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12
Computing Shapley values, manipulating value division schemes, and checking core membership in multiissue domains
 IN PROCEEDINGS OF THE NATIONAL CONFERENCE ON ARTIFICIAL INTELLIGENCE (AAAI
, 2004
"... Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computati ..."
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Cited by 73 (8 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents. In order for coalition formation to be successful, a key question that must be answered is how the gains from cooperation are to be distributed. Various solution concepts have been proposed, but the computational questions around these solution concepts have received little attention. We study a concise representation of characteristic functions which allows for the agents to be concerned with a number of independent issues that each coalition of agents can address. For example, there may be a set of tasks that the capacityunconstrained agents could undertake, where accomplishing a task generates a certain amount of value (possibly depending on how well the task is accomplished). Given this representation, we show how to quickly compute the Shapley value—a seminal value division scheme that distributes the gains from cooperation fairly in a certain sense. We then show that in (distributed) marginalcontribution based value division schemes, which are known to be vulnerable to manipulation of the order in which the agents are added to the coalition, this manipulation is NPcomplete. Thus, computational complexity serves as a barrier to manipulating the joining order. Finally, we show that given a value division, determining whether some subcoalition has an incentive to break away (in which case we say the division is not in the core) is NPcomplete. So, computational complexity serves to increase the stability of the coalition.
Complexity of Constructing Solutions in the Core Based on Synergies among Coalitions
 ARTIFICIAL INTELLIGENCE
, 2006
"... Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solut ..."
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Cited by 48 (2 self)
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Coalition formation is a key problem in automated negotiation among selfinterested agents, and other multiagent applications. A coalition of agents can sometimes accomplish things that the individual agents cannot, or can accomplish them more efficiently. Motivating the agents to abide by a solution requires careful analysis: only some of the solutions are stable in the sense that no group of agents is motivated to break off and form a new coalition. This constraint has been studied extensively in cooperative game theory: the set of solutions that satisfy it is known as the core. The computational questions around the core have received less attention. When it comes to coalition formation among software agents (that represent realworld parties), these questions become increasingly explicit. In this
Strategic Network Formation through Peering and Service Agreements
, 2010
"... We introduce a game theoretic model of network formation in an effort to understand the complex system of business relationships between various Internet entities (e.g., Autonomous Systems, enterprise networks, residential customers). This system is at the heart of Internet connectivity. In our mode ..."
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Cited by 26 (5 self)
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We introduce a game theoretic model of network formation in an effort to understand the complex system of business relationships between various Internet entities (e.g., Autonomous Systems, enterprise networks, residential customers). This system is at the heart of Internet connectivity. In our model we are given a network topology of nodes and links where the nodes act as the players of the game, and links represent potential contracts. Nodes wish to satisfy their demands, which earn potential revenues, but may have to pay their neighbors for links incident to them. We incorporate some of the qualities of Internet business relationships, including customerprovider and peering contracts. We show that every Nash equilibrium can be represented by a circulation flow of utility with certain constraints. This allows us to prove that the price of stability is at most 2 with respect to a natural objective function, but that prices of anarchy and stability can both be unbounded with respect to social welfare. We thus focus on the quality of equilibria achievable through centralized incentives, and show that if every payout is increased by a factor of 2, then there is a Nash equilibrium as good as the original centrally defined social optimum.
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
 in Proceedings of the 27th ACM Symposium on Principles of Distributed Computing
"... Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set o ..."
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Cited by 19 (2 self)
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Motivated by applications in social networks, peertopeer and overlay networks, we define and study the Bounded Budget Connection (BBC) game we have a collection of n players or nodes each of whom has a budget for purchasing links; each link has a cost as well as a length and each node has a set of preference weights for each of the remaining nodes; the objective of each node is to use its budget to buy a set of outgoing links so as to minimize its sum of preferenceweighted distances to the remaining nodes. We study the structural and complexitytheoretic properties of pure Nash equilibria in BBC games. We show that determining the existence of a pure Nash equilibrium in general BBC games is NPhard. We counterbalance this result by considering a natural variant, fractional BBC games where it is permitted to buy fractions of links and show that a pure Nash equilibrium always exists in such games. A major focus is the study of (n, k)uniform BBC games those in which all link costs, link lengths and preference weights are equal (to 1) and all budgets are equal (to k). We show that a pure Nash equilibrium or stable graph exists for all (n, k)uniform BBC games and that all stable graphs are essentially fair (i.e. all nodes have similar costs). We provide an explicit construction of a family of stable graphs that spans the spectrum from minimum total social cost to maximum total social cost. To be precise we show that that the price of stability is Θ(1) and the price of anarchy is Ω( n/k) and O( logk n
Reducibility among fractional stability problems
 in Proc. IEEE FOCS, 2009
"... Abstract — In a landmark paper [32], Papadimitriou introduced a number of syntactic subclasses of TFNP based on proof styles that (unlike TFNP) admit complete problems. A recent series of results [11], [16], [5], [6], [7], [8] has shown that finding Nash equilibria is complete for PPAD, a particular ..."
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Cited by 11 (2 self)
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Abstract — In a landmark paper [32], Papadimitriou introduced a number of syntactic subclasses of TFNP based on proof styles that (unlike TFNP) admit complete problems. A recent series of results [11], [16], [5], [6], [7], [8] has shown that finding Nash equilibria is complete for PPAD, a particularly notable subclass of TFNP. A major goal of this work is to expand the universe of known PPADcomplete problems. We resolve the computational complexity of a number of outstanding open problems with practical applications. Here is the list of problems we show to be PPADcomplete, along with the domains of practical significance: Fractional Stable
The cooperative game theory foundations of network bargaining games,”
 in International Colloquium on Automata, Languages and Programming,
"... Abstract. We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus are represented by weighted edges in our bipartite ..."
