Rationalizable variable-population choice functions

Summary. We analyze the rationalizability of variable-population social-choice functions in a welfarist framework. It is shown that fixed-population rationalizability and a weakening of congruence together are necessary and sufficient for rational choice, given a plausible dominance property that prevents the choice of alternatives involving low utility levels. In addition, a class of critical-level separable choice functions is characterized. This result, which extends an earlier axiomatization of a related class of bargaining solutions to a variable-population setting, is the first axiomatization of critical-level principles in a general choice-theoretic model. Received: November 30, 1999; revised version: September 11, 2000     

A simple proof of the Sato proposition on non-homothetic CES functions

Summary. Based on some elementary results on duality, the paper proposes a much simpler way of deriving the class of non-homothetic CES production functions which was derived as a solution to a partial differential equation that defines the elasticity of substitution. Received: February 11, 1998; revised version: April 28, 1998     

Equilibria in infinite dimensional commodity spaces revisited

Summary. The aim of the paper is to provide a new proof of the Mas-Colell–Richard existence of equilibrium result when preferences are non-transitive and incomplete. Our proof generalizes the main ideas of the Negishi approach to the case of unordered preferences. Received: January 10, 1996; revised version: November 23, 1999     

Disaggregation of excess demand and comparative statics with incomplete markets and nominal assets

Summary. We prove that locally, Walras' law and homogeneity characterize the structure of market excess demand functions when financial markets are incomplete and assets' returns are nominal. The method of proof is substantially different from all existing arguments as the properties of individual demand are also different. We show that this result has important implications and is part of a more general result that excess demand is an essentially arbitrary function not just of prices, but also of the exogenous parameters of the economy as asset returns, preferences, and endowments. Thus locally the equilibrium manifold, relating equilibrium prices to these parameters has also no structure. Received: September 17, 1996; revised version: November 7, 1997     

Efficient strategy-proof allocation functions in linear production economies

Summary. In a linear production model, we characterize the class of efficient and strategy-proof allocation functions, and the class of efficient and coalition strategy-proof allocation functions. In the former class, requiring equal treatment of equals allows us to identify a unique allocation function. This function is also the unique member of the latter class which satisfies uniform treatment of uniforms. Received: July 10, 1997 / Revised version: November 24, 1997     

Auctions with endogenous valuations: the snowball effect revisited

Summary. This paper looks at the determination of ownership of capacity when there are two ex-ante symmetric agents bidding for many units of capacity which are sold sequentially. It is shown that convexity of payoffs in the final stage of the game is sufficient to ensure monopolization of capacity, but that increasing returns to scale are not sufficient to ensure monopolization. Received: March 14, 1997; revised version: December 1, 1997     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Approximation by finite horizons of the undiscounted one-sector growth model

Summary. In this paper I give a method for finding long-run-average policies in the undiscounted economic growth problem using approximations by finite horizons. Required hypothesis is the strong interiority of T-horizon solutions. Received: March 25, 1996; revised version: July 29, 1997     

Exact nonradial input, output, and productivity measurement

Summary. The use of measures originally suggested by Bennet, Bowley, and Hicks in the context of cost of living, welfare, and consumer surplus measurement to measure inputs, outputs, and productivity is examined. Suitably normalized versions of the Bennet-Bowley measures are shown to be exact and superlative measures of input, output, and productivity indicators. Received: April 2, 2001; revised version: August 8, 2001     

A new class of deprivation-based generalized Gini indices

Summary. This paper attempts to merge two strands of the literature on relative deprivation and generalized Gini indices by designing a new class of generalized Gini indices based on the concept of relative deprivation. In this connection, rank-dependent marginal deprivation functions are introduced. A new class of generalized Gini indices is derived axiomatically. It turns out to be the sum of modified versions of the S-Gini and the I-Gini introduced by Donaldson and Weymark (1980). Received: December 23, 1998; revised version: November 9, 1999     

Strategy-proof and individually rational social choice functions for public good economies: A note

Summary. Serizawa [3] characterized the set of strategy-proof, individually rational, no exploitative, and non-bossy social choice functions in economies with pure public goods. He left an open question whether non-bossiness is necessary for his characterization. We will prove that non-bossiness is implied by the other three axioms in his characterization. Received: October 17, 1997; revised version: January 19, 1998     

The equivalence of the Dekel–Fudenberg iterative procedure and weakly perfect rationalizability

Summary. Two approaches have been proposed in the literature to refine the rationalizability solution concept: either assuming that a player believes that with small probability her opponents choose strategies that are irrational, or assuming that their is a small amount of payoff uncertainty. We show that both approaches lead to the same refinement if strategy perturbations are made according to the concept of weakly perfect rationalizability, and if there is payoff uncertainty as in Dekel and Fudenberg [J. of Econ. Theory 52 (1990), 243–267]. For both cases, the strategies that survive are obtained by starting with one round of elimination of weakly dominated strategies followed by many rounds of elimination of strictly dominated strategies. Received: 10 December 1998; revised version: 26 April 1999     

Utility and entropy

Summary. In this paper we study an astonishing similarity between the utility representation problem in economics and the entropy representation problem in thermodynamics. Received: May 17, 1999; revised version: October 16, 2000     

Alternating-offer bargaining over menus under incomplete information

Summary. This paper considers bargaining with one-sided private information and alternating offers where an agreement specifies both a transfer and an additional (sorting) variable. Moreover, both sides can propose menus. We show that for a subset of parameters the alternating-offer game has a unique equilibrium where efficient contracts are implemented in the first period. This stands in sharp contrast to the benchmarks of contract theory, where typically only the uninformed side proposes, and bargaining theory, where typically the agreement only specifies a transfer. Received: September 10, 2001; revised version: March 25, 2002 RID="*" ID="*" I benefitted from discussions with Benny Moldovanu, Holger Müller, and Roland Strausz, and from comments made by an anonymous referee.     

More on parametric characterizations of risk aversion and prudence

Summary. This note provides an alternative proof for the equivalence of decreasing absolute prudence (DAP) in the expected utility framework and in a two-parametric approach where utility is a function of the mean and the standard deviation. In addition, we elucidate that the equivalence of DAP and the concavity of utility as a function of mean and variance, which was shown to hold for normally distributed stochastics in Lajeri and Nielsen [4], cannot be generalized. Received: November 27, 2000; revised version: November 26, 2001 Correspondence to: T. Eichner     

Core concepts in economies where information is almost complete

Summary. The paper analyzes the properties of cores with differential information, as economies converge to complete information. Two core concepts are investigated: the private core, in which agents' net trades are measurable with respect to agents' private information, and the incentive compatible core, in which coalitions of agents are restricted to incentive compatible allocations. Received: March 15, 2000; revised version: August 24, 2000     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001