Sex differences in the structure and stability of children’s playground social networks and their overlap with friendship relations

Gender segregated peer networks during middle childhood have been highlighted as important for explaining later sex differences in behaviour, yet few studies have examined the structural composition of these networks and their implications. This short-term longitudinal study of 119 children (7-8 years) examined the size and internal structure of boys' and girls' social networks, their overlap with friendship relations, and their stability over time. Data collection at the start and end of the year involved systematic playground observations of pupils' play networks during team and non-team activities and measures of friendship from peer nomination interviews. Social networks were identified by aggregating play network data at each time point. Findings showed that the size of boy's play networks on the playground, but not their social networks, varied according to activity type. Social network cores consisted mainly of friends. Girl's social networks were more likely to be composed of friends and boys' networks contained friends and non-friends. Girls had more friends outside of the social network than boys. Stability of social network membership and internal network relations were higher for boys than girls. These patterns have implications for the nature of social experiences within these network contexts

On the Core of Dynamic Cooperative Games

We consider dynamic cooperative games, where the worth of coalitions varies over time according to the history of allocations. When defining the core of a dynamic game, we allow the possibility for coalitions to deviate at any time and thereby to give rise to a new environment. A coalition that considers a deviation needs to take the consequences into account because from the deviation point on, the game is no longer played with the original set of players. The deviating coalition becomes the new grand coalition which, in turn, induces a new dynamic game. The stage games of the new dynamical game depend on all previous allocation including those that have materialized from the deviating time on. We define three types of core solutions: fair core, stable core and credible core. We characterize the first two in case where the instantaneous game depends on the last allocation (rather than on the whole history of allocations) and the third in the general case. The analysis and the results resembles to a great extent the theory of non-cooperative dynamic games.Comment: 25 page

Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels

Cooperation between nodes sharing a wireless channel is becoming increasingly necessary to achieve performance goals in a wireless network. The problem of determining the feasibility and stability of cooperation between rational nodes in a wireless network is of great importance in understanding cooperative behavior. This paper addresses the stability of the grand coalition of transmitters signaling over a multiple access channel using the framework of cooperative game theory. The external interference experienced by each TX is represented accurately by modeling the cooperation game between the TXs in \emph{partition form}. Single user decoding and successive interference cancelling strategies are examined at the receiver. In the absence of coordination costs, the grand coalition is shown to be \emph{sum-rate optimal} for both strategies. Transmitter cooperation is \emph{stable}, if and only if the core of the game (the set of all divisions of grand coalition utility such that no coalition deviates) is nonempty. Determining the stability of cooperation is a co-NP-complete problem in general. For a single user decoding receiver, transmitter cooperation is shown to be \emph{stable} at both high and low SNRs, while for an interference cancelling receiver with a fixed decoding order, cooperation is stable only at low SNRs and unstable at high SNR. When time sharing is allowed between decoding orders, it is shown using an approximate lower bound to the utility function that TX cooperation is also stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX cooperation over a MAC is stable and improves achievable rates for each individual user.Comment: in review for publication in IEEE Transactions on Signal Processin

Core equivalence theorems for infinite convex games

We show that the core of a continuous convex game on a measurable space of players is a von Neumann-Morgenstern stable set. We also extend the definition of the Mas-Colell bargaining set to games with a measurable space of players, and show that for continuous convex games the core may be strictly included in the bargaining set but it coincides with the set of all countably additive payoff measures in the bargaining set. We provide examples which show that the continuity assumption is essential to our results

Laws of Scarcity for a Finite Game : Exact Bounds on Estimations

A "law of scarcity" is that scarceness is rewarded. We demonstrate laws of scarcity for cores and approximate cores of games. Furthermore, we show that equal treatment core payout vectors satisfy a condition of cyclic monotonicity. Our results are developed for parameterized collections of games and exact bounds on the maximum possible deviation of approximate core payo® vectors from satisfying a law of scarcity are stated in terms of the parameters describing the games. We note that the parameters can, in principle, be estimated.monotonicity ; cooperative games ; clubs ; games with side payments (TU games) ; cyclic monotonicity ; law of scarcity ; law of demand ; approximate cores ; effective small groups ; parameterized collections of games

A law of scarcity for games

The "law of scarcity" is that scarceness is rewarded; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.cooperative games, games with side payments (TU games), cyclic monotonicity, law of demand, approximate cores, effective small groups, parameterized collections of games.

A law of scarcity for games

The “law of scarcity” is that scarceness is rewarded ; recall, for example, the diamonds and water paradox. In this paper, furthering research initiated in Kelso and Crawford (1982, Econometrica 50, 1483-1504) for matching models, we demonstrate a law of scarcity for cores and approximate cores of games.cooperative games ; games with side payments (TU games) ; cyclic monotonicity ; law of demand ; approximate cores ; effective small groups ; parameterized collections of games

Taxation and stability in cooperative games

Cooperative games are a useful framework for modeling multi-agent behavior in environments where agents must collaborate in order to complete tasks. Having jointly completed a task and generated revenue, agents need to agree on some reasonable method of sharing their profits. One particularly appealing family of payoff divisions is the core, which consists of all coalitionally rational (or, stable) payoff divisions. Unfortunately, it is often the case that the core of a game is empty, i.e. there is no payoff scheme guaranteeing each group of agents a total payoff higher than what they can get on their own. As stability is a highly attractive property, there have been various methods of achieving it proposed in the literature. One natural way of stabilizing a game is via taxation, i.e. reducing the value of some coalitions in order to decrease their bargaining power. Existing taxation methods include the ε-core, the least-core and several others. However, taxing coalitions is in general undesirable: one would not wish to overly tamper with a given coalitional game, or overly tax the agents. Thus, in this work we study minimal taxation policies, i.e. those minimizing the amount of tax required in order to stabilize a given game. We show that games that minimize the total tax are to some extent a linear approximation of the original games, and explore their properties. We demonstrate connections between the minimal tax and the cost of stability, and characterize the types of games for which it is possible to obtain a tax-minimizing policy using variants of notion of the ε-core, as well as those for which it is possible to do so using reliability extensions. Copyright © 2013, International Foundation for Autonomous Agents and Multiagent Systems (www.ifaamas.org). All rights reserved