The number of commodities required to represent a market game

An n-person game with side payments that can arise from an economic market is called a market game. It is proved here that any n-person market game can be obtained from a market with at most n ? 1 commodities. Moreover, no smaller number will suffice in some cases (e.g., the unanimity game). This result is then applied to settle a question regarding market games with a continuum of traders.     

Essential aggregation procedures on restricted domains of preferences

The restricted domains of individuals' preferences that permit the construction of Arrow social welfare functions and nonmanipulable voting procedures in which each of n voters has some power are characterized. In this context a domain is the Cartesian product of n sets of strict preference orderings. Variants of this result are obtained under the additional requirement of neutrality and in the case when alternatives are vectors whose ith components affect only the ith voter. Kalai and Muller's analogous result (J. Econ. Theory16 (1977), 457–469) concerning nondictatorial procedures is discussed and proved as a corollary to the main theorem.     

Relative prices and real factor rewards: A reinterpretation

Two devices are generally available to increase the reward of a productive factor: (i) a direct subsidy to the factor, and (ii) an alteration in relative commodity prices. The Stolper-Samuelson result, whereby method (ii) suffices to improve the real reward of a productive factor in a 2×2 setting with no joint production is shown to be valid in the n-commodity, n-factor model.     

Diversification of interdependent prospects

This paper extends the stochastic dominance approach to the problem of diversification of interdependent prospects. One basic result is that a risk averter should always mix any two identically distributed prospects, regardless of the nature of the interdependence between them. A similar result holds for the case of n prospects, provided all the joint distribution functions of dimension n ? 1 are identical. When the n-dimensional joint distribution function is symmetric, then the optimal strategy is to put an equal amount into each prospect. The paper also provides conditions which make diversification optimal in the absence of identical marginal distributions.     

The information matrix test: Simplified calculation via a score test interpretation

In Chesher (1982) I show that the Information Matrix test introduced by White (1982) is a score test for parameter constancy. In this letter I show that this result leads to a simple computational procedure for calculating the Information Matrix test. The procedure involves computing, for a sample of n observations, n times the R² from the least squares regression of a column of ones on a matrix whose elements are functions of 1st and 2nd derivatives of the log density function.     

English auctions and the Stolper-Samuelson theorem

We prove that the English auction (with bidders that need not be ex ante identical and may have interdependent valuations) has an efficient ex post equilibrium. We establish this result for environments where it has not been previously obtained. We also prove two versions of the Stolper-Samuelson theorem, one for economies with n goods and n factors, and one for non-square economies. Similar assumptions and methods underlie these seemingly unrelated results.     

The expected probability of Condorcet's paradox

Let P(n,p) be the probability that there is a Condorcet winner on three alternatives for n (odd) voters. The vector p defines the probability that a randomly selected voter will have any of the six linear rankings on three alternatives as his or her preference ranking. It is shown that if all p vectors are equally likely, the expected value of P(n,p) is given by 15(n+3)²/[16(n+2)(n+4)].     

Low information nash equilibria for oligopolistic markets

This paper deals with an infinite horizon n firm oligopoly in which firms are assumed to have incomplete information about one another's actions and profit functions. An equilibrium concept is defined that is similar to the Nash non-cooperative equilibrium, but is suitable for the information assumptions of the model. The equilibrium uses a type of bounded rationality which makes firms' computations relatively easy. This is due to an implicit assumption that computation is costly and a Bayesian approach is prohibitively costly. This low information Nash equilibrium is proved to exist, and, in addition, an adaptive expectations decision process is described which, if followed by all firms, leads to the low information Nash equilibrium.     

Asymmetric English auctions

This paper studies equilibria of the n-bidder single-object English, or open ascending price, auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universität Kiel, Kiel, 1992, pp. 115-136.) showed that if the values satisfy a “single crossing” condition, then the two-bidder English auction has an efficient equilibrium. In this paper, two extensions of the single crossing condition, the “average crossing” condition and the “cyclical crossing” condition, are introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium.     

Characterization of the private alternatives domains admitting arrow social welfare functions

An n-person social choice problem is considered in which the alternatives are n dimensional vectors with the ith component of such a vector being the part of the alternative effecting individual i alone. Assuming that individuals are selfish (i is indifferent between any two alternatives that have the same ith component) we characterize all the families of permissible individual preferences that admit nondictatorial Arrow-type social welfare functions. We also show that the existence of such a function for a given family of preferences is independent of n provided that is greater than one.     

The network structure of the United States input-output table

Economists triangulate input-output tables in order to find a predominant direction in the interindustrial movement of goods and services. Typically, industries, such as Mining, which are far removed from Final Demand, are situated at one end of the input-output table after rearrangement. At the other end are industries that produce for Final Demand, such as Food and Automobiles. Triangulation yields a linear ordering of industries. Much greater detail than this on the complex directionalities of interindustrial flows is presented here. The maximum flow minimum cut algorithm of network flow theory is employed to identify production and consumption complexes. These are relatively self-contained blocks of industries. In each block, there is one industry — the node of the complex — whose total production (consumption) is greater than the amount produced (consumed) by all members of the collection for (from) non-members. Many production complexes have as their nodes primary industries — ones that would be situated near one end of the table after triangulation — and as their other members Final Demand-oriented industries — ones that would be located near the other end. If there arem industries in an input-output table, ann-member production complex is composed of one nodal industry with total output,P, and (n?1) other industries, which together as then-member complex sell less thanP to the (m?n) other industries. 200 production and 42 consumption complexes of the most highly detailed version of the 1967 U.S. input-output table available are presented.     