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Cited by 10 (0 self)
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Abstract. We study bargaining games between suppliers and manufacturers in a network context. Agents wish to enter into contracts in order to generate surplus which then must be divided among the participants. Potential contracts and their surplus are represented by weighted edges in our bipartite network. Each agent in the market is additionally limited by a capacity representing the number of contracts which he or she may undertake. When all agents are limited to just one contract each, prior research applied natural generalizations of the Nash bargaining solution to the networked setting, defined the new solution concepts of stable and balanced, and characterized the resulting bargaining outcomes. We simplify and generalize these results to a setting in which participants in only one side of the market are limited to one contract each. The core of our results uses a linearprogramming formulation to establish a novel connection between wellstudied cooperative game theory concepts and the solution concepts of core and prekernel defined for the bargaining games. This immediately implies one can take advantage of the results and algorithms in cooperative game theory to reproduce results such as those of Azar et al.
A BoundedDegree Network Formation Game
 In PODC ’08
"... Motivated by applications in peertopeer and overlay networks we define and study the Bounded Degree Network Formation (BDNF) game. In an (n, k)BDNF game, we are given n nodes, a bound k on the outdegree of each node, and a weight wvu for each ordered pair (v, u) representing the traffic rate fro ..."
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Cited by 7 (6 self)
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Motivated by applications in peertopeer and overlay networks we define and study the Bounded Degree Network Formation (BDNF) game. In an (n, k)BDNF game, we are given n nodes, a bound k on the outdegree of each node, and a weight wvu for each ordered pair (v, u) representing the traffic rate from node v to node u. Each node v uses up to k directed links to connect to other nodes with an objective to minimize its average distance, using weights wvu, to all other destinations. We study the existence of pure Nash equilibria for (n, k)BDNF games. We show that if the weights are arbitrary, then a pure Nash wiring may not exist. Furthermore, it is NPhard to determine whether a pure Nash wiring exists for a given (n, k)BDNF instance. A major focus of this paper is on uniform (n, k)BDNF games, in which all weights are 1. We describe how to construct a pure Nash equilibrium wiring given any n and k, and establish that in all pure Nash wirings the cost of individual nodes cannot differ by more than a factor of nearly 2, whereas the diameter cannot exceed O ( p nlog k n). We also analyze bestresponse walks on the configuration space defined by the uniform game, and show that starting from any initial configuration, strong connectivity is reached within Θ(n 2) rounds. Convergence to a pure Nash equilibrium, however, is not guaranteed. We present simulation results that suggest that loopfree bestresponse walks always exist, but may not be polynomially bounded. We also study a special family of regular wirings, the class of Abelian Cayley graphs, in which all nodes imitate the same wiring pattern, and show that if n is sufficiently large no such regular wiring can be a pure Nash equilibrium. 1
Mechanism design for the multicommodity flow game.” Working paper
, 2007
"... We study a collaborative multicommodity flow game where individual players own capacity on the edges of the network and share this capacity to deliver commodities. We present membership mechanisms, by adopting a rationality based approach using notions from game theory and inverse optimization, to a ..."
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Cited by 5 (1 self)
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We study a collaborative multicommodity flow game where individual players own capacity on the edges of the network and share this capacity to deliver commodities. We present membership mechanisms, by adopting a rationality based approach using notions from game theory and inverse optimization, to allocate benefits among the players in such a game.
The design and development of Mobile Ad Hoc Networks
"... Wireless (and hence mobile) communication networks have become an integral part of our society, significantly enhancing communication capabilities; mobile ad hoc networks (MANETs) extend this capability to any time/anywhere, providing connectivity without the need of an underlying infrastructure. T ..."
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Cited by 1 (1 self)
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Wireless (and hence mobile) communication networks have become an integral part of our society, significantly enhancing communication capabilities; mobile ad hoc networks (MANETs) extend this capability to any time/anywhere, providing connectivity without the need of an underlying infrastructure. This work aims to investigate the newcoming area of mobile ad hoc networks, focusing on research problems related to the design and development of routing protocols, both from a formal and technical point of view. wireless, mobile ad hoc network, protocol, routing. Index Terms I.
Preference Games and . . .
, 2009
"... We study the complexity of computing equilibria in two classes of network games based on flows fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fracti ..."
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We study the complexity of computing equilibria in two classes of network games based on flows fractional BGP (Border Gateway Protocol) games and fractional BBC (Bounded Budget Connection) games. BGP is the glue that holds the Internet together and hence its stability, i.e. the equilibria of fractional BGP games [15], is a matter of practical importance. BBC games [21] follow in the tradition of the large body of work on network formation games and capture a variety of applications ranging from social networks and overlay networks to peertopeer networks. The central result of this paper is that there are no fully polynomialtime approximation schemes (unless PPAD is in FP) for computing equilibria in both fractional BGP games and fractional BBC games. We obtain this result by proving the hardness for a new and surprisingly simple game, the preference game, which is reducible to both fractional BGP and BBC games. Generalizing both fractional BBC games and fractional BGP games, we define a new flowbased notion of equilibrium for matrix games – personalized equilibria. We prove not just the existence, but the existence of rational personalized equilibria for all matrix games, which implies the existence of rational equilibria for fractional BGP and BBC games. In particular, this provides an alternative proof and strengthening of the main result in [15]. For kplayer matrix games, where k = 2, we provide a combinatorial characterization leading to a polynomialtime algorithm for computing all personalized equilibria. For k ≥ 4, we prove that personalized equilibria are PPADhard to approximate in fully polynomial time. We believe that the concept of personalized equilibria has potential for realworld significance.