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22
Computing stable outcomes in hedonic games
 In Proc. 3rd International Symposium on Algorithmic Game Theory
, 2010
"... Abstract. We study the computational complexity of finding stable outcomes in symmetric additivelyseparable hedonic games. These coalition formation games are specified by an undirected edgeweighted graph: nodes are players, an outcome of the game is a partition of the nodes into coalitions, and ..."
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Abstract. We study the computational complexity of finding stable outcomes in symmetric additivelyseparable hedonic games. These coalition formation games are specified by an undirected edgeweighted graph: nodes are players, an outcome of the game is a partition of the nodes into coalitions, and the utility of a node is the sum of incident edge weights in the same coalition. We consider several natural stability requirements defined in the economics literature. For all of them the existence of a stable outcome is guaranteed by a potential function argument, so local improvements will converge to a stable outcome and all these problems are in PLS. The different stability requirements correspond to different local search neighbourhoods. For different neighbourhood structures, our findings comprise positive results in the form of polynomialtime algorithms for finding stable outcomes, and negative (PLScompleteness) results.
Circumventing the Price of Anarchy: Leading Dynamics to Good Behavior
"... Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all work to date on dynamics shows only convergence to some equilibrium, especially within a polynomial number of steps. In this work we study how age ..."
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Many natural games can have a dramatic difference between the quality of their best and worst Nash equilibria, even in pure strategies. Yet, nearly all work to date on dynamics shows only convergence to some equilibrium, especially within a polynomial number of steps. In this work we study how agents with some knowledge of the game might be able to quickly (within a polynomial number of steps) find their way to states of quality close to the best equilibrium. We consider two natural learning models in which players choose between greedy behavior and following a proposed good but untrusted strategy and analyze two important classes of games in this context, fair costsharing and consensus games. Both games have extremely high Price of Anarchy and yet we show that behavior in these models can efficiently reach lowcost states.
Approximating Pure Nash Equilibrium in Cut, Party Affiliation, and Satisfiability Games
"... Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLScom ..."
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Cited by 12 (1 self)
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Cut games and party affiliation games are wellknown classes of potential games. Schaffer and Yannakakis showed that computing pure Nash equilibrium in these games is PLScomplete. In general potential games, even the problem of computing any finite approximation to a pure equilibrium is also PLScomplete. We show that for any ɛ> 0, we design an algorithm to compute in polynomial time a (3 + ɛ)approximate pure Nash equilibrium for cut and party affiliation games. Prior to our work, only a trivial polynomial factor approximation was known for these games. Our approach extends beyond cut and party affiliation games to a more general class of satisfiability games. A key idea in our approach is a preprocessing phase that creates a partial order on the players. We then apply Nash dynamics to a sequence of restricted games derived from this partial order. We show that this process converges in polynomialtime to an approximate Nash equilibrium by strongly utilizing the properties of the partial order. This is in strong contrast to earlier results for some other classes of potential games that compute an approximate equilibrium by a direct application of Nash dynamics on the original game. In fact, we also show that such a technique cannot yield FPTAS for computing equilibria in cut and party affiliation games.
On strong equilibria in the max cut game
 In: Proc. of WINE 2009, Springer LNCS
, 2009
"... Abstract. This paper deals with two games defined upon well known generalizations of max cut. We study the existence of a strong equilibrium which is a refinement of the Nash equilibrium. Bounds on the price of anarchy for Nash equilibria and strong equilibria are also given. In particular, we show ..."
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Abstract. This paper deals with two games defined upon well known generalizations of max cut. We study the existence of a strong equilibrium which is a refinement of the Nash equilibrium. Bounds on the price of anarchy for Nash equilibria and strong equilibria are also given. In particular, we show that the max cut game always admits a strong equilibrium and the strong price of anarchy is 2/3. 1
Equilibria and Efficiency Loss in Games on Networks
"... Social networks are the substrate upon which we make and evaluate many of our daily decisions: our costs and benefits depend on whether—or how many of, or which of—our friends are willing to go to that restaurant, choose that cellular provider, already own that gaming platform. Much of the research ..."
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Social networks are the substrate upon which we make and evaluate many of our daily decisions: our costs and benefits depend on whether—or how many of, or which of—our friends are willing to go to that restaurant, choose that cellular provider, already own that gaming platform. Much of the research on the “diffusion of innovation,” for example, takes a gametheoretic perspective on strategic decisions made by people embedded in a social context. Indeed, multiplayer games played on social networks, where the network’s nodes correspond to the game’s players, have proven to be fruitful models of many natural scenarios involving strategic interaction. In this paper, we embark on a mathematical and general exploration of the relationship between 2person strategic interactions (a “base game”) and a “networked” version
Decentralized Dynamics for Finite Opinion Games
, 2012
"... Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations. In the spirit of the field, we study the computation of sol ..."
