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.     

Stationary cardinal utility and optimal growth under uncertainty

In the literature on multiperiod planning under uncertainty, it is generally postulated that preferences may be represented by a von Neumann-Morgenstern utility index that is additive over time. This paper accomplishes two objectives: First, an axiomatic basis is provided for a more general class of non-additive utility indices defined over infinite consumption streams. Second, this class of utility functions is applied to extend existing results (J. Econ. Theory4 (1972), 479–513; J. Econ. Theory11 (1975), 329–339) on the nature of optimal growth under uncertainty. Of particular interest are the existence and stability of a stochastic steady state.     

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).     

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.     

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.     

A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

Measures of technical efficiency

Färe and Lovell (J. Econom. Theory19 (1978), 150–162) suggest four properties that a measure of technical efficiency should satisfy; the commonly employed Debreu-Farrell measure fails three of them. Necessary and sufficient conditions for a measure to satisfy the four conditions are provided and recently proposed measures are analyzed in the light of this result. Also, it is argued that the Debreu-Farrell measure has several desirable properties when one takes account of (1) (perhaps unknown) market prices and the relationship between technical and economic efficiency and (2) its characterization as a measure of economic efficiency using the shadow prices implicit in the production technology.     

On Forward Induction and Evolutionary and Strategic Stability

We analyze which normal form solution concepts capture the notion of forward induction, as defined by E. van Damme (1989, J. Econ. Theory48, 476-496) in the class of generic two player normal form games preceded by an outside option. We find that none of the known strategic stability concepts (including Mertens stable sets and hyperstable sets) capture this form of forward induction. On the other hand, we show that the evolutionary concept of EES set (J. Swinkels, 1992, J. Econ. Theory57, 306-332) is always consistent with forward induction. Journal of Economic Literature Classification Number: C72.     

Location models as models of product choice

Markets in which firm choice of product is an economic decision are commonly analyzed using a variant of the location model pioneered by Hotelling (Econ. J.39 (1929), 41–57). This paper develops a framework for formalizing the idea that a set of consumers with preferences defined over an abstract set of commodities can be represented as if they behaved as is typically assumed in the goods-as-locations models. With this framework in place, we are able to derive the preference assumptions underlying the two most common versions of these models, and also to uncover the foundations of the now well-known principle of minimum differentiation.     

Performance incentives and planning under uncertainty

The paper discusses the use of the performance-incentive function (PIF) by planning organizations when there is subjective or objective uncertainty. It is proved that a PIF can be constructed that achieves both allocational and distributional optimality, when there is subjective uncertainty about the conditions of production and both the center and the producer are risk-averse. When there is objective uncertainty, however, it is shown that it is not, in general, possible for the center to achieve these two objectives simultaneously. J. Comp. Econ., Sept. 1979, 3(3), pp. 217–232. United States Air Force Academy, Colorado 80840; and University of California, Berkeley, California 94720.     

Generic 4 × 4 Two Person Games Have at Most 15 Nash Equilibria

The maximal generic number of Nash equilibria for two person games in which the two agents each have four pure strategies is shown to be 15. In contrast to Keiding (1997),Games Econ. Behav.21, 148–160, who arrives at this result by referring to the enumeration of Grünbaum and Sreedharan (1967),J. Combin. Theory2, 437–465, our argument is based on a collection of lemmas that constrain the set of equilibria. Several of these pertain to any common numberdof pure strategies for the two agents.Journal of Economic LiteratureClassification Number: C72.     

Evolution in Games with Endogenous Mistake Probabilities

J. Bergin and B. Lipman (Econometrica64 (1996), 943-956) show that the selection effect from the random mutations in the adaptive population dynamics in M. Kandori, G. Mailath, and R. Rob (Econometrica61 (1993), 29-56) and P. Young (Econometrica61 (1993), 57-84) is due to restrictions on how these mutation rates vary across population states. We here model mutation rates as endogenously determined mistake probabilities, by assuming that players with some effort can control the probability of implementing the intended strategy. This is shown to corroborate the results in Kandori-Mailath-Rob (1993) and, under certain regularity conditions, those in Young (1993). Journal of Economic Literature Classification Number: C72.     

