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24
Locally stable marriage with strict preferences
 In Proc. 40th Intl. Coll. Automata, Languages and Programming (ICALP
, 2013
"... Abstract. We study twosided matching markets with locality of information and control. Each male (female) agent has an arbitrary strict preference list over all female (male) agents. In addition, each agent is a node in a fixed network. Agents learn about possible partners dynamically based on th ..."
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Abstract. We study twosided matching markets with locality of information and control. Each male (female) agent has an arbitrary strict preference list over all female (male) agents. In addition, each agent is a node in a fixed network. Agents learn about possible partners dynamically based on their current network neighborhood. We consider convergence of dynamics to locally stable matchings that are stable with respect to their imposed information structure in the network. While existence of such states is guaranteed, we show that reachability becomes NPhard to decide. This holds even when the network exists only among one side. In contrast, if only one side has no network and agents remember a previous match every round, reachability is guaranteed and random dynamics converge with probability 1. We characterize this positive result in various ways. For instance, it holds for random memory and for memory with the most recent partner, but not for memory with the best partner. Also, it is crucial which partition of the agents has memory. Finally, we conclude with results on approximating maximum locally stable matchings. 1
Analysis of stochastic matching markets
 Intl. Journal of Game Theory
"... Abstract. Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? ..."
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Abstract. Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In this paper we are going to provide answers to these and similar questions, posed by economists and computer scientists. In the first part of the paper we give an alternative proof for the theorems by Diamantoudi et al. and Inarra et al. which imply that the corresponding stochastic processes are absorbing Markov chains. Our proof is not only shorter, but also provides upper bounds for the number of steps needed to stabilise the system. The second part of the paper proposes new techniques to analyse the behaviour of matching markets. We introduce the Stable Marriage and Stable Roommates Automaton and show how the probabilistic model checking tool PRISM may be used to predict the outcomes of stochastic interactions between myopic agents. In particular, we demonstrate how one can calculate the probabilities of reaching different matchings in a decentralised market and determine the expected convergence time of the stochastic process concerned. We illustrate the usage of this technique by studying some wellknown marriage and roommates instances and randomly generated instances. 1
Socially stable matchings
 in the Hospitals / Residents problem. CoRR Technical Report 1303.2041. Available from http://arxiv.org/abs/1303.2041
"... In twosided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their ..."
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In twosided matching markets, the agents are partitioned into two sets. Each agent wishes to be matched to an agent in the other set and has a strict preference over these potential matches. A matching is stable if there are no blocking pairs, i.e., no pair of agents that prefer each other to their assigned matches. In this paper we study a generalization of stable matching motivated by the fact that, in most centralized markets, many agents do not have direct communication with each other. Hence even if some blocking pairs exist, the agents involved in those pairs may not be able to coordinate a deviation. We model communication channels with a bipartite graph between the two sets of agents which we call the social graph, and we study socially stable matchings. A matching is socially stable if there are no blocking pairs that are connected by an edge in the social graph. Socially stable matchings vary in size and so we look for a maximum socially stable matching. We prove that this problem is NPhard and, assuming the unique games conjecture, hard to approximate within a factor of 3 2 − ɛ, for any constant ɛ. Weapproximation algorithm. complement the hardness results with a 3 2 1
Hedonic Coalition Formation in Networks
"... Coalition formation is a fundamental problem in the organization of many multiagent systems. In large populations, the formation of coalitions is often restricted by structural visibility and locality constraints under which agents can reorganize. We capture and study this aspect using a novel ne ..."
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Coalition formation is a fundamental problem in the organization of many multiagent systems. In large populations, the formation of coalitions is often restricted by structural visibility and locality constraints under which agents can reorganize. We capture and study this aspect using a novel networkbased model for dynamic locality within the popular framework of hedonic coalition formation games. We analyze the effects of networkbased visibility and structure on the convergence of coalition formation processes to stable states. Our main result is a tight characterization of the structures based on which dynamic coalition formation can stabilize quickly. Maybe surprisingly, polynomialtime convergence can be achieved if and only if coalition formation is based on complete or star graphs.
Friendship and stable matching
 In Proc. 21st European Symp. Algorithms (ESA
, 2013
"... We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, co ..."
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We study stable matching problems in networks where players are embedded in a social context, and may incorporate friendship relations or altruism into their decisions. Each player is a node in a social network and strives to form a good match with a neighboring player. We consider the existence, computation, and inefficiency of stable matchings from which no pair of players wants to deviate. When the benefits from a match are the same for both players, we show that incorporating the wellbeing of other players into their matching decisions significantly decreases the price of stability, while the price of anarchy remains unaffected. Furthermore, a good stable matching achieving the price of stability bound always exists and can be reached in polynomial time. We extend these results to more general matching rewards, when players matched to each other may receive different utilities from the match. For this more general case, we show that incorporating social context (i.e., “caring about your friends”) can make an even larger difference, and greatly reduce the price of anarchy. We show a variety of existence results, and present upper and lower bounds on the prices of anarchy and stability for various matching utility structures. 1
Chapter 9 Social Networks
"... Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 9.1. 12 ..."
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Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 9.1. 12
Chapter 8 Social Networks
"... Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 8.1. ..."
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Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 8.1.
Chapter 8 Social Networks
"... Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 8.1. 12 ..."
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Distributed computing is applicable in various contexts. This lecture exemplarily studies one of these contexts, social networks, an area of study whose origins date back a century. To give you a first impression, consider Figure 8.1. 12
On Finding Better Friends in Social Networks
"... Abstract. We study the dynamics of a social network. Each node has to decide locally which other node it wants to befriend, i.e., to which other node it wants to create a connection in order to maximize its welfare, which is defined as the sum of the weights of incident edges. This allows us to mode ..."
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Abstract. We study the dynamics of a social network. Each node has to decide locally which other node it wants to befriend, i.e., to which other node it wants to create a connection in order to maximize its welfare, which is defined as the sum of the weights of incident edges. This allows us to model the cooperation between nodes where every node tries to do as well as possible. With the limitation that each node can only have a constant number of friends, we show that every local algorithm is arbitrarily worse than a globally optimal solution. Furthermore, we show that there cannot be a best local algorithm, i.e., for every local algorithm exists a social network in which the algorithm performs arbitrarily worse than some other local algorithm. However, one can combine a number of local algorithms in order to be competitive with the best of them. We also investigate a slightly different valuation variant. Nodes include another node’s friends for their valuation. There are scenarios in which this does not converge to a stable state, i.e., the nodes switch friends indefinitely. We also analyze the consequences if ending a friendship permanently damages it.