Group Activity Selection from Ordinal Preferences

Darmann, Andreas

doi:10.1007/978-3-319-23114-3_3

Cited by 17 publications

(16 citation statements)

References 8 publications

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“…Nash stability [18] plays a key role since it yields a social agreement among the agents even without having any negotiation. Many researchers have investigated conditions under which a Nash stable partition is guaranteed to exist and to be determined [18], [42]- [44]. Among them, the works in [43], [44] mainly addressed an anonymous hedonic game, in which each agent considers the size of a coalition to which it belongs instead of the identities of the members.…”

Section: B Hedonic Gamesmentioning

confidence: 99%

“…For the fully-connected network case, it becomes O(n 2 a ) because of d G = 1. Note that this algorithmic complexity is less than that of the centralized algorithm, i.e., O(n 2 a · n t ), in [44]. Every agent at each iteration investigates n t + 1 of selectable task-coalition pairs including t φ given a locally-known valid partition (as shown in Line 5 in Algorithm 1).…”

Section: A Algorithmic Complexity (Scalability)mentioning

confidence: 99%

“…Many researchers have investigated conditions under which a Nash stable partition is guaranteed to exist and to be determined [18], [42]- [44]. Among them, the works in [43], [44] mainly addressed an anonymous hedonic game, in which each agent considers the size of a coalition to which it belongs instead of the identities of the members. Recently, Darmann [44] showed that selfish agents who have social inhibition (i.e., preference toward a coalition with a fewer number of members) could converge to a Nash stable partition in an anonymous hedonic game.…”

Section: B Hedonic Gamesmentioning

confidence: 99%

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Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System

2018

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This paper proposes a novel game-theoretical autonomous decision-making framework to address a task allocation problem for a swarm of multiple agents. We consider cooperation of self-interested agents, and show that our proposed decentralized algorithm guarantees convergence of agents with social inhibition to a Nash stable partition (i.e., social agreement) within polynomial time. The algorithm is simple and executable based on local interactions with neighbor agents under a stronglyconnected communication network and even in asynchronous environments. We analytically present a mathematical formulation for computing the lower bound of suboptimality of the solution, and additionally show that 50% of suboptimality can be at least guaranteed if social utilities are non-decreasing functions with respect to the number of co-working agents. The results of numerical experiments confirm that the proposed framework is scalable, fast adaptable against dynamical environments, and robust even in a realistic situation.

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Section: B Hedonic Gamesmentioning

confidence: 99%

Section: A Algorithmic Complexity (Scalability)mentioning

confidence: 99%

Section: B Hedonic Gamesmentioning

confidence: 99%

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Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System

2018

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“…After the conference version of our paper has been published, several authors explored the complexity of finding good allocations in GASP, both in the approvalbased model, which is the focus of our work (Lee and Vassilevska Williams 2017), and in the ordinal model, where each agent ranks pairs of the form '(activity, group size)' (Darmann 2015). Igarashi et al (2017a, b) and subsequently Gupta et al (2017) considered a variant of GASP where agents are connected by a social network and members of each group have to form a connected subgraph in this network; they adapt the solution concepts that we propose to this richer setting, and put forward a number of algorithms and complexity results.…”

Section: Related Workmentioning

confidence: 99%

Group activity selection problem with approval preferences

et al. 2017

Self Cite

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We consider a setting where one has to organize one or several group activities for a set of agents. Each agent will participate in at most one activity, and her preferences over activities depend on the number of participants in the activity. The goal is to assign agents to activities based on their preferences in a way that is socially optimal and/or stable. We put forward a general model for this setting, which is a natural generalization of anonymous hedonic games. We then focus on a special case of our model where agents' preferences are binary, i.e., each agent classifies all pairs of the form '(activity, group size)' into ones that are acceptable and ones that are not. We formulate several solution concepts for this scenario, and study them from the computational point of view, providing hardness results for the general case as well as efficient algorithms for settings where agents' preferences satisfy certain natural constraints.

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“…In [3], Darmann re-introduced the General Group Activity Selection Problem, considering the agents' ordinal preferences where each agent can determine the (activity, group size) pair. He analyzed the computational complexity for finding a stable assignment using k-approval scores and considering Nash and core stability.…”

Section: Related Litreturementioning

confidence: 99%

Stable Beneficial Group Activity Formation

Al-Anbaki¹,

Sleit²,

Sharieh³

2016

ijacsa

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Abstract-Computational models are one of the very powerful tools for expressing everyday situations that are derived from human interactions. In this paper, an investigation of the problem of forming beneficial groups based on the members' preferences and the coordinator's own strategy is presented . It is assumed that a coordinator has a good intention behind trimming members' preferences to meet the ultimate goal of forming the group. His strategy is justified and evaluated by Nash stability. There are two variations of the problem: the Anonymous Stable Beneficial Group Activity Formation and the General Stable Beneficial Group Activity Formation. The computational complexity of solving both variations has been analyzed. Finding stable groups needs non-polynomial time algorithm to be solved. A polynomial time solution is presented and enhanced with examples.

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Group Activity Selection from Ordinal Preferences

Cited by 17 publications

References 8 publications

Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System

Anonymous Hedonic Game for Task Allocation in a Large-Scale Multiple Agent System

Group activity selection problem with approval preferences

Stable Beneficial Group Activity Formation

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