Topological Distance Games

TL;DR

This paper introduces topological distance games (TDGs), a new class of strategic games where agents' utilities depend on their inherent preferences and their distances in a topology graph, blending features of hedonic, social distance, and Schelling games.

Contribution

The paper defines TDGs, analyzes the existence and complexity of stable outcomes, and explores the dynamics of beneficial jumps within this new framework.

Findings

Stable outcomes guaranteed in certain special cases.

Jump stable assignments may not always exist.

Beneficial jump dynamics are studied.

Abstract

We introduce a class of strategic games in which agents are assigned to nodes of a topology graph and the utility of an agent depends on both the agent's inherent utilities for other agents as well as her distance from these agents on the topology graph. This model of topological distance games (TDGs) offers an appealing combination of important aspects of several prominent settings in coalition formation, including (additively separable) hedonic games, social distance games, and Schelling games. We study the existence and complexity of stable outcomes in TDGs -- for instance, while a jump stable assignment may not exist in general, we show that the existence is guaranteed in several special cases. We also investigate the dynamics induced by performing beneficial jumps.