discontinuous games, we determine the stability properties of competitive prices in large economies.     

Efficient communication in the electronic mail game

The literature on the electronic mail game shows that players' mutual expectations may lock them into requiring an inefficiently large number of confirmations and confirmations of confirmations from one another. This paper shows that this result hinges on the assumption that, with the exception of the first message, each player can only send a message when receiving an immediately preceding message. We show that, once this assumption is lifted, equilibria involving confirmations of confirmations no longer pass standard refinements of the Nash equilibrium, and are no longer evolutionary stable.     

Admissible market data structures: A complete characterization

This paper characterizes the market data which, if observed by traders in a stochastic exchange environment, will permit the general existence of (rational) expectations equilibria. It is proved that if a trader observes and conditions his expectations on some nonconstant market data, he must observe at least the equilibrium price and his own equilibrium trade. Any data which do not satisfy this requirement, such as the price alone, or the price and the volume of trade, will fail to permit the existence of an expectations equilibrium for some otherwise well-behaved stochastic environment.     

The cournot oligopoly and competitive equilibria as solutions to non-linear complementarity problems

The Cournot oligopoly and competitive equilibria are identified with solutions to non-linear complementarity problems, which leads to integration of the existence and stability proofs of these equilibria.     

Inflation and growth in a disequilibrium macroeconomic model

The purpose of this paper is to study the dynamics of temporary equilibria in a disequilibrium growth model. Dynamics rests upon adjustment mechanisms of prices, capital stock, money balances, and labour supply. Wage dynamics is supposed to be influenced by indexation processes, and this question is related to the investment behaviour of firms. We give sufficient conditions for existence, unicity, and asymptotic stability of steady states of this model. We also show that steady states correspond to a long-run Phillips curve, which is vertical when inflationary expectations are fully reflected in wage and price changes.     

ECONOMIC FLUCTUATIONS WITH INTERACTIVE AGENTS: DYNAMIC AND STOCHASTIC EXTERNALITIES*

This paper proposes a general modelling framework for macroeconomic dynamic behaviour of a large collection of interacting agents, and illustrates the procedure for a simple case of agents having the same binary decision set. Evolution over time of the fractions of agents using the same technology is modelled as a birth-and-death stochastic process with endogenized transition rates, and its master equation (Chapman-Kolmogorov backward equation) is expanded into power series in the total number of agents in the model. The first term of the expansion is the aggregate (macroeconomic) dynamic model. Stochastic dynamics of the proportions of agents using the same technology can exhibit multiple equilibria; this paper discusses an example with one locally unstable and two locally stable equilibria, with some simulation computer runs. There are two results of broad implication. One is the demonstration that stochastic dynamics allocates positive probabilities to all locally stable equilibria. Stochastic dynamics thus stands in sharp contrast to deterministic dynamics. In the latter, history (initial conditions) and expectations (often exogenously introduced discontinuous changes in trajectories) uniquely select the basin of attraction in which trajectories are eventually located. The second is the illustration of the usefulness of jump Markov processes in general, and birth-and-death processes in particular in economic modelling. Among several results specific to these processes, we show that the mean first passage time from one locally stable equilibrium to another is proportional to the exponential function of the height of the potential barrier separating the two basins of attraction of these two locally stable equilibria.     

The existence and computation of competitive equilibria in markets with an indivisible commodity

This paper considers an exchange economy called a generalized assignment market, in which sellers and buyers trade one indivisible commodity possibly with product differentiation for a perfectly divisible commodity. The existence of a competitive equilibrium in this economy is proved using Kakutani's fixed point theorem. This existence theorem is applied to a production economy in which sellers are formulated as producers with convex cost functions. Two examples of housing markets are provided and their competitive equilibria are numerically calculated.     

