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.     

Correlated equilibrium and sunspot equilibrium

Summary We show by an example that the sunspot equilibria of a competitive economy are not equivalent to the correlated equilibria if sunspots generate transfers between (extrinsic) states of nature (through a contingent commodities market). Nevertheless, we prove that the sunspot equilibrium allocations of a standard overlapping generations economy coincide with the (strategic form) correlated equilibrium allocations of a natural market game mimicking the economy.     

Econometrics and equilibrium models

In Rational Econometric Man, Edward Nell and Karim Errouaki present a welcome and timely case for the view that econometrics and econometric model-building may not be the magic tools to solve all empirical questions despite what many seem to have thought they were in the 1960s. Here I examine some possible problems with econometric models that have to do with their usually taking the form of equilibrium models. Some of these problems were recognized by Trygve Haavelmo decades ago. And as Aris Spanos has recently discussed, the problems are often the result of what we say in our textbooks. Some problems have to do with what we mean by econometric parameters and others with how we use probabilities.     

Environmental performance and equilibrium

Abstract.  In this paper we show why firms' or industries' rankings in terms of environmental performance depend not only on the technology but also on market equilibrium. Between two industries committed to the same environmental constraint, the more eco-efficient is the one with the higher output level. By comparing industries and firms, we show that the rankings are not robust, for they are affected by market outcome. The role of eco-efficiency in firms' profitability in equilibrium is also scrutinized. All this shows that the usual eco-efficiency indicators are inadequate. To tackle this problem, we propose a sound indicator.     

Mistaken self-perception and equilibrium

Summary. Motivated by real-world information economics problems and by experimental findings on overconfidence, this paper introduces a general epistemic construction to model strategic interaction with incomplete information, where the players self-perception may be mistaken. This allows us to rigorously describe equilibrium play, by formulating appropriate equilibrium concepts. We show that there always exist objective equilibria, where the players correctly anticipate each others strategies without attempting to make sense of them, and that these outcomes coincide with the equilibria of an associated Bayesian game with subjective priors. In population games, these equilibria can also be always introspectively rationalized by the players, despite their possibly mistaken self-perception.Received: Received: May, 12, 2003; revised version: 3 December 2004, Revised: 3 December 2004, JEL Classification Numbers: J31, D82, D83.I thank Massimiliano Amarante, Eddie Dekel, Massimo Marinacci, Jean Francois Mertens, Giuseppe Moscarini, Paolo Siconolfi, Marciano Siniscalchi, Joel Sobel, and an anonymous referee.     

Excess demand functions, equilibrium prices, and existence of equilibrium

Summary. For continuous aggregate excess demand functions of economies, the existing literature (e.g. Sonnenschein (1972, 1973), Mantel (1974), Debreu (1974), Mas-Colell (1977), etc.) achieves a complete characterization only when the functions are defined on special subsets of positive prices. In this paper, we allow the functions to be defined on a larger class of price sets, (allowing, for example the closed unit simplex, including its boundary). Besides characterizing excess demands for a larger class of economies, our extension provides a useful tool for proving other results. It allows us to characterize the equilibrium price set for a larger class of economies. It also permits extending Uzawa's observation (1962), by showing that Brouwer's Fixed-Point Theorem is implied by the Arrow-Debreu Equilibrium Existence Theorem (1954, Theorem I). Received: October 18, 1995; revised version June 28, 1996     

Program equilibrium

In a computerized setting, players' strategies can be implemented by computer programs, to be executed on a shared computational devise. This situation becomes typical to new Internet economies, where agent technologies play a major role. This allows the definition of a program equilibrium. Following the fundamental ideas introduced by von Neumann in the 1940s (in parallel to his seminal contribution to game theory), a computer program can be used both as a set of instructions, as well as a file that can be read and compared with other files. We show that this idea implies that in a program equilibrium of the one-shot prisoners dilemma mutual cooperation is obtained. More generally, we show that the set of program equilibrium payoffs of a game coincides with the set of feasible and individually rational payoffs of it.     

