Overlapping expectations and Hart's conditions for equilibrium in a securities model

Hart (J. Econ. Theory9 (1974), 293–311) gave conditions for equilibrium to exist in a securities model where each agent undertakes asset transactions to maximize expected utility of wealth. These conditions rule out agents wanting to undertake unbounded balanced transactions to reach a Pareto superior allocation given their expectations. With mild extra assumptions to make agents unwilling to risk incurring unbounded losses on their portfolios, Hart's conditions become equivalent to an assumption of “overlapping expectations,” which is comparable to a much weaker form of Green's “common expectations” (Econometrica41 (1973), 1103–1124).     

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.     

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.     

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”).     

We can't disagree forever

Under the assumption of common priors, if the information partitions of two agents are finite, then simply by communicating back and forth and revising their posteriors the two agents will converge to a common equilibrium posterior, even though they may base their posteriors on quite different information. Furthermore, given any integer, n, one can construct an example in which the revision process not only takes n steps to converge, but no evident revision occurs—for (n?1) steps both agents repeat the same conflicting posteriors—until the last step, when the two agents decide to agree. Common knowledge of each other's posterior does not necessarily lead agents to the posterior they would have agreed upon had information been directly exchanged. On the other hand, the examples that are characterized by a discrepancy between the direct and indirect communication equilibrium, are rare: with probability 1, the revision process constructed here leads the two agents in one step to the direct communication equilibrium.     

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.     

Budget preferences and direct utility

This paper extends a result of Sakai, who presented conditions for indirect preferences from which a utility function can be deduced if demand is single valued. It will be shown that—adding a “partial Lipschitz condition”—Sakai's theorem can be extended to multi-valued demand. Our result follows from the extension of a theorem of Hurwicz and Richter, who have shown that, under certain hypotheses on demand correspondences, an upper semicontinuous utility function f exists, so that the set of utility maximal elements μ_f(B) is contained in the choice set h(B) for every budget B. By our partial Lipschitz condition h(B) ?- μ_f(B) also follows.     

Zero-sum condition: A necessary and sufficient condition for a transitive voting system

A simple and quick way to ascertain whether or not any given majority voting system can always produce a transitive social preference orderings without imposing any restriction on the distribution of diverse individual preference orderings is to examine whether all individual voting (preference) vectors satisfy the Addition Rule or not. This conclusion was obtained by first reformulating the voting mechanism into that of a linear mapping from T^m defined by q = Σp_i. It was found that the subset P of T that can accommodate all possible individual preference ordering profiles and such that every sum vector q = Σ p_i of its member vectors p_i is contained in T can be expressed as P = {p: p∈ T, s(p) = 0}. It was also pointed out that this is equivalent to the requirement that all individual preference (voting) functions must satisfy the Addition Rule. Finally, Borda's Rule and Saposnik's Contributive Rule were shown to be examples of transitive voting rules which satisfy these necessary and sufficient conditions.     

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     

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).     

Multi-unit auctions with budget limits

We study multi-unit auctions for bidders that have a budget constraint, a situation very common in practice that has received relatively little attention in the auction theory literature. Our main result is an impossibility: there is no deterministic auction that (1) is individually rational and dominant-strategy incentive-compatible, (2) makes no positive transfers, and (3) always produces a Pareto optimal outcome. In contrast, we show that Ausubel?s “clinching auction” satisfies all these properties when the budgets are public knowledge. Moreover, we prove that the “clinching auction” is the unique auction that satisfies all these properties when there are two players. This uniqueness result is the cornerstone of the impossibility result. Few additional related results are given, including some results on the revenue of the clinching auction and on the case where the items are divisible.     

Money in the pure consumption loan model

The purpose of this paper is to show how modern techniques of Temporary competitive equilibrium analysis can be applied to models of the “pure consumption loan model” type. One considers Samuelson's simplest model where traders live two periods and where money is the only store of value. It is proved that a temporary equilibrium exists if price expectations are sufficiently independent of current prices. A stationary market equilibrium is shown to exist if there is a set of traders (i) whose total resources are greater when they are young than when they are old, (ii) who are indifferent between present and future consumption. It is proved that this existence theorem still holds if the economy is sufficiently “close” to an economy which has this property. A stationary market equilibrium is shown to be Pareto optimal if all traders hold positive cash balances. It may be inefficient if this condition is not satisfied, for some traders may then be willing to borrow, which they cannot do in this model.     