Belief-Based Refinements in Signalling Games

There are many economic problems which, when modelled as games of incomplete information, give rise to many sequential equilibria, severely limiting the usefulness of the model. There has recently been a large literature devoted to "refining" the set of equilibria in order to reduce this multiplicity by restricting the set of admissible disequilibrium beliefs. This paper argues that the logical foundations of some refinements and the equilibria they focus on are problematic and, further, proposes an alternative refinement that avoids the difficulties. We also provide an existence theorem covering a broad class of signalling games often studied in economics. Journal of Economic Literature Classification Numbers: C72, C70, D82.     

Equilibrium and optimality: Some imprints of David Gale

The paper is a review of some of the themes to which David Gale made lasting contributions. It touches upon a number of the fundamental issues in the Walrasian equilibrium theory (existence, uniqueness and stability), the overlapping generations model (non-optimality and indeterminacy of competitive equilibria), the von Neumann equilibrium (as a turnpike), and in the theory of decentralized intertemporal allocation through competitive prices (efficiency and golden rules, duality and existence of optimal programs).     

MARKET ECONOMIES WITH AN ENDOGENOUS SOCIAL DIVISION OF LABOR

I consider a general equilibrium model of a competitive market economy in which production is conducted through an endogenous social division of labor. I represent economic decision makers as “consumer–producers,” who consume as well as produce commodities. In this approach, the emergence of a nontrivial social division of labor is guided by Increasing Returns to Specialization (IRSpec) in production. Under IRSpec, I show existence of competitive equilibria, the two fundamental theorems of welfare economics, and characterize these equilibria. Markets equilibrate through the adjustment of the social division of labor; the production technologies completely determine the equilibrium prices.     

Approximate equilibria in microeconomic rational expectations models

For general equilibrium models in which prices transmit information among asymmetrically informed traders, strict rational expectations approximate equilibria are defined. A state-dependent price function is an ε-equilibrium if, when agents use their own information and that conveyed by prices, aggregate excess demand (in each state of the world) does not exceed ε. For any positive ε, existence requires only very mild assumptions—continuity and compact support. Moreover, there are revealing ε-equilibria for all smooth economies satisfying a dimensionality condition. In an open neighborhood of this case, existence of maximally revealing ε-equilibria holds.     

Informational efficiency with ambiguous information

This paper proves the existence of fully revealing rational expectations equilibria for almost all sets of beliefs when investors are ambiguity averse and have preferences that are characterized by Choquet expected utility with a convex capacity. The result implies that strong-form efficient equilibrium prices exist even when many investors in the market make use of information in a way that is substantially different from traditional models of financial markets.     

Monetary Neutrality and Optimality with Symmetric Partial Information

The neutrality and optimality of countercyclical monetary policy are examined in a representative economy featuring competitive equilibria in multiple markets and rational expectations based on a form of private information about current stochastic innovations in the economy. A necessary and sufficient condition for the neutrality of monetary policy is stated in terms of restrictions on the parameters of the linear rule describing prospective monetary feedback. Optimal monetary policy is fully characterized in terms of an alternative set of parameter restrictions. Optimal monetary feedback completely stabilizes deviations in commodity output by eliminating the influence of those current innovations about which agents cannot directly observe from the rational expectations of agents. [311]     

Competitive equilibria of economies with a continuum of consumers and aggregate shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of competitive equilibrium is proven and a recursive characterization is established. In particular, it is shown that for any competitive equilibrium, there is a payoff equivalent competitive equilibrium that is generated by a suitably defined recursive equilibrium.     

Industrialization and Expectations in a Small Open Economy

The degree of industrialization in a country can be measured by the diversity of intermediate goods produced in the country. I construct a small-country model in which this diversity is determined endogenously in the process of industrialization. My model shows that the character istics of equilibria depend on the substitutability among intermediate goods; particularly when the substitutability is large, there may be multiple equilibria. When such equilibria exist, optimistic expectations lead to a high degree of industrialization but pessimistic expectations yield a low degree of industrialization.
JEL Classification Numbers: O14, F43, F12