Waiting times and equilibrium selection

Summary. This paper shows how graphs can be used to calculate waiting times in models of equilibrium selection. It also shows how reducing the state space can simplify the calculations of both waiting times and selected equilibria. The results are applied to potential games and games with strategic complementarities.Received: 31 December 2002, Revised: 25 October 2003, JEL Classification Numbers: C72, C73.Alan Beggs: I am grateful to an anonymous referee for helpful comments.     

Power sharing and electoral equilibrium

This paper considers a model of (consensual) democracy where political parties engage first in electoral competition, and they share policy-making power afterward according with the votes gathered in the election. The paper uncovers the difficulties to guarantee stability in this institutional setting; and it provides a condition of symmetry on parties’ political motivations that ensures the existence of pure strategy equilibrium under a broad family of power sharing rules, ranging from fully proportional to winner-take-all. The equilibrium analysis shows that power sharing and ideology exert a centrifugal force on policy platforms that increases party polarization, with the paradoxical result that consensual democracies can actually lead to more radical electoral campaigns than winner-take-all.     

Monopolistic equilibrium and involuntary unemployment

This note provides a simple example of an economy in which involuntary unemployment may be the consequence of monopolistic behavior on the product market.     

Financial constraints and unemployment equilibrium

The aim of this paper is to show that a robust determination of unemployment equilibria can be based on the integration of credit rationing into a general equilibrium model. We first review some of the Keynesian macroeconomic models. We show that the problems bequeathed by Keynes’ legacy are only partially solved by the strand of the new Keynesian economics based on market imperfections and endogenous rigidities. In order to overcome these problems we refer to credit rationing. In particular, we build a simple general equilibrium model in which prices are–in principle–perfectly flexible and credit rationing implies unemployment equilibria.     

Migration equilibrium and variational inequalities

"In this paper, an equilibrium model of human migration is presented which can handle many classes of migrants and locations, in addition to equalities and inequalities. The equilibrium conditions are stated and then formulated as a variational inequality problem. Qualitative properties and computational aspects are briefly discussed."     

Network formation and stable equilibrium

We study the non-cooperative formation of a (directed) network that builds upon one-way immediate links. Our novel feature is that we require circular paths of links for productive activities. This captures more clearly the higher level of coordination that is often required for network formations than models such as those of Jackson and Wolinsky [A strategic model of social and economic networks, J. Econ. Theory 71 (1996) 44-74] and Bala and Goyal [A non-cooperative model of network formation, Econometrica 68 (2000) 1181-1229], in that in our model a single agent's unilateral action is limited in affecting the network structure. We completely characterize the class of Nash equilibria by showing that the minimality of a graph is both necessary and sufficient (Theorem 1). We also propose the concept of a stable network that is similar to the pairwise stability of Jackson and Wolinsky (1996). We show that stable equilibria are a wheel, a trivial network, or a sub-wheel partitioned network (Theorem 2). We modify the Bala and Goyal (2000) dynamic process with inertia, and obtain the convergence to stable equilibria regardless of the initial state (Theorem 3).     

General equilibrium and resource economics

Summary. For a number of reasons a large class of general equilibrium models from the field of resource economics does not allow for an equilibrium analysis along the lines of the theory of infinite dimensional commodity spaces. The reasons concern the choice of the commodity space and the applicability of properness assumptions with respect to preferences and the technology. This paper illustrates the difficulties and shows for a prototype model how the problems can successfully be tackled by the use of a limit argument on equilibria in the truncated economies. Received: May 2, 1996; revised version: May 13, 1998     

Additive values and market equilibrium

This letter is based on the simple observation that in equilibrium, values must be additive, i.e., the value of a basket of goods is equal to the sum of the values of the items contained in the basket. The observation combined with the conditions of Pareto optimality, gives an easy way to many well known results in the theory of equilibrium under uncertainty.