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.     

Consistent collusion-proofness and correlation in exchange economies

We present a feasible strategic market mechanism with finitely many agents whose Nash, semi-strong Nash and coalition-proof Nash equilibria fully implement the Walrasian equilibria. We define a strategic equilibrium concept, called correlated semi-strong equilibrium, and show that the Walrasian equilibria can be implemented by these equilibria, and also by the coalition-proof correlated equilibria of our mechanism. We show that these two concepts, suitably modified with transfers, fully implement the Pareto optimal allocations.     

On characterizing the probability of survival in a large competitive economy

We consider a Walrasian exchange economy in which an agent is characterized by a utility function, a random endowment vector, and a function that specifies the minimum expenditure necessary for survival at a given price system. If at any equilibrium price system, the income of the agent is no more than the minimum expenditure for survival, it is ruined. The main results characterize the probability of ruin when the number of agents is large. The implications of stochastic dependence among agents are explored.     

The endogenous formation of cartels

We discuss large but finite linear market games which are represented as minima of finitely many measures. These games describe markets in which the agents decompose into finitely many disjoint groups each of which holds a corner of the market. Most solution concepts like the core, the Shapley value, or the Walrasian equilibrium tend to favor the short side of such market excessively. That is, in the replicated limit or in the continuum version, the short side is awarded all the possible profits even though cooperation within the grand coalition is required. We show that vNM-Stable Sets differ markedly. For large but finite player sets we exhibit vNM solutions that assign wealth to the long side of the market. It turns out that the shape of the generic vNM-Stable Set suggests cartelization of the market.Received: 29 March 2000, Accepted: 26 October 2001, JEL Classification: C71, D70     

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.     

Representation of non-transferable utility games by coalition production economies

We prove that every compactly generated non-transferable utility (NTU) game can be generated by a coalition production economy. The set of Walrasian payoff vectors for our induced coalition production economy coincides with the inner core of the balanced cover of the original game. This equivalence depends heavily on our representation. We exemplify that this equivalence need not hold in other representations. We also give a sufficient condition for the existence of a Walrasian equilibrium for our induced coalition production 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.     

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.     

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).     

Equilibrium in a market with intermediation is Walrasian

We show that a profit maximizing monopolistic intermediary may behave approximately like a Walrasian auctioneer by setting bid and ask prices nearly equal to Walrasian equilibrium prices. In our model agents choose to trade either through the intermediary or privately. Buyers (sellers) trading through the intermediary potentially trade immediately at the ask (bid) price, but sacrifice the spread as gains. A buyer or seller who trades privately shares all the gains to trade with this trading partner, but risks costly delay in finding a partner. We show that as the cost of delay vanishes, the equilibrium bid and ask prices converge to the Walrasian equilibrium prices. Received: 2 February 1996 / Accepted: 28 March 1997     

An equivalence theorem for a differential information economy

In a pure exchange economy with differential information and a finite set of traders, physical commodities and states of nature, we characterize the Walrasian expectations or Radner equilibria by using the veto power of the grand coalition. We prove that an allocation x is a Radner equilibrium allocation if and only if it is “privately non-dominated” by the grand coalition in every economy obtained by perturbing the original initial endowments in the direction of x. The first and second welfare theorems become particular cases of our main result. Since the deterministic Arrow–Debreu–McKenzie model is a special case of the differential information economy model we also provide a new characterization of the Walrasian equilibria.     

On iterative procedures of asymptotic inference

Abstract  An informal discussion is given on performing an unconstrained maximization or solving non-linear equations of statistics by iterative methods with the quadratic termination property. It is shown that if a miximized function, e.g. likelihood, is asymptotically quadratic, then for asymptotically efficient inference finitely many iterations are needed.     

A limit theorem for systems of social interactions

In this paper, we establish a convergence result for equilibria in systems of social interactions with many locally and globally interacting players. Assuming spacial homogeneity and that interactions between different agents are not too strong, we show that equilibria of systems with finitely many players converge to the unique equilibrium of a benchmark system with infinitely many agents. We prove convergence of individual actions and of average behavior. Our results also apply to a class of interaction games.     

Measuring the set of blocking coalitions in infinite dimensional economies

The classical core-Walras equivalence is investigated via the measurement of the set of blocking coalitions. In the framework of continuum economies with an infinite dimensional space of commodities, we find the measure of the set of coalitions that block a non-competitive Pareto optimal allocation. Then, from the relation between coalitions of a continuum economy with a finite number of types and fuzzy coalitions of an economy with finitely many agents, the previous results are translated as results on the measure of blocking fuzzy coalitions. Both results imply classically formulated core-Walras equivalence theorems. Finally, the measure of blocking "social communication structures" is determined.     

