The rate of convergence of the core for a purely competitive sequence of economies

The purpose of the paper is to show that for ‘most’ purely competitive sequences of economies on a compact set of agents' characteristics the core converges to the set of equilibria at least as fast as the inverse of the number of agents. It is assumed that agents have smooth, convex preferences with non-zero Gaussian curvature. This rate of convergence is obtained for a purely competitive sequence with regular limit distribution.     

Smooth preferences and the regularity of equilibria

To study equilibria we describe an economy by its distribution of consumers' preferences and endowments. All preferences are smooth and weakly convex. Demand of an economy need not be single valued, but there is an open dense set of economies for which demand is a C¹-function in a neighborhood of the equilibrium prices. We call an economy regular if its excess demand is transversal to zero. A regular economy has locally unique equilibria. It is shown that regular economies form an open dense set on which the equilibrium price correspondence varies continuously and the number of equilibria is locally constant.     

Arbitrage and equilibrium in unbounded exchange economies with satiation

In his seminal paper on arbitrage and competitive equilibrium in unbounded exchange economies, Werner (1987) proved the existence of a competitive equilibrium, under a price no-arbitrage condition, without assuming either local or global nonsatiation. Werner’s existence result contrasts sharply with classical existence results for bounded exchange economies which require, at minimum, global nonsatiation at rational allocations. Why do unbounded exchange economies admit existence without local or global nonsatiation? This question is the focus of our paper. First, we show that in unbounded exchange economies, even if some agents’ preferences are satiated, the absence of arbitrage is sufficient for the existence of competitive equilibria, as long as each agent who is satiated has a nonempty set of useful net trades– that is, as long as agents’ preferences satisfy weak nonsatiation. Second, we provide a new approach to proving existence in unbounded exchange economies. The key step in our new approach is to transform the original economy to an economy satisfying global nonsatiation such that all equilibria of the transformed economy are equilibria of the original economy. What our approach makes clear is that it is precisely the condition of weak nonsatiation – a condition considerably weaker than local or global nonsatiation – that makes possible this transformation.     

Economies with a mean demand function

The present paper shows one way to look at G. Debreu and W. Hildenbrand's conjecture that certain atomless economies have mean demand functions. We conclude within the continuity framework that an economy gives rise ‘in general’ to a continuous mean demand function, and that the class of all atomless economies is ‘big’ in the space of all economies with a continuous mean demand function. The same problems are reconsidered within the framework of a space of differentiable preferences at the end.     

Core and equilibria in coalitional asymmetric information economies

We study coalitional economies under uncertainty and asymmetric information, assuming a finitely additive measure space of agents and finitely many possible states of nature. We introduce a suitable core notion showing that it is equivalent to Walrasian expectations equilibria. The finitely additive approach proposed in the paper permits also asymmetric information economy with countably many agents, rather than requiring only a continuum. Moreover, it allows us to overcome well-known criticisms related to the interpretation of individual private core notions.     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

Erratum to “Do pure indivisibilities prevent core equivalence? Core equivalence theorem in an atomless economy with purely indivisible commodities only” [J. Math. Econ. 41 (4–5) (2005) 571–601]

We consider a pure exchange economy with a continuum of agents and finitely many indivisible commodities. Every commodity can be consumed only in integer amounts. Thus, agents’ preferences are locally satiated and no commodity bundle has necessarily local cheaper points. We introduce a core which is an intermediate concept between the strong core and the weak core. In our economy, this core is the most natural concept in the sense that it coincides with the set of all exactly feasible Walras allocations.     

Nash-implementation of competitive equilibria via a bounded mechanism

We deal with the problem of providing incentives for the implementation of competitive outcomes in a pure-exchange economy with finitely many households. We construct a feasible price-quantity mechanism, which fully implements Walras equilibria via Nash equilibria in fairly general environments. Traders’ preferences need neither to be ordered nor continuous. In addition, the mechanism is such that no pure strategy is weakly dominated, hence is bounded (in the sense of Jackson 1992). In particular it makes no use of any integer game.     

Nash implementation with an infinite-dimensional trade space

This paper deals with the problem of implementing the Walras correspondence via Nash equilibria, in exchange economies with infinitely many commodities and finitely many households with possibly non-ordered preferences. We explicitly construct a feasible mechanism enjoying some features, which have natural economic meanings. Under a fairly weak boundary condition, this game fully implements the Walras equilibria. If this condition is not fulfilled, our mechanism nevertheless implements the constrained Walras equilibria. Received: 11 December 2003, Accepted: 29 July 2005 JEL Classification: D41, D43, D51 We thank (without implicating) Prof. Jean-Marc Bonnisseau and Cuong Le Van for helpful comments. The views expressed in this paper reflect those of the authors and not necessarily those of Calyon.     