Bargaining one-dimensional social choices

We analyze bargaining over the one-dimension characteristic of a public good among n impatient players when decisions require q favorable votes, q?2. Stationary subgame perfect equilibrium strategies are characterized for all games with deterministic protocol. We provide a monotonicity condition (satisfied by all single-peak, strictly quasi-concave and concave utilities) that assures uniqueness for every q whenever player's utilities are symmetric around the peak. Without symmetry, the monotonicity condition assures uniqueness for qualified majorities, q>n/2, provided that agents are sufficiently patient and utilities satisfy an additional regularity condition. Asymptotic uniqueness is assured for qualified majorities by imposing only the monotonicity condition.     

The network of weighted majority rules and its geometric realizations

In a previous work the first author considered the network G(n,p) of weighted majority rules (WMR) for n decision makers whose competencies are given by their probabilities p=(p₁,…,p_n) of making a correct decision. On this paper we consider chains of decision profiles, which must occur in G(n,p) in a fixed order, and show that they can be mapped onto straight lines in a low-dimensional geometric realization. The minimal number of directions which must used to separate all edges is given as the chromatic number of a certain incidence graph. We also define degenerate networks in which several nodes coalesce.     

Pure exchange equilibrium of dynamic economic models

This paper studies competitive equilibrium over time of a one good model in which the agents are members of a population which grows at a constant rate. Each agent lives for n periods and in the i-th period of his life receives an endowment of e_i units of goods. Goods can neither be produced nor stored. The model is thus the n-period generalization of the two- and three-period models studied by Samuelson in [4]. We seek to ascertain the structure of the time paths of consumption in these models. Our results can be summarized roughly as follows: In general, there will exist two kinds of steady state paths, (i) golden rule paths in which the rate of interest equals the growth rate of population and (ii) “balanced” paths in which the aggregate assets or indebtedness of the society as a whole is zero (a fundamental fact about dynamic models is that it is possible for aggregate debt not to equal aggregate credit as it must in the static case). A model is termed classical if in the golden rule state aggregate assets are negative (or debt positive) and Samuelson (following [4]) in the opposite case. It is conjectured that the golden rule program is globally stable in the classical case and the balanced program is stable in the Samuelson case. This is established for the special case n = 2.     

Passing the Buck On the acceptance of responsibility

In the Passing the Buck game, the n members of a group decide in a given order whether or not to incur costs so that they can fix a certain problem for the benefit of the group. Passing the Buck means that one relies on the service of a successor. The decision is influenced by social preferences and by strategic considerations. We derive three main conclusions from experiments with n=3 and n=4. (i) The unique perfect Baysian equilibrium of the Passing the Buck game with incomplete information about the preferences of other players generally fits the data, however with two interesting exceptions. (ii) Backward induction breaks down if it requires more than two steps, i.e., for the first player in the game with n=4. (iii) Making one of the members of the group an “expert” who alone is competent to fix the problem is connected with a change of social preferences.     

A progress report on Kelly's majority conjectures

LetC(m, n) be the proportion of n-voter profiles on m alternatives that have a majority winner. Jerry Kelly conjectured that C(m, n) > C(m + 1, n) for m ? 3 and n = 3 and n ? 5, and C(m, n) > C(m, n + 2) for m ? 3 and n ? 3. We prove these for special cases.     

An efficiency theorem for incompletely known preferences

There are n agents who have von Neumann-Morgenstern utility functions on a finite set of alternatives A. Each agent i's utility function is known to lie in the nonempty, convex, relatively open set Ui. Suppose L is a lottery on A that is undominated, meaning that there is no other lottery that is guaranteed to Pareto dominate L no matter what the true utility functions are. Then, there exist utility functions ui∈Ui for which L is Pareto efficient. This result includes the ordinal efficiency welfare theorem as a special case.     

Extension of Oi's price instability theorem

Oi's theorem that product price variability raises the average profit of a single-product perfectly competitive firm is generalized in this paper to cover the case of an n-commodity firm. Under similar conditions to those mentioned by Oi for the single-product case, commodity (factor or product) price instability raises the average profit of an n-commodity perfectly competitive firm.     

Sufficient conditions for D-stability

Sufficient conditions for an n by n matrix to be D-stable are surveyed. Use is made of some transformations under which the D-stables are invariant and relations among the conditions are given. The verifiability of the thirteen conditions cited is also discussed. The lack of an effective characterization of D-stability motivates the discussion.     

Substituting one risk increase for another: A method for measuring risk aversion

This paper defines the rate of substitution of one stochastic change to a random variable for another. It then focuses on the case where one of these changes is an nth degree risk increase, and the other is an m  th degree risk increase, where n>m?1$n>m?1$. The paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree Ross more risk averse partial order. The implications for local intensity measures of nth degree risk aversion are also examined. The analysis organizes the existing results as well as generates new ones.