The effects of total factor productivity and export shocks on a small open economy with unemployment

The paper analyzes the dynamic effects of a supply side shock and a demand side shock, which hit an open economy with unemployment. The supply side shock is modeled as a reduction in total factor productivity, whereas the demand side shock is caused by a drop in exports. The model builds upon the small one-sector two-good open economy framework described in Turnovsky (2000, chapter 11.3). In contrast to this standard framework, in which Walrasian labor markets are assumed, search unemployment and wage bargaining are introduced, and unemployment results from time consuming and costly matching of vacancies with searching agents. Using a plausible calibration of the model, the dynamic adjustments of unemployment, output, and other economic key variables are analyzed. We find that a negative export shock primarily has effects on consumption and welfare, but not on unemployment and output, whereas the supply side shock leads to considerable responses of unemployment, output, consumption and welfare. If both shocks together hit the economy, the changes in consumption and welfare almost double.     

Pareto efficiency in the jungle

We revisit the jungle economy of Piccione and Rubinstein (Econ J 117(July):883–896, 2007) in which the allocation of resources is driven by coercion. In this economy the unique equilibrium satisfies lexicographic maximization. We show that relaxing the assumptions on consumption sets and preferences slightly, allocations other than lexicographic maximizers can be jungle equilibria. We attribute this result to single unilateral taking where a stronger agent takes goods from only one weaker agent. Once multiple unilateral takings are introduced, we show that jungle equilibria coincide with lexicographic maximization under weak assumptions. However, we also present examples of equilibria that are Pareto inefficient, where voluntary gift giving by stronger agents is needed to achieve Pareto efficiency and even voluntary trade has a role in the jungle.     

The equilibrium set of infinite dimensional Walrasian economies and the natural projection

The natural projection plays a fundamental role to understand the behavior of the Walrasian economies. In this paper, we extend this method to analyze the behavior of infinite dimensional economies. We introduce the definition of the social equilibrium set, and we show that there exists a bijection between this set and the Walrasian equilibrium set of an infinite dimensional economy. In order to describe the main topological characteristics of both sets, we analyze the main differential characteristics of the excess utility function and then, we extend the method of the natural projection as suggested by Y. Balasko.     

The core of the inductive limit of a direct system of economies with a communication structure

This paper studies direct systems of finite, that is with finitely many agents, communication structures, finite (balanced and superadditive) NTU games and finite economies. The inductive limit of such a system is again a communication structure, an NTU game or an economy, this time possibly with infinitely many agents. As a matter of fact, each infinite communication structure, each infinite NTU game and each infinite economy, is the inductive limit of a direct system of finite communication structures, finite NTU games and finite economies. A communication game is an NTU game with a communication structure on the set of players. To each economy, there corresponds a balanced and superadditive NTU game. To each economy with a communication structure on the set of agents, there corresponds a communication game. In the paper it is proved that the core of the inductive limit of a direct system of communication games is not empty and in fact the intersection of the cores of the finite communication games of the direct system. It follows that each infinite economy (with or without a communication structure on the set of agents) has a nonempty core. A direct system of economies is a generalisation of the Debreu and Scarf [Debreu, G., Scarf, H. A limit theorem on the core of an economy, International Economic Review 4, pp. 235–246.] example of `replica economies'. The proof of the nonemptiness of the core of the inductive limit of a direct system of economies is along the lines of the proof by Debreu and Scarf. As by-product it is shown that an NTU game is totally balanced if and only if all its finite subgames are balanced.     

On the aubin-like characterization of competitive equilibria in infinite dimensional economies

For an exchange economy with finitely many agents and a commodity space which is infinite dimensional, it is proved that competitive equilibria are the same as allocations belonging to the fuzzy core of the economy. The latter is further characterized as a subset of the ordinary core of a suitably associated continuum economy.

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Riassunto Per un'economia di puro scambio con un numero finito di agenti e uno spazio dei beni di dimensione non necessariamente finita, si prova che gli equilibri Walrasiani possono essere caratterizzati come allocazioni che appartengono al nucleo fuzzy dell'economia. Inoltre, queste ultime allocazioni sono in corrispondenza biunivoca con allocazioni di tipo semplice che si trovano nel nucleo ordinario di un'opportuna economia che ha [0,1] come spazio rappresentativo dello spazio degli agenti.

     

Can we identify Walrasian allocations?

Abstract. We consider a discrete time, pure exchange infinite horizon economy with consumers and consumption goods per period. Within the framework of decentralized mechanisms, we show that for any given consumption trade at any period of time, say at time one, the consumers will need in general an infinite dimensional (informational) space to identify such a trade as an intertemporal Walrasian one. However, we show a set of environments where the Walrasian trades at each period of time can be achieved as the equilibrium trades of a sequence of decentralized competitive mechanisms, using only both current prices and quantities to coordinate decisions. Received: 1 December 1999 / Accepted: 31 October 2000