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Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations. In the spirit of the field, we study the computation of solution concepts by means of decentralized dynamics. These are algorithms in which players move in turns to improve their own utility and the hope is that the system reaches an “equilibrium” quickly. We study these dynamics for the class of opinion games, recently introduced by [1]. These are games, important in economics and sociology, that model the formation of an opinion in a social network. We study bestresponse dynamics and show that the convergence to Nash equilibria is polynomial in the number of players. We also study a noisy version of bestresponse dynamics, called logit dynamics, and prove a host of results about its convergence rate as the noise in the system varies. To get these results, we use a variety of techniques developed to bound the mixing time of Markov chains, including coupling, spectral characterizations and bottleneck ratio.
Near Optimality in Covering and Packing Games by Exposing Global
 Information, CoRR
"... Covering and packing problems can be modeled as games to encapsulate interesting social and engineering settings. These games have a high Price of Anarchy in their natural formulation. However, existing research applicable to specific instances of these games has only been able to prove fast converg ..."
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Covering and packing problems can be modeled as games to encapsulate interesting social and engineering settings. These games have a high Price of Anarchy in their natural formulation. However, existing research applicable to specific instances of these games has only been able to prove fast convergence to arbitrary equilibria. This paper studies general classes of covering and packing games with learning dynamics models that incorporate a central authority who broadcasts weak, socially beneficial signals to agents that otherwise only use local information in their decisionmaking. Rather than illustrating convergence to an arbitrary equilibrium that may have very high social cost, we show that these systems quickly achieve nearoptimal performance. In particular, we show that in the public service advertising model of [1], reaching a small constant fraction of the agents is enough to bring the system to a state within a logn factor of optimal in a broad class of set cover and set packing games or a constant factor of optimal in the special cases of vertex cover and maximum independent set, circumventing social inefficiency of bad local equilibria that could arise without a central authority. We extend these results to the learnthendecide model of [2], in which agents use any of a broad class of learning algorithms to decide in a given round whether to behave according to locally optimal behavior or the behavior prescribed by the broadcast signal. The new techniques we use for analyzing these games could be of broader interest for analyzing more general classic optimization problems in a distributed fashion. 1
Constant Price of Anarchy in Network Creation Games via Public Service Advertising
"... Network creation games have been studied in many different settings recently. These games are motivated by social networks in which selfish agents want to construct a connection graph among themselves. Each node wants to minimize its average or maximum distance to the others, without paying much t ..."
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Network creation games have been studied in many different settings recently. These games are motivated by social networks in which selfish agents want to construct a connection graph among themselves. Each node wants to minimize its average or maximum distance to the others, without paying much to construct the network. Many generalizations have been considered, including nonuniform interests between nodes, general graphs of allowable edges, bounded budget agents, etc. In all of these settings, there is no known constant bound on the price of anarchy. In fact, in many cases, the price of anarchy can be very large, namely, a constant power of the number of agents. This means that we have no control on the behavior of network when agents act selfishly. On the other hand, the price of stability in all these models is constant, which means that there is chance that agents act selfishly and we end up with a reasonable social cost. In this paper, we show how to use an advertising campaign (as introduced in SODA 2009 [2]) to find such efficient equilibria in (n, k)uniform bounded budget connection game [10]; our result holds for k = ω(log(n)). More formally, we present advertising strategies such that, if an α fraction of the agents agree to cooperate in the campaign, the social cost would be at most O(1/α) times the optimum cost. This is the first constant bound on the price of anarchy that interestingly can be adapted to different settings. We also generalize our method to work in cases that α is not known in advance. Also, we do not need to assume that the cooperating agents spend all their budget in the campaign; even a small fraction (β fraction) of their budget is sufficient to obtain a constant price of anarchy.
The effects of diversity in aggregation games
 In Innovation in Computer Science
, 2011
"... Abstract: Aggregation of entities is a widely observed phenomenon in economics, sociology, biology and other fields. It is natural to ask how diverse and competitive entities can achieve high levels of aggregation. In order to answer this question we provide a gametheoretical model for aggregation. ..."
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Abstract: Aggregation of entities is a widely observed phenomenon in economics, sociology, biology and other fields. It is natural to ask how diverse and competitive entities can achieve high levels of aggregation. In order to answer this question we provide a gametheoretical model for aggregation. We consider natural classes of strategies for the individuals and show how this affects aggregation by studying the price of anarchy of the resulting game. Our analysis highlights the advantages of populations with diverse strategies (heterogeneous populations) over populations where all individuals share the same strategy (homogeneous populations). In particular, we prove that a simple heterogeneous population composed of leaders (individuals that tend to invest) and followers (individuals that look for shortterm rewards) achieves asymptotically lower price of anarchy compared to any homogeneous population, no matter how elaborate its strategy is. This sets forth the question of how diversity affects the problem solving abilities of populations in general. We hope that our work will lead to further research in games with diverse populations and in a better understanding of aggregation games.