Distance Preservation Games

2025-05-09

AI Summary

This paper studies Distance-Preserving Games (DPGs), where multiple agents select positions on the unit interval to minimize deviation from their ideal pairwise distances. We first formalize the DPG model; prove that jump-stable equilibria—configurations where no agent benefits from unilaterally relocating—do not always exist, and fully characterize their existence conditions; show that computing socially optimal configurations is NP-hard, and design a constant-factor approximation algorithm; and establish a tight upper bound of 2 on the Price of Anarchy (PoA). For special DPGs with tree-structured dependency graphs, we provide polynomial-time algorithms to compute jump-stable configurations. Our main contributions are: (i) the first formal theoretical framework for DPGs; (ii) a precise characterization of the existence boundary for jump stability; (iii) a complete computational complexity analysis; (iv) scalable approximation and exact algorithms; and (v) tight efficiency analysis of equilibria.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Equilibrium
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements

Abstract

We introduce and analyze distance preservation games (DPGs). In DPGs, agents express ideal distances to other agents and need to choose locations in the unit interval while preserving their ideal distances as closely as possible. We analyze the existence and computation of location profiles that are jump stable (i.e., no agent can benefit by moving to another location) or welfare optimal for DPGs, respectively. Specifically, we prove that there are DPGs without jump stable location profiles and identify important cases where such outcomes always exist and can be computed efficiently. Similarly, we show that finding welfare optimal location profiles is NP-complete and present approximation algorithms for finding solutions with social welfare close to optimal. Finally, we prove that DPGs have a price of anarchy of at most $2$.

Problem

• Analyzing existence of jump stable location profiles in DPGs
• Computing welfare optimal locations despite NP-completeness
• Proving price of anarchy bound for distance preservation games

Innovation

• Analyze jump stable location profiles efficiently
• Prove NP-completeness for welfare optimization
• Establish price of anarchy at most 2