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

Taxation and Stability in Cooperative Games

ABSTRACT Cooperative games are a useful framework for modeling multiagent 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

Industrial Symbiotic Networks as Coordinated Games

We present an approach for implementing a specific form of collaborative industrial practices-called Industrial Symbiotic Networks (ISNs)-as MC-Net cooperative games and address the so called ISN implementation problem. This is, the characteristics of ISNs may lead to inapplicability of fair and stable benefit allocation methods even if the collaboration is a collectively desired one. Inspired by realistic ISN scenarios and the literature on normative multi-agent systems, we consider regulations and normative socioeconomic policies as two elements that in combination with ISN games resolve the situation and result in the concept of coordinated ISNs.Comment: 3 pages, Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018

Bounds on the Cost of Stabilizing a Cooperative Game

This is the author accepted manuscript. The final version is available from the AI Access Foundation via the DOI in this record.A key issue in cooperative game theory is coalitional stability, usually captured by the notion of the core—the set of outcomes that are resistant to group deviations. However, some coalitional games have empty cores, and any outcome in such a game is unstable. We investigate the possibility of stabilizing a coalitional game by using subsidies. We consider scenarios where an external party that is interested in having the players work together offers a supplemental payment to the grand coalition, or, more generally, a particular coalition structure. This payment is conditional on players not deviating from this coalition structure, and may be divided among the players in any way they wish. We define the cost of stability as the minimum external payment that stabilizes the game. We provide tight bounds on the cost of stability, both for games where the coalitional values are nonnegative (profit-sharing games) and for games where the coalitional values are nonpositive (cost-sharing games), under natural assumptions on the characteristic function, such as superadditivity, anonymity, or both. We also investigate the relationship between the cost of stability and several variants of the least core. Finally, we study the computational complexity of problems related to the cost of stability, with a focus on weighted voting games.DFGEuropean Science FoundationNRF (Singapore)European Research CouncilHorizon 2020 European Research Infrastructure projectIsrael Science FoundationIsrael Ministry of Science and TechnologyGoogle Inter-University Center for Electronic Markets and AuctionsEuropean Social Fund (European Commission)Calabria Regio

Game theoretical models for clustering and resource sharing in macro-femtocells networks

One of the main challenges of cellular network operators is to keep a good network quality for their users. In most cases, network quality decreases in indoor environments causing users to switch from one operator to another. A promising solution to cope with this issue is the deployment of femtocells that are used mainly at homes to enhance the mobile network coverage. In fact, higher penetration of broadband and mobile phones with high requirements of new applications such as video conferencing and internet games are promoting femtocell market. However, the deployment of femtocells in existing macrocell networks is a very challenging task due to the high complexity of the resource allocation. In this thesis, we focus on proposing several solutions to address the resource allocation problem in macro-femtocell networks with dense deployment of femtocells based on clustering techniques. Clustering techniques are used to reduce the resource allocation complexity of dense-femtocell networks since the resources are allocated locally within each cluster. Furthermore, a cluster head is responsible for the allocation of resources to femtocells within the cluster which avoids the co-tier interference. The clustering techniques have been widely used for distributed resource allocation in heterogeneous networks through the use of game theory models. In this work, three distributed resource allocation algorithms based on cooperative and evolutionary games are proposed. In the first part, we discuss the resource allocation problem for the non-dense deployment of femtocells. Toward this goal, a coalitional game is used to incentive femtocells in the formation of clusters. The approach decomposes in: (i) a base station selection algorithm for public users, (ii) a clustering algorithm based on cooperative game theory and (iii) a resource allocation within each cluster based on the PSO technique. Besides, an interference control mechanism enabled femtocells to leave its current cluster when the interference levels are higher than an interference threshold. In the second part, we focus on a fair allocation of resources for macro-femtocell networks. We develop a clustering algorithm based on a cooperative game for non-dense femtocell network. The Shapley value is applied to find the marginal contribution of every femtocell to all the possible groups of femtocells, thus, finding the fair amount of resources to be allocated to each femtocell within a cluster. This solution is only applied for non-dense femtocell deployment due to that the complexity of calculating the Shapley value increases significantly with a large number of femtocells. Stability criteria based on the ε-concept of game theory is utilized to find the set of stable clusters. Finally, the analysis of the resource allocation for dense-femtocell deployment is addressed through an evolutionary game theory (EGT) model. It is assumed that EGT requires bounded rationality from players, this reduces the complexity and allows the dense deployment of femtocells. In addition, we demonstrate that the set of clusters formed with EGT are stable by means of the replicator dynamics. The proposed model also includes system analysis for users with low mobility such as pedestrians and cyclists