Pareto ordering of distributions

In this paper, the state of an economy is described by a production plan and a distribution on the product space of agents' characteristics and the commodity space. An ordering on the set of states will be introduced and after a study of the structure of this ordering it will be shown that the close relationship between price equilibria and optimal states remains true in this framework.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

Stationary Markov equilibria on a non-compact self-justified set

The existence of stationary processes of temporary equilibria is examined in an OLG model, where there are finitely many commodities and consumers in each period, and endowments profiles and expectations profiles are subject to stochastic shocks. A state space is taken as the set of all payoff-relevant variables, and dynamics of the economy is captured as a stochastic process in the state space. In our model, however, the state space does not necessarily admit a compact-truncation consistent with the intertemporal restrictions because distributions over expectations profiles may have non-compact supports. As shown in Duffie et al. [Duffie, D., Geanakoplos, J., Mas-Colell, A., McLennan, A., 1994. Stationary Markov equilibria. Econometrica 62, 745–781), such a compact-truncation, called a self-justified set, is essential for the existence of stationary Markov equilibria. We extend their existence theorem so as to be applicable to our model.     

Characterization of optima in smooth Pareto economic systems

Simple techniques of calculus and geometry are used to study and characterize the optima of pure exchange economies in which the utility functions are smooth but not necessarily convex. It is also shown how one can reduce the problem of optimizing p functions on the manifold of states to that of maximizing a single function on a submanifold of this space. Two models are described: one in which a person cannot trade to an optimum unless he starts at one; and one in which a person cannot even get near a local Pareto optimum along continuous ‘trade curves’ from most initial distributions. Finally, the set of optima is described for a generic set of utility mappings.     

Existence of financial equilibria with restricted participation

We consider a two-date model of a financial exchange economy with finitely many agents having nonordered preferences and portfolio constraints. There is a market for physical commodities at any state today or tomorrow and financial transfers across time and across states are allowed by means of finitely many nominal assets or numéraire assets. We prove a general existence result of equilibria for such a financial exchange economy in which portfolios are defined by linear constraints, extending the framework of linear equality constraints by Balasko et al. (1990), and the existence results in the unconstrained case by Cass (1984, 2006), Werner (1985), Duffie (1987), and Geanakoplos and Polemarchakis (1986). Our main result is a consequence of an auxiliary result, also of interest for itself, in which agents’ portfolio constraints are defined by general closed convex sets and the financial structure is assumed to satisfy a “nonredundancy-type” assumption, weaker than the ones in Radner (1972) and Siconolfi (1989).     

The strong sequential core for two-period economies

The strong sequential core for two-stage economies with a possibly incomplete set of assets in period zero and trade in commodities in period one consists of those goods allocations that are in the classical core and moreover, after realization of the state of nature, in the core of the economy where executed asset contracts serve as initial endowments. The strong sequential core coincides with the classical core when all possible state-contingent contracts may serve as an asset. For finance economies it is shown that the strong sequential core is generically empty when there is an incomplete set of assets. Outside the setting of finance economies, we show that the strong sequential core can be empty even if there is a complete set of assets. If the set of constrained feasible allocations resulting from trading in assets, is enlarged to include also allocations outside the agents’ consumption sets, then a complete set of assets is sufficient for the equivalence of the resulting semi-strong sequential core and the classical core.     

When does the manufacturing reshoring strategy create value?

Reshoring has gained a lot of attention recently by academics and practitioners alike, and is promising to become even more relevant in the aftermath of the COVID-19 pandemic. Building on earlier research on the effects of reshoring announcements on the short-term market value of the firm, this work employs an event-study methodology and aims to understand under which circumstances the market perceives reshoring as potentially more (or less) value-creating. The analysis of a sample of 64 reshoring instances from 2005 to 2019, announced by 54 firms from eight developed economies, suggests that investors are more confident in the firm's future cash-flow potential when: a) it invests in productive activities at home, instead of overseas, i.e. ‘kept-from-offshoring’ (as opposed to actual relocations of activities, i.e. ‘back-reshoring’); b) the reshoring instance is communicated as a ‘plan’ (rather than a fixed ‘decision’); c) no state- or government-induced financial incentives are involved; d) the motivations are primarily ‘cost-efficiency seeking’ (rather than ‘customer perceived value seeking’).     

Sequential regularity in smooth production economies

In general equilibrium models where agents trade sequentially in multiple periods, the equilibria that endogenously occur in later periods can be robustly indeterminate if production sets are not everywhere differentiable (as. for example, with linear activities). The present paper proves that if technology is smooth, then equilibria are sequentially regular. That is. the equilibria of the endogenously generated economies occurring in later periods that confirm the unanimous expectations formed by agents in earlier periods are regular (and thus, for example, isolated from other equilibria). The paper also proves and utilizes the standard result that the overall intertemporal equilibria are regular.