Comments on goodness-of-fitmeasures in binary choice models by frank windmeijer

Review of OPTIMAL CONTROL, EXPECTATIONS AND UNCERTAINTY by Sean Holly and Andrew Hughes Hallett by Scott David Hakala Southern Methodist Univ., Dept. of Economics, Dallas, Tx 75275.     

An Approximation Scheme for Bin Packing with Conflicts

In this paper we consider the following bin packing problem with conflicts. Given a set of items V = {1,..., n} with sizes s₁,..., s (0,1) and a conflict graph G = (V, E), we consider the problem to find a packing for the items into bins of size one such that adjacent items (j, j) E are assigned to different bins. The goal is to find an assignment with a minimum number of bins. This problem is a natural generalization of the classical bin packing problem.We propose an asymptotic approximation scheme for the bin packing problem with conflicts restricted to d-inductive graphs with constant d. This graph class contains trees, grid graphs, planar graphs and graphs with constant treewidth. The algorithm finds an assignment for the items such that the generated number of bins is within a factor of (1 + ) of optimal provided that the optimum number is sufficiently large. The running time of the algorithm is polynomial both in n and in .     

On Stalnaker's Notion of Strong Rationalizability and Nash Equilibrium in Perfect Information Games

Counterexamples to two results by Stalnaker (Theory and Decision, 1994) are given and a corrected version of one of the two results is proved. Stalnaker's proposed results are: (1) if at the true state of an epistemic model of a perfect information game there is common belief in the rationality of every player and common belief that no player has false beliefs (he calls this joint condition strong rationalizability), then the true (or actual) strategy profile is path equivalent to a Nash equilibrium; (2) in a normal-form game a strategy profile is strongly rationalizable if and only if it belongs to C , the set of profiles that survive the iterative deletion of inferior profiles.     

Strategy-proof division with single-peaked preferences and individual endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and individual endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying Pareto optimality, strategy-proofness, reversibility, and an equal-treatment condition. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his individual endowment. Received: 8 September 1995/Accepted: 30 October 1996     

Ageing and the labor market

Generation size and structure may have substantial effects on the labor market. This perspective is crucial for the German economy which is one of the most rapidly ageing societies. The paper studies the effects of relative cohort size and relative cohort age on unemployment. The time-series analysis employs cointegration techniques to discriminate between short-run and long-run developments. The econometric investigations suggest that in the long-run, there is no sufficient evidence that young cohorts experience higher unemployment rates if their cohort size is relatively high. In the short-run, there is in general a positive impact of relative cohort size and relative cohort age on unemployment.Revised version of Discussion Paper No. 90-25, University of Munich. A first draft of this paper was written, when I was visiting CentER, Tilburg University. I wish to thank Sijbren Cnossen, John De New, Horst Krämer, Walter Krämer, Winfried Schmahl, Christoph M. Schmidt, Bernard M. S. van Praag, Michael R. Veall, Jürgen Wolters, the participants of the ISPE-conference and three referees of this journal for helpful comments, John De New, Lucie Merkle and Martin Milhleisen for able research assistance, and the German Science Foundation (DFG) for financial support. The paper has also benefited from a research visit to Université Catholique de Louvain, Louvain-la-Neuve.     

The optimum growth rate for population reconsidered

This article gives exact general conditions for the existence of an interior optimum growth rate for population in the neoclassical two-generations-overlapping model. In an economy where high (low) growth rates of population lead to a growth path that is efficient (inefficient), there always exists an interior optimum growth rate for population. In all other cases, there exists no interior optimum. The Serendipity Theorem, however, does, in general, not hold in an economy with government debt. Moreover, the growth rate for population that leads an economy with debt to a golden rule allocation can never be optimal.      

Stability and Nash implementation in matching markets with couples

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (J Econ Theory 21: 75–106, 2005, Theorem 3.3) and show that for any weakly responsive couples market, there always exists a “double stable” matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets, the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.     

Rational choice and revealed preference without binariness

 This paper attempts to provide a unified account of the rationalization of possibly non-binary choice-functions by “Extended Preference Relations” (relations between sets and elements). The analysis focuses on transitive EPRs for which three choice-functional characterizations are given, two of them based on novel axioms. Transitive EPRs are shown to be rationalizable by sets of orderings that are “closed under compromise”; this novel requirement is argued to be the key to establish a canonical relationship between sets of orderings and choice-functions. The traditional assumption of “binariness” on preference relations or choice functions is shown to be analytically unhelpful and normatively unfounded; non-binariness may arise from “unresolvedness of preference”, a previously unrecognized aspect of preference incompleteness. Received: 28 August 1995/Accepted: 14 February 1996