Absorbing and generalized stable sets

Within the framework of an abstract system we establish the existing relationship between the following two solutions: The absorbing sets solution and the generalized stable sets solution.We are grateful to an anonymous referee for helpful comments. Financial support from the project 9/UPV-00035.321-13699/2001 is grateful acknowledged. Inarra gratefully acknowledges the hospitality of Brown University and the financial support from the Ministerio de Educación, Cultura y Deporte, PR 2003-0287.     

A necessary and sufficient condition for stable matching rules to be strategy-proof

We study one-to-one matching problems and analyze conditions on preference domains that admit the existence of stable and strategy-proof rules. In this context, when a preference domain is unrestricted, it is known that no stable rule is strategy-proof. We introduce the notion of the no-detour condition, and show that under this condition, there is a stable and group strategy-proof rule. In addition, we show that when the men’s preference domain is unrestricted, the no-detour condition is also a necessary condition for the existence of stable and strategy-proof rules. As a result, under the assumption that the men’s preference domain is unrestricted, the following three statements are equivalent: (i) a preference domain satisfies the no-detour condition, (ii) there is a stable and group strategy-proof rule, (iii) there is a stable and strategy-proof rule.     

UNIVERSITY COMPETITION,GRADING STANDARDS,AND GRADE INFLATION

We develop a model of strategic grade determination by universities distinguished by their distributions of student academic abilities. Universities choose grading standards to maximize the total wages of graduates, taking into account how the grading standards affect firms' productivity assessment and job placement. We identify conditions under which better universities set lower grading standards, exploiting the fact that firms cannot distinguish between “good” and “bad”“A’'s. In contrast, a social planner sets stricter standards at better universities. We show how increases in skilled jobs drive grade inflation, and determine when grading standards fall faster at better schools. (JEL I21)     

Games implementing the stable rule of marriage problems in strong Nash equilibria

In a marriage problem, we introduce a condition called “exclusive matchability (EM)”: the condition mainly says that each pair of a man and a woman can choose to be a matching pair regardless of others' actions. This condition is essential to strong Nash implementation of the stable rule. We show that any mechanism which satisfies exclusive matchability implements the stable rule in strong Nash equilibria. Received: 17 May 1999/Accepted: 30 August 2001 I would like to thank anonymous referees for their helpful comments. Financial support from the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged.     

Subgame perfect implementation of stable matchings in marriage problems

We study a sequential matching mechanism, an extensive form game of perfect information, to implement stable matchings in marriage problems. It is shown that the SPE (subgame perfect equilibrium) of this mechanism leads to the unique stable matching when the Eeckhout (Econ Lett 69:1–8, 2000) condition for the existence of a unique stable matching holds. This result does not extend to preferences that violate the Eeckhout condition, even if the matching problem has a unique stable matching. We then introduce a weaker condition, called the α ^M condition, under which the SPE outcome of the men-move-first mechanism is the men-optimal stable matching. The α ^M condition is necessary and sufficient for the men-optimal stable matching to be Pareto optimal for men.     

How stable is the core discussion network?

Researchers have paid increasing attention to the core discussion network, the set of people we turn to when discussing important matters. Because the core discussion network is theorized to be composed of people's closest ties, not fleeting acquaintances, it is expected to be largely stable, evolving slowly over the span of people's lives. However, recent studies have shown that networks are strongly affected by the contexts in which people interact with others, and as people experience life course transitions, they also often enter new contexts – school, college, work, marriage, and retirement. We ask whether, as actors enter new social contexts, the core discussion network remains stable or changes rapidly. Based on original, longitudinal, qualitative and quantitative data on the experience of first-year graduate students in three academic departments in a large university, we examine the stability of the core discussion network over the first 6 and 12 months in this new context. We test four competing hypotheses that focus on strength of ties, new opportunities, obligations, and routine activity and predict, respectively, stasis, expansion, shedding, and substitution. We find that the core discussion network changes remarkably quickly, with little or no lag, and that it appears to do so because both the obligations that people face and the routine activities they engage in are transformed by new institutional environments. Findings suggest that core discussion network may be less a “core” network than a highly contextual support network in which people are added and dropped as actors shift from environment to environment.     

