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 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

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