# The Complexity of Manipulation of k-Coalitional Games on Graphs

arXiv: https://arxiv.org/abs/2408.07368 · HTML: https://mlsanity.com/paper/2408.07368/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 25 references that are in the map.
- First posted on arXiv 14 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [Hedonic Games and Treewidth Revisited](https://mlsanity.com/paper/2202.06925/) (2022)
- [Mechanism Design for Team Formation](https://mlsanity.com/paper/1501.00715/) (2015)
- [Degree-constrained 2-partitions of graphs](https://mlsanity.com/paper/1801.06216/) (2018)
- [The Number of Minimum k-Cuts: Improving the Karger-Stein Bound](https://mlsanity.com/paper/1906.00417/) (2019)
- [Finding All Global Minimum Cuts In Practice](https://mlsanity.com/paper/2002.06948/) (2020)
- [Manipulation of k-Coalitional Games on Social Networks](https://mlsanity.com/paper/2105.09852/) (2021)

## Built on by (most cited first, 1 of 1)

- [Agentic Algorithm Engineering: Improving Shared-Memory Exact Minimum Cuts](https://mlsanity.com/paper/2609.07204/) (2026)

## Abstract (arXiv)

In many settings, there is an organizer who would like to divide a set of agents into k coalitions, and cares about the friendships within each coalition. Specifically, the organizer might want to maximize utilitarian social welfare, maximize egalitarian social welfare, or simply guarantee that every agent will have at least one friend within his coalition. However, in many situations, the organizer is not familiar with the friendship connections, and he needs to obtain them from the agents. In this setting, a manipulative agent may falsely report friendship connections in order to increase his utility. In this paper, we analyze the complexity of finding manipulation in such k-coalitional games on graphs. We also introduce a new type of manipulation, socially-aware manipulation, in which the manipulator would like to increase his utility without decreasing the social welfare. We then study the complexity of finding socially-aware manipulation in our setting. Finally, we examine the frequency of socially-aware manipulation and the running time of our algorithms via simulation results.