Friendship and Stable Matching

We study the inefficiency of equilibria for congestion games when players are (partially) altruistic. We model altruistic behavior by assuming that player i's perceived cost is a convex combination of 1 − α i times his direct cost and α i times the social cost. Tuning the parameters α i allows smooth interpolation between purely selfish and purely altruistic behavior. Within this framework, we study primarily altruistic extensions of (atomic and nonatomic) congestion games, but also obtain some results on fair cost-sharing games and valid utility games.We derive (tight) bounds on the price of anarchy of these games for several solution concepts. Thereto, we suitably adapt the smoothness notion introduced by Roughgarden and show that it captures the essential properties to determine the robust price of anarchy of these games. Our bounds show that for atomic congestion games and cost-sharing games, the robust price of anarchy gets worse with increasing altruism, while for valid utility games, it remains constant and is not affected by altruism.However, the increase in the price of anarchy is not a universal phenomenon: For general nonatomic congestion games with uniform altruism, the price of anarchy improves with increasing altruism. For atomic and nonatomic symmetric singleton congestion games, we derive bounds on the pure price of anarchy that improve as the average level of altruism increases. (For atomic games, we only derive such bounds when cost functions are linear.) Since the bounds are also strictly lower than the robust price of anarchy, these games exhibit natural examples in which pure Nash equilibria are more efficient than more permissive notions of equilibrium.

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“…For instance, such analyses are carried out in analyzing the price of anarchy and stability in Anshelevich et al [2012] and Buehler et al [2011].…”

Section: Subsequent Workmentioning

confidence: 99%

Altruism and Its Impact on the Price of Anarchy

Chen

Keijzer

Kempe

et al. 2014

ACM Trans. Econ. Comput.

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“…In [22] we extended some of the results shown here (the NP-hardness result in Theorem 2 and the existence result in Theorem 4) to other variants of matching games, such as considerate or friendship matching [4] that capture externalities among agents. In addition, we provided a tight characterization for a class of games with more general dynamic restrictions on the set of available blocking coalitions.…”

Section: Related Workmentioning

confidence: 87%

Locally Stable Marriage with Strict Preferences

Hoefer

Wagner

2013

Automata, Languages, and Programming

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We study stable matching problems with locality of information and control. In our model, each agent is a node in a fixed network and strives to be matched to another agent. An agent has a complete preference list over all other agents it can be matched with. Agents can match arbitrarily, and they learn about possible partners dynamically based on their current neighborhood. We consider convergence of dynamics to locally stable matchings -states that are stable with respect to their imposed information structure in the network. In the two-sided case of stable marriage in which existence is guaranteed, we show that the existence of a path to stability becomes NP-hard to decide. This holds even when the network exists only among one partition of agents. In contrast, if one partition has no network and agents remember a previous match every round, a path to stability 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 cache memory with the most recent partner, but not for cache memory with the best partner. Also, it is crucial which partition of the agents has memory. Finally, we present results for centralized computation of locally stable matchings, i.e., computing maximum locally stable matchings in the two-sided case and deciding existence in the roommates case. * An extended abstract of this paper has been published in the proceedings of the 40th Intl. Colloquium on Automata, Languages, and Programming (ICALP 2013) [21].

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“…In this paper, we study the impact of profit distribution on fairness and efficiency in the resulting coalition formation games. It is known that completely arbitrary sharing can lead to non-existence of stable states or arbitrarily high price of anarchy [3]. Similar to recent work [20], our focus is to design good profit or credit distribution schemes such that the stable states implement good outcomes.…”

Section: Introductionmentioning

confidence: 95%

“…Directly related to our work are [4,5] which address the price of anarchy in stable matching and related models. Very recently, we have studied the price of anarchy under different edge-based profit sharing schemes [3]. In contrast, this paper concentrates on designing profit shares to guarantee good stable matchings.…”

Section: Related Workmentioning

confidence: 99%

Designing Profit Shares in Matching and Coalition Formation Games

Hoefer

Wagner

2013

Web and Internet Economics

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Abstract. Matching and coalition formation are fundamental problems in a variety of scenarios where agents join efforts to perform tasks, such as, e.g., in scientific publishing. To allocate credit or profit stemming from a joint project, different communities use different crediting schemes in practice. A natural and widely used approach to profit distribution is equal sharing, where every member receives the same credit for a joint work. This scheme captures a natural egalitarian fairness condition when each member of a coalition is critical for success. Unfortunately, when coalitions are formed by rational agents, equal sharing can lead to high inefficiency of the resulting stable states. In this paper, we study the impact of changing profit sharing schemes in order to obtain good stable states in matching and coalition formation games. We generalize equal sharing to sharing schemes where for each coalition each player is guaranteed to receive at least an α-share. This way the coalition formation can stabilize on more efficient outcomes. In particular, we show a direct trade-off between efficiency and equal treatment. If k denotes the size of the largest possible coalition, we prove an asymptotically tight bound of k 2 α on prices of anarchy and stability. This result extends to polynomial-time algorithms to compute good sharing schemes. Further, we show improved results for a novel class of matching problems that covers the well-studied case of two-sided matching.

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Friendship and Stable Matching

Cited by 17 publications

References 28 publications

Altruism and Its Impact on the Price of Anarchy

Altruism and Its Impact on the Price of Anarchy

Locally Stable Marriage with Strict Preferences

Designing Profit Shares in Matching and Coalition Formation Games

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