Cooperative Games with Overlapping Coalitions

Chalkiadakis, Georgios; Elkind, Edith; Markakis, Evangelos; Polukarov, Maria; Jennings, Nicholas R.

doi:10.1613/jair.3075

Cited by 94 publications

(139 citation statements)

References 40 publications

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“…However, there is a closely related paper to ours on TU-games with overlapping coalitions [13]. In the latter paper the general model introduced is essentially the TU version of our stable allocation problem with contributions, that we study in Section 5.…”

Section: Related Literaturementioning

confidence: 99%

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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Abstract. In this paper we investigate some new applications of Scarf's Lemma. First, we introduce the notion of fractional core for NTU-games, which is always nonempty by the Lemma. Stable allocation is a general solution concept for games where both the players and their possible cooperations can have capacities. We show that the problem of finding a stable allocation, given a finitely generated NTU-game with capacities, is always solvable by a variant of Scarf's Lemma. Then we describe the interpretation of these results for matching games. Finally we consider an even more general setting where players' contributions in a joint activity may be different. We show that a stable allocation can be found by the Scarf algorithm in this case as well, and we demonstrate the usage of this method for the hospitals resident problem with couples. This problem is relevant in many practical applications, such as NRMP (National Resident Matching Program).

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Section: Related Literaturementioning

confidence: 99%

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Bir

Fleiner

2016

Discrete Optimization

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“…The academic game is a non-transferable utility game with overlapping coalitions and is related to several types of coalitional games, such as threshold task games ( [6]) and coalitional skill games (Bachrach and Rosenchein [4]). …”

Section: Related Workmentioning

confidence: 99%

“…Given that an agent can be involved in multiple projects simultaneously, it is important that one estimates correctly the reactions from the rest of the agents before agreeing to participate in a deviation. We follow the recent literature on overlapping coalition formation games ( [6], Zick, Chalkiadakis, and Elkind [25]), and study sensitive reactions to a deviation. In short, when agent i is involved in a deviation from a coalition structure CS, i can expect that:…”

Section: Discrete Budgetsmentioning

confidence: 99%

The authorship dilemma: alphabetical or contribution?

Ackerman

Brânzei

2016

Auton Agent Multi-Agent Syst

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Scientific communities have adopted different conventions for ordering authors on publications. Are these choices inconsequential, or do they have significant influence on individual authors, the quality of the projects completed, and research communities at large? What are the trade-offs of using one convention over another? In order to investigate these questions, we formulate a basic two-player game theoretic model, which already illustrates interesting phenomena that can occur in more realistic settings.We find that alphabetical ordering can improve research quality, while contribution-based ordering leads to a denser collaboration network and a greater number of publications. Contrary to the assumption that free riding is a weakness of the alphabetical ordering scheme, this phenomenon can occur under any contribution scheme, and the worst case occurs under contributionbased ordering. Finally, we show how authors working on multiple projects can cooperate to attain optimal research quality and eliminate free riding given either contribution scheme.

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“…Players form groups (that require permission to join) that compete for this project, but only one group receives a payoff. Chalkiadakis et al [7] define a cooperative game that is similar to our threshold model, but it has additional constraints on the project payoff functions, and there is an infinite number of each type of project. Augustine et al [1] define non-cooperative project selection games based on monotone convex cooperative games and provide quality of equilibria and convergence results for them.…”

Section: Related Workmentioning

confidence: 99%

Profit Sharing with Thresholds and Non-monotone Player Utilities

Anshelevich

Postl

2016

Theory Comput Syst

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We study profit sharing games in which players select projects to participate in and share the reward resulting from that project equally. Unlike most existing work, in which it is assumed that the player utility is monotone in the number of participants working on their project, we consider non-monotone player utilities. Such utilities could result, for example, from "threshold" or "phase transition" effects, when the total benefit from a project improves slowly until the number of participants reaches some critical mass, then improves rapidly, and then slows again due to diminishing returns.Non-monotone player utilities result in a lot of instability: strong Nash equilibrium may no longer exist, and the quality of Nash equilibria may be far away from the centralized optimum. We show, however, that by adding additional requirements such as players needing permission to leave a project from the players currently on this project, or instead players needing permission to a join a project from players on that project, we ensure that strong Nash equilibrium always exists. Moreover, just the addition of permission to leave already guarantees the existence of strong Nash equilibrium within a factor of 2 of the social optimum. In this paper, we provide results on the existence and quality of several different coalitional solution concepts, focusing especially on permission to leave and join projects, and show that such requirements result in the existence of good stable solutions even for the case when player utilities are non-monotone.

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Cooperative Games with Overlapping Coalitions

Cited by 94 publications

References 40 publications

Fractional solutions for capacitated NTU-games, with applications to stable matchings

Fractional solutions for capacitated NTU-games, with applications to stable matchings

The authorship dilemma: alphabetical or contribution?

Profit Sharing with Thresholds and Non-monotone Player Utilities

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