Oscillations in the stable starless core Barnard 68

New molecular line observations of the Bok globule Barnard 68 in HCO+ irrefutably confirm the complex pattern of red and blue asymmetric line profiles seen across the face of the cloud in previous observations of CS. The new observations thus strengthen the previous interpretation that Barnard 68 is undergoing peculiar oscillations. Furthermore, the physical chemistry of B68 indicates that the object is much older than the sound crossing time and is therefore long-lived. A model is presented for the globule in which a modest external pressure perturbation is shown to lead to oscillations about a stable equilibrium configuration. Such oscillations may be present in other stable starless cores as manifested by a similar signature of inward and outward motions.Comment: Accepted for MNRAS letters, 5 pages, 7 figure

A theory of stability in many-to-many matching markets

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set and with the predictions of a non-cooperative bargaining model. The setwise-stable set possesses the conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to-one, models. We provide results for a number of core-like solutions, besides the setwise-stable set

On core stability and extendability

This paper investigates conditions under which the core of a TU cooperative game is stable. In particular the author extends the idea of extendability to find new conditions under which the core is stable. It is also shown that these new conditions are not necessary for core stability.core stability, stable core, extendability

Cores and Stable Sets for Interval-Valued Games

In this paper, interval-type solution concepts for interval-valued cooperative games like the interval core, the interval dominance core and stable sets are introduced and studied. The notion of I-balancedness is introduced, and it is proved that the interval core of an interval-valued cooperative game is nonempty if and only if the game is I-balanced. Relations between the interval core, the dominance core and stable sets of an interval-valued game are established.cooperative games;interval games;the core;the dominance core;stable sets

The Socially Stable Core in Structured Transferable Utility Games

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players, for instance a hierarchical ordering or a dominance relation.The social structure is utilized to refine the core of the game, being the set of payoffs to the players that cannot be improved upon by any coalition of players.For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function.We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power.The socially stable core of the game consists of the core elements that are socially stable.In case the social structure is such that every player in a coalition has the same power, social stability reduces to balancedness and the socially stable core coincides with the core.We show that the socially stable core is non-empty if the game itself is socially stable.In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors.Convex TU-games have a non-empty socially stable core, irrespective of the power function.When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector.We demonstrate the usefulness of the concept of the socially stable core by two applications.One application concerns sequencing games and the other one the distribution of water.game theory;utility theory

A Theory of Stability in Many-to-many Matching Markets

We develop a theory of stability in many-to-many matching markets. We give conditions under which the setwise-stable set, a core-like concept, is nonempty and can be approached through an algorithm. The usual core may be empty. The setwise-stable set coincides with the pairwise-stable set, and with the predictions of a non-cooperative bargaining model. The set-wise stable set possesses the canonical conflict/coincidence of interest properties from many-to-one, and one-to-one models. The theory parallels the standard theory of stability for many-to-one, and one-to- one, models. We provide results for a number of core-like solutions, besides the setwise-stable set.many-to-many matchings, substitutability, tarski fixed point theorem, setwise stability, core

Stable Roommate Problem with Diversity Preferences

In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences [Bredereck et al., 2019]: each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents' preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem. Moreover, for the classic setting with rooms of size two, we present a linear-time algorithm that computes an outcome that is core and exchange stable as well as Pareto optimal. Many of our results for the stable roommate problem extend to the stable marriage problem.Comment: accepted to IJCAI'2

Computational Complexity in Additive Hedonic Games

We investigate the computational complexity of several decision problems in hedonic coalition formation games and demonstrate that attaining stability in such games remains NP-hard even when they are additive. Precisely, we prove that when either core stability or strict core stability is under consideration, the existence problem of a stable coalition structure is NP-hard in the strong sense. Furthermore, the corresponding decision problems with respect to the existence of a Nash stable coalition structure and of an individually stable coalition structure turn out to be NP-complete in the strong sense

The Stable Core and Dynamic Periphery in Top Management Teams

This study explores how top management teams make strategic decisions. The findings indicate that the top management team performs a variety of monitoring and control functions within most firms, but that a single team with stable composition does not make strategic choices in most organizations. Instead, different groups, with members from multiple organizational levels, form to make various strategic decisions. A stable subset of the top team forms the core of each of these multiple decision‐making bodies. The findings offer a possible explanation for inconsistent findings in the top management team literature, and suggest several new directions for future senior team research

Size Monotonicity and Stability of the Core in Hedonic Games

We show that the core of each strongly size monotonic hedonic game is not empty and is externally stable. This is in sharp contrast to other sufficient conditions for core non-emptiness which do not even guarantee the existence of a stable set in such games.Core, Hedonic Games, Monotonicity, Stable Sets