Distance Preservation Games
Haris Aziz, Hau Chan, Patrick Lederer, Shivika Narang, Toby Walsh

TL;DR
This paper introduces distance preservation games where agents position themselves to maintain ideal distances, analyzing stability, optimality, computational complexity, and efficiency bounds of such configurations.
Contribution
It formally defines DPGs, proves existence and computational complexity results, and provides algorithms and bounds for stable and welfare-optimized solutions.
Findings
Some DPGs lack jump stable profiles.
Finding welfare optimal profiles is NP-complete.
Price of anarchy is at most 2.
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 .
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Taxonomy
TopicsGame Theory and Voting Systems · Game Theory and Applications · Auction Theory and Applications
