Group Activity Selection on Social Networks

TL;DR

This paper studies a new variant of the group activity selection problem on social networks, analyzing the computational complexity of finding stable outcomes depending on network structure and activity assignment constraints.

Contribution

It introduces a social network-based GASP variant and characterizes the complexity of finding stable outcomes under different activity assignment rules and network topologies.

Findings

Stable outcomes are easy to find on acyclic networks with multiple groups.

Determining Nash stability is NP-hard on simple networks like paths and stars.

Fixed-parameter tractability results are obtained relative to the number of activities.

Abstract

We propose a new variant of the group activity selection problem (GASP), where the agents are placed on a social network and activities can only be assigned to connected subgroups. We show that if multiple groups can simultaneously engage in the same activity, finding a stable outcome is easy as long as the network is acyclic. In contrast, if each activity can be assigned to a single group only, finding stable outcomes becomes intractable, even if the underlying network is very simple: the problem of determining whether a given instance of a GASP admits a Nash stable outcome turns out to be NP-hard when the social network is a path, a star, or if the size of each connected component is bounded by a constant. On the other hand, we obtain fixed-parameter tractability results for this problem with respect to the number of activities.