8 research outputs found
Cooperative Games with Overlapping Coalitions
In the usual models of cooperative game theory, the outcome of a coalition
formation process is either the grand coalition or a coalition structure that
consists of disjoint coalitions. However, in many domains where coalitions are
associated with tasks, an agent may be involved in executing more than one
task, and thus may distribute his resources among several coalitions. To tackle
such scenarios, we introduce a model for cooperative games with overlapping
coalitions--or overlapping coalition formation (OCF) games. We then explore the
issue of stability in this setting. In particular, we introduce a notion of the
core, which generalizes the corresponding notion in the traditional
(non-overlapping) scenario. Then, under some quite general conditions, we
characterize the elements of the core, and show that any element of the core
maximizes the social welfare. We also introduce a concept of balancedness for
overlapping coalitional games, and use it to characterize coalition structures
that can be extended to elements of the core. Finally, we generalize the notion
of convexity to our setting, and show that under some natural assumptions
convex games have a non-empty core. Moreover, we introduce two alternative
notions of stability in OCF that allow a wider range of deviations, and explore
the relationships among the corresponding definitions of the core, as well as
the classic (non-overlapping) core and the Aubin core. We illustrate the
general properties of the three cores, and also study them from a computational
perspective, thus obtaining additional insights into their fundamental
structure
Cooperative games with overlapping coalitions
In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitionsāor overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure
Coalitional Games with Overlapping Coalitions for Interference Management in Small Cell Networks
In this paper, we study the problem of cooperative interference management in
an OFDMA two-tier small cell network. In particular, we propose a novel
approach for allowing the small cells to cooperate, so as to optimize their
sum-rate, while cooperatively satisfying their maximum transmit power
constraints. Unlike existing work which assumes that only disjoint groups of
cooperative small cells can emerge, we formulate the small cells' cooperation
problem as a coalition formation game with overlapping coalitions. In this
game, each small cell base station can choose to participate in one or more
cooperative groups (or coalitions) simultaneously, so as to optimize the
tradeoff between the benefits and costs associated with cooperation. We study
the properties of the proposed overlapping coalition formation game and we show
that it exhibits negative externalities due to interference. Then, we propose a
novel decentralized algorithm that allows the small cell base stations to
interact and self-organize into a stable overlapping coalitional structure.
Simulation results show that the proposed algorithm results in a notable
performance advantage in terms of the total system sum-rate, relative to the
noncooperative case and the classical algorithms for coalitional games with
non-overlapping coalitions
Mathematical foundations of elasticity
[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute
Stability Via Convexity and LP Duality in OCF Games
The core is a central solution concept in cooperative game theory, and therefore it is important to know under what conditions the core of a game is guaranteed to be non-empty. Two notions that prove to be very useful in this context are Linear Programming (LP) duality and convexity. In this work, we apply these tools to identify games with overlapping coalitions (OCF games) that admit stable outcomes. We focus on three notions of the core defined in (Chalkiadakis et al. 2010) for such games, namely, the conservative core, the refined core and the optimistic core. First, we show that the conservative core of an OCF game is non-empty if and only if the core of a related classic coalitional game is non-empty. This enables us to improve the result of (Chalkiadakis et al. 2010) by giving a strictly weaker sufficient condition for the non-emptiness of the conservative core. We then use LP duality to characterize OCF games with non-empty refined core; as a corollary, we show that the refined core of a game is non-empty as long as the superadditive cover of its characteristic function is convex. Finally, we identify a large class of OCF games that can be shown to have a non-empty optimistic core using an LP based argument
Government intervention and agricultural performance in China
This study reassesses agricultural performance in China during the economy's transition
from a centrally planned system to one increasingly reliant on the market mechanisms.
The essence of economic reform was to reduce direct intervention by the government in
the operation of the economy and to allow more decision-making autonomy to economic
agents. But the process of reform is not yet complete. The Chinese economy today is
neither a perfectly free market nor a stylized central planning system.
The central argument is that the agricultural sector is being increasingly integrated with
the rest of the Chinese economy, and the world economy through the process of
economic liberalization. Economy-wide policies and changes elsewhere are as important
as sector-specific policies in affecting agricultural performance. At the same time,
restrictions on factor movements and price distortions remain and affect agriculture's
response to exogenous changes. Agriculture's response to initial reforms has been seen
as a 'miracle'; growth jumped to 7 per cent between 1979 and 1984. The relative
contraction of agricultural production in 1985 and years after is less clearly understood.
A simple illustrative model is constructed for theoretical analysis. This framework is
applied to understand agricultural growth in China and it is found that dramatic changes
in farmers' feasible choice set were dominant factors determining agricultural growth and
contraction in the second half of the 1980s. This case underlines the importance of
restrictions on factor mobility in the Chinese economy. Changes in factor markets may
sometimes offset changes in price structure and require particular attention in analysis.
Price policies for grain m China were endogenously determined through bargaining
between farmers and the state. In the early stages of economic development under a
repressive and vindictive central state system, farmers tend to be weak in the state-farmer
policy game. This study develops a state-farmer agricultural policy game framework. Farmers' relative bargaining power is negatively correlated with agriculture's share in the
economy and the share if agricultural population, and positively correlated with income
per capita and the market price of grain. Farmers in China were still relatively weak in
policy game with the government. But it can be expected that farmers' bargaining power
will continue to increase as the economy develops. There is a danger that with growing
bargaining position demand for agricultural subsidies will grow.
Farmers' production decisions are guided by a combination of policy regulations and
market signals, but their behaviour can be modelled by profit maximization framework
given careful data adjustment. Supply elasticities estimated through an application of the
McFadden unit profit function indicate that continuation of grain self-sufficiency will be
both difficult and costly.
To understand both direct and indirect effects of policy on agriculture, a computable
general equilibrium model is built. A set of experiments including changes in the world
market, economic reforms such as tariff reduction, variation in macroeconomic policies
and a rapid expansion of rural industry are undertaken. The Chinese economy and the
agricultural sector adjust to exogenous change but the adjustment is smaller than it
would be in the case of perfect factor mobility. Money becomes non-neutral in the
presence of price distortion in Chinese economy