Some extensions of a claim of Aumann in an axiomatic model of knowledge

The paper begins by presenting an axiomatic model of simple and iterated knowledge. A formal definition of the intuitive notion of common knowledge is given and shown equivalent to previous characterizations. It is shown that agents have information partitions. The second part generalizes Aumann's (Ann. Statist.4 (1976), 1236–1239) well-known propositions about common knowledge between two rational agents of each other's probability assignments. It is shown that: common knowledge of decisions—if these are rational—implies a common decision for like-minded agents; and that a “dialogue” in decisions leads to a common decision. A “no-trade” theorem is given which includes trade under complete uncertainty.     

On equilibrium in Hart's securities exchange model

In this paper, we use a no unbounded arbitrage condition to give a very direct proof of the existence of equilibrium in Hart's unbounded securities exchange model (J. Econ. Theory, 9 (1974), 293–311). We also examine the relationship between the no unbounded arbitrage condition and the sufficiency conditions of Hart, ibid. and Hammond (J, Econ. Theory, 31 (1983), 170–175). We present an example to show that if traders are not sufficiently risk averse, then Hammond's overlapping expectations condition is not, in general, equivalent to the no unbounded arbitrage condition or Hart's sufficiency conditions, and therefore, is not sufficient to guarantee the existence of equilibrium. We also present an example to show that it is possible for the no unbounded arbitrage condition to hold without overlapping expectations, and therefore, it is possible for equilibrium to exist without overlapping expectations.     

Nash equilibrium search for the best alternative

In a recent paper, Weitzman (Econometrica47 (1979) 641–654) described a policy of “optimal search for the best alternative.” The present paper is concerned with the development and characterization of a policy of “Nash equilibrium search for the best alternative.” Specifically, it is shown that, under certain monotonicity assumptions, and under the assumption that firms have incomplete information regarding the results of rivals' search behavior, a Nash equilibrium search policy exists and has the same form as Weitzman's optimal search policy.     

Price Level Determinacy under a Pure Interest Rate Peg

In this article we reexamine a famous result by T. J. Sargent and N. Wallace (1975, Journal of Political Economy83, 241–254) according to which a “pure interest rate peg” leads to nominal price indeterminacy. We use P. Weil's (1991, International Economic Review32, 37–53) generalization of the Sidrauski–Brock model, where arrival of new “generations” of infinitely lived agents is allowed, and we obtain the following results: (i) Nominal indeterminacy holds in the traditional Sidrauski–Brock framework; (ii) This nominal indeterminacy disappears as soon as new generations arrive in time, via some rigorous version of Patinkin's “real balance effect”; (iii) A multiplicity of solutions may still remain, but full determinacy occurs in some cases, depending notably on fiscal policy or the distribution of endowments in time. Journal of Economic Literature Classification Numbers: E4, E5     

Political system and economic efficiency: The east European context

Sections 1 and 2 reexamine the proposition about democratization of socialism as a factor of economic efficiency—in the light of the challenge contained in the article by Stanislaw Gomutka, “Economic Factors in the Democratization of Socialism and the Socialization of Capitalism” (J. Comp. Econ., Dec. 1977, 1, 4:389–406). The author takes issue with Gomulka's conclusions, which view democracy as of little relevance for economic efficiency under socialism. Dissident views on the link between democracy and efficiency are discussed. Section 3 goes beyond this controversy in an attempt to analyze the prospects and efficiency aspects of a limited change within the existing Soviet-type political system (“Kadarism”).     

Information,trade and common knowledge

In any voluntary trading process, if agents have rational expectations, then it is common knowledge among them that the equilibrium trade is feasible and individually rational. This condition is used to show that when risk-averse traders begin at a Pareto optimal allocation (relative to their prior beliefs) and then receive private information (which disturbs the marginal conditions), they can still never agree to any non-null trade. On markets, information is revealed by price changes. An equilibrium with fully revealing price changes always exists, and even at other equilibria the information revealed by price changes “swamps” each trader's private information.     

