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Social Distance Games
"... In this paper we introduce and analyze social distance games, a family of nontransferable utility coalitional games where an agent’s utility is a measure of closeness to the other members of the coalition. We study both social welfare maximisation and stability in these games using a graph theoreti ..."
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In this paper we introduce and analyze social distance games, a family of nontransferable utility coalitional games where an agent’s utility is a measure of closeness to the other members of the coalition. We study both social welfare maximisation and stability in these games using a graph theoretic perspective. We use the stability gap to investigate the welfare of stable coalition structures, and propose two new solution concepts with improved welfare guarantees. We argue that social distance games are both interesting in themselves, as well as in the context of social networks. 1
Computational Analysis of Connectivity Games with Applications to the Investigation of Terrorist Networks
 PROCEEDINGS OF THE TWENTYTHIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... We study a recently developed centrality metric to identify key players in terrorist organisations due to Lindelauf et al. [2013]. This metric, which involves computation of the Shapley value for connectivity games on graphs proposed by Amer and Gimenez [2004], was shown to produce substantially bet ..."
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Cited by 6 (4 self)
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We study a recently developed centrality metric to identify key players in terrorist organisations due to Lindelauf et al. [2013]. This metric, which involves computation of the Shapley value for connectivity games on graphs proposed by Amer and Gimenez [2004], was shown to produce substantially better results than previously used standard centralities. In this paper, we present the first computational analysis of this class of coalitional games, and propose two algorithms for computing Lindelauf et al.’s centrality metric. Our first algorithm is exact, and runs in time linear by number of connected subgraphs in the network. As shown in the numerical simulations, our algorithm identifies key players in the WTC 9/11 terrorist network, constructed of 36 members and 125 links, in less than 40 minutes. In contrast, a generalpurpose Shapley value algorithm would require weeks to solve this problem. Our second algorithm is approximate and can be used to study much larger networks.
Potential games are necessary to ensure pure Nash equilibria in cost sharing games
 Mathematics of Operations Research
"... We consider the problem of designing distribution rules to share ‘welfare ’ (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; ho ..."
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Cited by 5 (1 self)
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We consider the problem of designing distribution rules to share ‘welfare ’ (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants; however, a characterization of the space of distribution rules that guarantee the existence of a Nash equilibrium is unknown. Our work provides an exact characterization of this space for a specific class of scalable and separable games, which includes a variety of applications such as facility location, routing, network formation, and coverage games. Given arbitrary local welfare functions W, we prove that a distribution rule guarantees equilibrium existence for all games (i.e., all possible sets of resources, agent action sets, etc.) if and only if it is equivalent to a generalized weighted Shapley value on some ‘ground ’ welfare functions W′, which can be distinct from W. However, if budgetbalance is required in addition to the existence of a Nash equilibrium, then W ′ must be the same as W. We also provide an alternate characterization of this space in terms of ‘generalized’ marginal contributions, which is more appealing from the point of view of computational tractability. A possibly surprising consequence of our result is that, in order to guarantee equilibrium existence in all games with any fixed local welfare functions, it is necessary to work within the class of potential games.
Trust And Distrust Across Coalitions Shapley Value Centrality Measures For Signed Networks
"... Signed social networks are social networks with edges indicative of both trust and distrust. We propose novel game theoretic centrality measures for signed networks, which first generalize degreebased centrality from nodes to sets, and then compute individual node centralities using the concept of ..."
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Signed social networks are social networks with edges indicative of both trust and distrust. We propose novel game theoretic centrality measures for signed networks, which first generalize degreebased centrality from nodes to sets, and then compute individual node centralities using the concept of Shapley Value. We derive closed form expressions for the Shapley Value for most of these measures. Moreover, we demonstrate that some of these measures give improved AP (average precision) compared to net positive indegree for the task of detecting troll users, in the Slashdot signed network. 1
Two Coalitional Models for Network Formation and Matching Games
"... I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis comprises of two separate game theoretic m ..."
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I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii This thesis comprises of two separate game theoretic models that fall under the general umbrella of network formation games. The first is a coalitional model of interaction in social networks that is based on the idea of social distance, in which players seek interactions with similar others. Our model captures some of the phenomena observed on such networks, such as homophily driven interactions and the formation of small worlds for groups of players. Using social distance games, we analyze the interactions between players on the network, study the properties of efficient and stable networks, relate them to the underlying graphical structure of the game, and give an approximation algorithm for finding optimal social welfare. We then show that efficient networks are not necessarily stable, and stable networks do not necessarily maximise welfare. We use the stability gap to investigate the
Measuring Network Centrality Using Hypergraphs
"... Networks abstracted as graph lose some information related to the superdyadic relation among the nodes. We find natural occurrence of hyperedges in coauthorship, cocitation, social networks, email networks, weblog networks etc. Treating these networks as hypergraph preserves the superdyadic r ..."
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Networks abstracted as graph lose some information related to the superdyadic relation among the nodes. We find natural occurrence of hyperedges in coauthorship, cocitation, social networks, email networks, weblog networks etc. Treating these networks as hypergraph preserves the superdyadic relations. But the primal graph or Gaifmann graph associated with hypergraphs converts each hyperedge to a clique losing again the nary relationship among nodes. We aim to measure Shapley Value based centrality on these networks without losing the superdyadic information. For this purpose, we use cooperative games on single graph representation of a hypergraph such that Shapley value can be computed efficiently[1]. We propose several methods to generate simpler graphs from hypergraphs and study the efficacy of the centrality scores computed on these constructions.
Declaration
, 2013
"... I Liangchuan Gu of Robinson College, being a candidate for the M.Phil in Advanced Computer Science, hereby declare that this report and the work described in it are my own work, unaided except as may be specified below, and that the report does not contain material that has already been used to any ..."
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I Liangchuan Gu of Robinson College, being a candidate for the M.Phil in Advanced Computer Science, hereby declare that this report and the work described in it are my own work, unaided except as may be specified below, and that the report does not contain material that has already been used to any substantial extent for a comparable purpose. Total word count: 14,937