Temporal risk and the nature of induced preferences

It has been known since the work of H. Markowitz (“Portfolio Selection: Efficient Diversification of Investments,” Yale Univ. Press, 1959) and J. Mossin (Amer. Econ. Rev.59 (1969), 172–174) that even an individual whose underlying preferences satisfy the von Neumann-Morgenstern axioms will not choose over delayed (i.e., “temporal”) risky prospects in a manner which can be modelled as expected utility maximizing. Since most economically important instances of risk taking (insurance, real investment, agriculture, career training) involve delayed as opposed to immediately resolved risk, the standard use of expected utility theory to model such decisions must be questioned. In this paper the technique of “generalized expected utility analysis” (M. J. Machina, Econometrica50 (1982), 277–323) and the theory of support functions (R. T. Rockafellar, “Convex Analysis,” Princeton Univ. Press, 1970) are applied to exactly model and hence determine the nature of preferences over temporal risky prospects.     

Agriculture and the Transition to the Market in Asia

This paper examines the role of agriculture in the transition from central planning to market-based economies in Asia through an analysis of the experience of countries in Southeast Asia, i.e., Lao PDR and Viet Nam, and Central Asia, i.e., Kazakstan and the Kyrgyz Republic. In Southeast Asia, reforms met with a very rapid and positive supply response in agriculture that helped to sustain the broader economy. In Central Asia, economic reforms have thus far failed to arrest a deep and widespread economic depression across all sectors, including agriculture. Focusing on the significant differences in the initial conditions and structure of agriculture, the reasons for this contrasting experience are analyzed. The likely prospects and the problems posed by the unfinished reform agenda are also examined.J. Comp. Econom.,October 1997,25(2), pp. 256–280. Asian Development Bank, Manila, 0980, Philippines.     

Proportional taxation: Nonexistence of stable structures in an economy with a public good

Guesnerie and Oddou [J. Econom. Theory25 (1981), 67–91] raised the open question whether an economy, in which the production of a public good is financed via proportional taxation, has a stable structure. By means of the first example a negative answer to this question is provided. The second example shows that a stable structure may fail to exist even if all the individuals have the same initial endowments in private good.     

Super-modularity: Applications to convex games and to the greedy algorithm for LP

L. S. Shapley (Internat. J. Game Theory1 (1971), 11–26) showed that if a game is convex, then all the marginal worth vectors are members of the core. J. Edmonds (in “Combinatorial Structures and Their Applications” (R. Guy et al., Eds.), pp. 69–87, Gordon & Breach, New York, 1970) considered a class of linear programming problems for which the greedy algorithm works. The present paper unifies these studies, and establishes the converse of each theorem.     

Free access vs private ownership: A comparison

Weitzman (J. Econ. Theory8 (1974), 225–234) has established that under free access properties of average or better quality will be overutilised relative to the efficient private property equilibrium. This leaves open the question of what happens to the low quality properties. It is shown here that there are conflicting considerations and the outcome is ambigous. Necessary and sufficient conditions are obtained for less of a variable input to be attracted to a site when access is free than when a private owner makes a charge for access.     

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.     

Supportability and anonymous equity

W. W. Sharkey and L. G. Telser (J. Econom. Theory18 (1978), 23–37) feel that invulnerability of a natural monopoly to the threat of competitive entry is well reflected in the concept of supportability. G. R. Faulhaber and S. B. Levinson (Amer. Econom. Rev.71 (1981), 1083–1091) point out that supportability is necessary for the achievability of anonymous equity, i.e., absence of consumer subsidies in public enterprise pricing. This paper reconciles supportability with market clearance and shows that supportability is sufficient for the achievability of anonymous equity.     

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.