Coordination Games on Graphs
Krzysztof R. Apt, Bart de Keijzer, Mona Rahn, Guido Schaefer, Sunil, Simon

TL;DR
This paper studies coordination games on graphs, analyzing the existence, properties, and computational complexity of various equilibria including Nash, k-equilibria, and strong equilibria, and evaluates their efficiency through price of anarchy and stability.
Contribution
It introduces and analyzes the existence and properties of multiple equilibrium concepts in coordination games on graphs, including new complexity results for computing strong equilibria.
Findings
Pure Nash and 2-equilibria always exist.
Strong equilibria exist in certain special cases.
The price of anarchy for pure Nash equilibria can be unbounded.
Abstract
We introduce natural strategic games on graphs, which capture the idea of coordination in a local setting. We study the existence of equilibria that are resilient to coalitional deviations of unbounded and bounded size (i.e., strong equilibria and k-equilibria respectively). We show that pure Nash equilibria and 2-equilibria exist, and give an example in which no 3-equilibrium exists. Moreover, we prove that strong equilibria exist for various special cases. We also study the price of anarchy (PoA) and price of stability (PoS) for these solution concepts. We show that the PoS for strong equilibria is 1 in almost all of the special cases for which we have proven strong equilibria to exist. The PoA for pure Nash equilbria turns out to be unbounded, even when we fix the graph on which the coordination game is to be played. For the PoA for k-equilibria, we show that the price of anarchy…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGame Theory and Applications · Game Theory and Voting Systems · Economic theories and models