Rational responses and rational conjectures

This paper utilizes a pure-trade imperfect-competition model and discusses the rationality problem arising from the fact that agents have to make conjectures about the markets to set prices optimally. The objective is to show that there may be inefficient allocations with the agents behaving rationaly. In the same context Hahn (Rev. Econ. Stud.45 (1978), 1–17) proposed a notion of rationality under which the existence results obtained were negative. This paper argues that Hahn's is a strong notion of rationality that requires the mechanism to be incentive compatible. Thus, an alternative notion that refers exclusively to the rationality of the conjectures is proposed, and positive results on existence obtained.     

The stability of the cournot oligopoly model: A reassessment

The stability properties of the Cournot oligopoly model are examined for the continuous adjustment process. Sufficient conditions for instability are established which are shown to be of significance when the number of firms, n, is small. Local and global stability are shown under appropriate conditions which for global stability include the restriction n ? 5. The proof of global stability corrects a well-known proof by F. Hahn (Rev. Econ. Stud.29 (1962), 329–331). Results for the discrete time adjustment process are reported and the restrictiveness of the model's assumptions are discussed.     

On the existence of equilibria in economies with infinitely many commodities and without ordered preferences

The present paper deals with the existence of equilibria in economies whose commodity space is L_∞(M, M, μ) and where the agents' preferences need not be complete or transitive. Applying a fixed point theorem of Browder, an equilibrium existence theorem for abstract economies (generalized qualitative games) is proven where each agent's choice set is contained in an arbitrary topological vector space. With the help of this theorem the existence of Walrasian general equilibrium for a suitably specified economic model is obtained. The final result is a generalization of T. F. Bewley's (J. Econ. Theory4 (1972), 514–540) equilibrium existence theorem to the case of non-ordered preferences.     

On the informational efficiency of the competitive resource allocation process

The purpose of this paper is to formalize the competitive process as a parametric process, and then prove the minimality of its message space among the message spaces for a broad class of parametric processes that includes the class of processes considered by Hurwicz (in “Studies in Resource Allocation Processes” (K. J. Arrow and L. Hurwicz, Eds.), pp. 413–423, Cambridge Univ. Press, Cambridge, 1977), Mount and Reiter (J. Econ. Theory6 (1974), 161–192), and Osana (J. Econ. Theory17 (1978), 66–78). The proof of this result turns crucially on the “asymmetry property” (which is stronger than the well-known “uniqueness property” of Hurwicz) and on an injectiveness lemma which is applicable to parametric processes.     

Core allocations and the dimension of the cone of efficiency price vectors

Let (R₁,…,R_k) be an arbitrary partition of the grand coalition in an atomless exchange economy with k “large enough.” We prove that an optimal allocation x belongs to the core if and only if x cannot be improved upon by any coalition that includes at least one of the R_i's. K is “large enough” if k ? r + 1, where r is the linear dimension of the cone P of the efficiency price vectors for x. Recall that it is always true that r ? n, when n is the number of commodities in the market, and that under differentiability and interiority r = 1; thus k can be chosen to be 2 (i.e., for any coalition R, an allocation x belongs to the core of the market if and only if x is not blocked by any coalition that either contains R or contains its complement).     

The Phillips Curve and Optimal Policy in a Structural Signal Extraction Model

We study a monetary economy subject to “signal extraction” problems, and investigate within that framework the positive and normative aspects of monetary policy. As in Lucas (1972, Journal of Economic Theory,4, 103–124; 1973, American Economic Review, 63, 326–334), imperfect signal perception generates macroeconomic correlations similar to those found in the “Phillips curve” literature. Moving to normative aspects, we find that, when aggregate shocks are present, traditional nonactivist policies do not permit reaching the first best, and that an intelligent activist policy always leads to better outcomes. The specific characteristics and effectiveness of this optimal policy also depend crucially on the problem of signal extraction. Journal of Economic Literature Classification Number: E5.     

The economics of joint ventures in centrally planned and labor-managed economies

The paper analyzes the allocational and distributional issues connected with the operation of joint ventures by firms in Yugoslavia, several Eastern European countries and the People's Republic of China with Western firms. A variable-bargaining-power model is used to examine the behavior of joint ventures under the various institutional circumstances of these countries. Contrary to Brada's conclusions (J. Comp. Econ.1(2):167–181, June 1977), the present study indicates that the behavior of joint ventures in most of these countries is likely to be quite similar.     