Reputation and imperfect information

A common observation in the informal literature of economics (and elsewhere) is that is multistage “games,” players may seek early in the game to acquire a reputation for being “tough” or “benevolent” or something else. But this phenomenon is not observed in some formal game-theoretic analyses of finite games, such as Selten's finitely repeated chain-store game or in the finitely repeated prisoners' dilemma. We reexamine Selten's model, adding to it a “small” amount of imperfect (or incomplete) information about players' payoffs, and we find that this addition is sufficient to give rise to the “reputation effect” that one intuitively expects.     

A new approach to the incorporation of attributes into consumer theory

A framework is developed which can be used to analyze a large class of consumption situations which cannot be handled by Lancaster's model. To achieve this end, a certain “expansion” of attribute space is performed. Subsequently, we formally define the notions of mixability and effective number of goods$\text{n}$. This new model degenerates into Lancaster's model for the special case when $\text{n}\text{= 1}$.     

Substantive Rationality and Backward Induction

S. Modica and A. Rustichini (1994, Theory and Decision37, 107–124) provided a logic for reasoning about knowledge where agents may be unaware of certain propositions. However, their original approach had the unpleasant property that nontrivial unawareness was incompatible with partitional information structures. More recently, Modica and Rustichini (1999, Games Econ. Behav.27, 265–298) have provided an approach that allows for nontrivial unawareness in partitional information structures. Here it is shown that their approach can be viewed as a special case of a general approach to unawareness considered by R. Fagin and J. Y. Halpern (1988, Artificial Intelligence34, 39–76). Journal of Economic Literature Classification Numbers: D80, D83.     

Starting Small and Commitment

I study a model of a long-term partnership with two-sided incomplete information. The partners jointly determine the stakes of their relationship and individually decide whether to cooperate with or betray each other over time. I characterize the extremal—interim incentive efficient—equilibria. In these equilibria, the partners generally “start small,” and the level of interaction grows over time. The types of players separate quickly. Further, cooperation between “good” types is viable regardless of how pessimistic the players are about each other initially. The quick nature of separation in an extremal equilibrium contrasts with the outcome selected by a strong renegotiation criterion (as studied in Watson (1999, J. Econ. Theory85, 52–90). Journal of Economic Literature Classification Numbers: C72, C73, D74.     

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.     

What economic agents do: How cognition and interaction lead to emergence and complexity

Kohn (The Cato Journal, 24(3):303–339, 2004) has argued that the neoclassical conception of economics—what he terms the “value paradigm”—has experienced diminishing marginal returns for some time. He suggests a new perspective is emerging—one that gives more import to economic processes and less to end states, one that bases behavior less on axioms and more on laboratory experiments. He calls this the “exchange paradigm”. He further asserts that it is the mathematization of economics that is partially at fault for leading the profession down a methodological path that has become something of a dead end. Here I suggest that the nascent research program Kohn has rightly spotted is better understood as distinct from its precursors because it is intrinsically dynamic, permits agent actions out of equilibrium, and treats such actions as occurring within networks. Analyzing economic processes having these characteristics is mathematically very difficult and I concur with Kohn’s appeal to computational approaches. However, I claim it is so-called multi-agent systems and agent-based models that are the way forward within the “exchange paradigm,” and not the cellular automata (Wolfram, A new kind of science, 2002) that Kohn seems to promote. Agent systems are generalizations of cellular automata and support the natural abstraction of individual economic agents as software agents.     

The so-called “transformation problem” revisited: A comment

This comment shows that Lipietz's Marxist transformation theorem represents but a simple, though useful reinterpretation of obvious mathematical consequences of a standard Sraffa model—by making appropriate use of its known degree of freedom. Labor values are not involved in this new interpretation of conventional prices of production. A proposal is therefore made how their role in Marx's transformation may be investigated further on the basis of Lipietz's theorem and its interpretation of the “value of labor power”.     

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

The existence of competitive equilibrium in Laffont's (J. Econ. Theory10 (1975)) model of adverse selection with costly information is studied. The existence of an equilibrium with finite prices is demonstrated without unusual restrictions on preferences or the technology of information production. This is made possible by changing the way in which the behaviour of information producing agents is modelled, and allowing for some public information.