Stable and Pareto optimal group activity selection from ordinal preferences

Darmann, Andreas

doi:10.1007/s00182-018-0612-3

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…Skibski and Michalak (2020) studied the fair allocation of payoffs in cooperative games with externalities, where agents form coalitions and the value of each coalition is defined not only by the members of the coalition but also by the other coalitions; however, there is no resource shared among the agents. One exception is the group activity selection game (Darmann, Elkind, Kurz, Lang, Schauer, & Woeginger, 2012;Darmann, 2018;Eiben, Ganian, & Ordyniak, 2018), where agents are assigned to different group activities and their utilities depend on the type of activity (similar to resources in our model) as well as the members in the same group. Despite the similarity, group activity selection games usually employ different modeling assumptions, e.g., every agent always has the choice of deviating to singleton activities (i.e., by being alone), which is not feasible in our model, or the supply of activities are not fixed, unlike that of the dorms.…”

Section: Related Workmentioning

confidence: 99%

Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

Gan

2023

jair

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We study a fair resource sharing problem, where a set of resources are to be shared among a group of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, who share the same resource with them. Clearly, the strong notion of envy-freeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even deciding the existence of such a strongly envy-free assignment is an intractable problem. Hence, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envyfreeness, can be achieved. Under this relaxed notion, an agent envies another only when they envy both the resource and the mates of the other agent. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dormmates. We show that when the capacity of each dorm is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment. Nevertheless, the result breaks immediately when the capacity increases to 3, in which case even Pareto envyfreeness cannot be guaranteed. In addition to the existential results, we also investigate the utility guarantees of (Pareto) envy-free assignments in our model.

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Section: Related Workmentioning

confidence: 99%

Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

Gan

2023

jair

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“…Our work is also related to models from cooperative game theory, such as hedonic games [11,22,5] and group activity selection games [19,18,21]. In hedonic games, the agents form coalitions and their utilities are decided solely by the members in the coalition, without any resource in the model.…”

Section: Related Workmentioning

confidence: 99%

Fair Resource Sharing with Externailities

Gan,

Li,

2020

Preprint

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We study a fair resource sharing problem, where a set of resources are to be shared among a set of agents. Each agent demands one resource and each resource can serve a limited number of agents. An agent cares about what resource they get as well as the externalities imposed by their mates, whom they share the same resource with. Apparently, the strong notion of envyfreeness, where no agent envies another for their resource or mates, cannot always be achieved and we show that even to decide the existence of such a strongly envy-free assignment is an intractable problem. Thus, a more interesting question is whether (and in what situations) a relaxed notion of envy-freeness, the Pareto envy-freeness, can be achieved: an agent i envies another agent j only when i envies both the resource and the mates of j. In particular, we are interested in a dorm assignment problem, where students are to be assigned to dorms with the same capacity and they have dichotomous preference over their dorm-mates. We show that when the capacity of the dorms is 2, a Pareto envy-free assignment always exists and we present a polynomial-time algorithm to compute such an assignment; nevertheless, the result fails to hold immediately when the capacities increase to 3, in which case even Pareto envy-freeness cannot be guaranteed. In addition to the existential results, we also investigate the implications of envy-freeness on proportionality in our model and show that envy-freeness in general implies approximations of proportionality.

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“…Both verification and finding a poa are hard in such games [2]. Darmann [9] studies a group activity selection model in which players have preferences not only on the activity, but also on the number of participants in their coalition. He provides an efficient algorithm to find a poa, if each player wants to share an activity with as many, or as few players as possible.…”

Section: -Person Roomsmentioning

confidence: 99%

Pareto Optimal Coalitions of Fixed Size

Cseh¹,

Fleiner²,

Harján³

2019

jMID

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We tackle the problem of partitioning players into groups of fixed size, such as allocating eligible students to shared dormitory rooms. Each student submits preferences over the other individual students. We study several settings, which differ in the size of the rooms to be filled, the orderedness or completeness of the preferences, and the way of calculating the value of a coalition-based on the best or worst roommate in the coalition. In all cases, we determine the complexity of deciding the existence, and then finding a Pareto optimal assignment, and the complexity of verifying Pareto optimality for a given assignment.

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Stable and Pareto optimal group activity selection from ordinal preferences

Cited by 6 publications

References 18 publications

Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

Your College Dorm and Dormmates: Fair Resource Sharing with Externalities

Fair Resource Sharing with Externailities

Pareto Optimal Coalitions of Fixed Size

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