Aggregation and the existence of a social utility function

In a well-known paper Gorman (Econometrica21 (1953)) established that the necessary and sufficient condition for the existence of an aggregate, or social, utility function, independent of the distribution of income, is that all individuals' income consumption paths be parallel straight lines. Recently Chipman (J. Econ. Theory8 (1974)), building on the paper of Hurwicz and Uzawa (in “Preference Utility and Demand”) has shown that if the distribution of income is proportional and individual preferences are homothetic, aggregate consumption behavior obeys the necessary integrability conditions. It is shown here that the consistency of aggregate behavior can be derived from more general conditions than the ones used by Chipman and Gorman. Examples of demand systems from which aggregate behavior implies a social utility function are provided. It is then shown that if individual demand functions are linear in income—a form employed by both Gorman and Chipman—it is not necessary that the distribution of income be fixed.     

Exact aggregation and Generalized Slutsky Conditions

This article indicates a natural connection between Generalized Slutsky Conditions and demand structures of the exact aggregation form. It is shown that Generalized Slutsky Conditions are assured when the number of consumers is greater than or equal to the number of goods, if and only if demands are of a generalized exact aggregation form. This result provides some understanding of the properties of aggregate demand and allowable differences between consumers, as well as naturally generalizing W. M. Gorman's (Econometrica21 (1953), 63–80) famous conditions for the integrability of aggregate demand.     

Soviet agricultural procurement pricing: A study in perversity

The relationship between Soviet agricultural procurement prices and quantities is examined in the light of the existence of bonuses for above-trend sales (BATS) and zonal price differentiation (ZPD). That BATS leads to a positive relationship between prices and quantities as harvest conditions vary is shown to hold for the individual farm. Planners are apt, however, to be more concerned with the “average” price of a crop, which is closely related to the subsidy bill. This price is more likely to be “perverse” under ZPD than BATS, although neither guarantees perversity. Data suggest that such perversity is a common occurrence. J. Comp. Econ., March 1985, 9(1), pp. 24–45. Illinois State University, Normal, Illinois 61761.     

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.     

Capital as a commitment: Strategic investment to deter mobility

This paper analyzes how an early entrant in a market can exploit its head start by strategic investment. The analysis is based on Spence's paper, Investment strategy and growth in a new market, (Bell J. Econ., 10 (1979), 1–19). We frist study the investment game in the no-discounting case, which embodies the key features of mobility deterrence. We establish the existence of a set of perfect equilibria and suggest that one particular equilibrium is most reasonable. This equilibrium, also valid with discounting, involves the follower firm being forever deterred from investing to its steady-state reaction curve, in contrast to Spence's proposed solution.     

The long-run and short-run demand for money: Additional evidence

This paper presents estimates of Chow's money-demand equations using Chow's data. The equations are adjusted for autocorrelation using two autocorrelation transformations, the standard Cochrane-Orcutt transformation that deletes “initial” observations, and one that does not delete these observations. The estimates focus on the question of the asset versus the transactions specifications. The results reaffirm Chow's original conclusion which supported the asset motive and, thereby, reversed nearly all of the findings recently reported by Lieberman (1980). The paper concludes that one should be wary about using the Cochrane-Orcutt transformation, especially when the ratio of the number of deleted observations to total observations is large.     

Coalition-Proof Nash Equilibria II. Applications

In Bernheim, Peleg, and Whinston (“Coalition-Proof Equilibria. I. Concepts,” J. Econ. Theory 42 (1987), 1–12), we proposed the notion of Coalition-Proof Nash equilibrium and Perfectly Coalition-Proof Nash equilibrium as solution concepts for strategic environments in which players can freely discuss their strategies, but cannot make binding commitments. This paper undertakes applications to several economic problems, including the behavior of Cournot oligopolists, oligopolistic entry deterrence, cooperation in finite horizon games, and social choice rule implementation.