Cost range and the stable network structures

The work of this paper concerns with the stable structures in different cost range identified by Doreian in his paper [Doreian, P., 2006. Actor network utilities and network evolution. Social Networks 28, 137–164]. We point out some problems with his Theorem 4 and present our corrections to that theorem.     

Stable sets and standards of behaviour

In this paper we present a constructive, behavioural and axiomatic approach to the notion of a stable set as a model of the standard of behaviour of a social organisation. The socially stable set we introduce is a generalisation of the von Neumann-Morgenstern stable set. In contrast with the original version, our stability concept is always solvable. The standard of behaviour, reflecting the established conceptual order of a society or organisation, emerges from a dominance relation on alternative conceptions that are relevant with regard to a certain issue. This common social choice phenomenon, that permeates our societies and organisations, we have tried to clarify. Two axiomatic characterisations as well as a construction algorithm for socially stable sets are presented. These characterisations are based on behavioural postulates regarding the individual or collective strategic behaviour of effective sets. Relations between socially stable sets and other notions of stability are discussed. Received: 4 May 1998/13 March 2000     

Voting games,indifference, and consistent sequential choice rules

We present four choice functions which characterize the stationary points of sequential search rules derived from a preference relation over outcomes. These functions are contrasted with others in the literature in terms of narrowness of choice as well as their ability to satisfy certain normative and consistency conditions, and it is shown how two of these sets arise as the set of equilibrium outcomes of a voting game under different tie-breaking assumptions.We would like to thank Nicholas Miller for introducing us and two anonymous referees for valuable comments and suggestions.     

A note on the paper ‘cost range and the stable network structures’

The analysis in the paper ‘cost range and the stable network structures’ missed a stable structure —— a line. We explain its reason and reinforce the initial conclusion.     

Bayesian implementation in exchange economies with state dependent preferences and feasible sets

This paper considers Bayesian and Nash implementation in exchange economic environments with state dependent preferences and feasible sets. We fully characterize Bayesian implementability for both diffuse and non-diffuse information structures. We show that, in exchange economic environments with three or more individuals, a social choice set is Bayesian implementable if and only if closure, non-confiscatority, Bayesian monotonicity, and Bayesian incentive compatibility are satisfied. As such, it improves upon and contains as special cases previously known results about Nash and Bayesian implementation in exchange economic environments. We show that the individual rationality and continuity conditions, imposed in Hurwicz et al. [12], can be weakened to the non-confiscatority and can be dropped, respectively, for Nash implementation. Thus we also give a full characterization for Nash implementation when endowments and preferences are both unknown to the designer. Received: 4 March 1996 / Accepted: 8 September 1997     

Free triples,large indifference classes and the majority rule

We study classes of voting situations where agents may exhibit a systematic inability to distinguish between the elements of certain sets of alternatives. These sets of alternatives may differ from voter to voter, thus resulting in personalized families of preferences. We study the properties of the majority relation when defined on restricted domains that are the cartesian product of preference families, each one reflecting the corresponding agent’s objective indifferences, and otherwise allowing for all possible (strict) preference relations among alternatives. We present necessary and sufficient conditions on the preference domains of this type, guaranteeing that majority rule is quasi-transitive and thus the existence of Condorcet winners at any profile in the domain, and for any finite subset of alternatives. Finally, we compare our proposed restrictions with others in the literature, to conclude that they are independent of any previously discussed domain restriction.     

Communicating equality through policy documents: On legitimacy,double logic and stable translations

This article discusses gender mainstreaming (GMS) as a strategy to implement gender equality in public work organizations by analysing discourse in terms of the theoretical notions of translation and circulation in organizations to shed light on how gender equality and the mainstreaming strategy are formulated in the documents which govern the Swedish fire and rescue services. More specifically, it looks at how the goals regarding gender equality are circulated and translated. The results show that gender equality as a practice is created in the translation of national goals in terms of the local context and its specific gender equality challenges. Furthermore, the article discusses how vague formulations in the documents are stabilized through circulation between the government and the public agency in question. The results indicate the central role played by maintaining stable translations over time and the presence of a double logic of change in the processes, as well as the importance of legitimizing gender equality initiatives.     

On the volume-ranking of opportunity sets in economic environments

We provide a characterization of the volume-ranking of opportunity sets as defined on the set of all polyconvex sets, i.e. finite unions of convex, compact, Euclidean sets. In fact, such a domain is large enough to encompass most of the opportunity sets typically encountered in economic environments, including non-linear or even non-convex budget sets, and opportunity sets arising from production sets. Our result relies on a valuation-based volume-characterization theorem due to Klain and Rota (Introduction to Geometric Probability, Cambridge University Press, Cambridge, 1997) and helps to highlight some quite unusual conditions under which the volume-ranking can be justified as a freedom-ranking of opportunity sets. Therefore, it may also help to understand why the latter has been so conspicuously ignored in welfare analysis. Thanks are due to Larry Kranich, Massimo Marinacci, Uri Rothblum, Ernesto Screpanti, John Weymark, Yongsheng Xu, Claudio Zoli and two anonymous referees for helpful comments and suggestions.     

A new old solution for weak tournaments

This article uncovers dynamic properties of the von Neumann–Morgenstern solution in weak tournaments and majoritarian games. We propose a new procedure for the construction of choice sets from weak tournaments, based on dynamic stability criteria. The idea is to analyze dynamic versions of tournament games. The exploration of a specific class of Markov perfect equilibria in these “dynamic tournament games” yields a new solution concept for weak tournaments—the A-stable set. The alternatives in an A-stable set constitute persistent, long-run policy outcomes in the corresponding dynamic tournament games. We find that, in any weak tournament, the class of A-stable sets coincides with that of von Neumann–Morgenstern stable sets.     

Stable sets and cores for multi-criteria simple games and for their extensions

In this article we deal with multi-criteria simple games which constitute an extension of the basic framework of voting systems and related social-choice situations. We generalize two closely related solution concepts for these games, the stable sets and the core. A relationship between stable sets and minimal winning coalitions is established. Two generalizations of the core for multi-criteria simple games are characterized in terms of veto players. In addition, extended multi-criteria simple games obtained from different aggregation operations, such as union, intersection, marginalization, and composition, are introduced. It is shown that a voting system can be established when these operations are applied to complex voting systems.     

Generalized average rules as stable Nash mechanisms to implement generalized median rules

We consider a problem in which a policy is chosen from a one-dimensional set over which voters have single-peaked preferences. While Moulin (Public Choice 35:437–455, 1980) and others subsequent works have focused on strategy-proof rules, Renault and Trannoy (Mimeo 2011) and Renault and Trannoy (J Pub Econ Theory 7:169–199, 2005) have shown that the average rule implements a generalized median rule in Nash equilibria and provide an interpretation of the parameters in Moulin’s rule. In this article, we first extend their result by showing that a wide range of voting rules which includes the average rule can implement Moulin’s rule in Nash equilibria. Moreover, we show additionally that within this class, generalized average rules are Cournot stable. That is, from any strategy profile, any best response path must converge to a Nash equilibrium.     

Separations,Reconciliations, and Living Apart in Cohabiting and Marital Unions

Using data from a panel study of White young adults containing complete marital and cohabiting union histories from age 15 through 31, our goal is to track and compare the paths along which young adults arrange and time the entries and exits from marital and cohabiting unions. We focus on the incidence, duration, and outcomes of 2 dimensions that embrace residential separation: (a) separations that relate to discord in the relationship and (b) living apart from the partner or spouse for reasons other than discord. Our results show that union trajectories are dynamic and involve a heterogeneous and multidirectional array of transitions. We also find consistent differences supporting the idea that marital unions are more stable and durable than cohabiting unions.     

A note on generalized stable sets

A solution concept is introduced that is able to deal with cyclic relations. The concept is a generalization of the Von Neumann-Morgenstern solution concept of stable set and is therefore called the concept of generalized stable set. Its point of departure is the transitive closure of an asymmetric relation. A characterization theorem and an existence theorem are presented.The author would like to thank Thom Bezembinder, Maurice Salles and Harrie de Swart for their useful comments.