STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
UAI '00 Proceedings of the 16th Conference on Uncertainty in Artificial Intelligence
Graphical Models for Game Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Correlated equilibria in graphical games
Proceedings of the 4th ACM conference on Electronic commerce
Pure Nash equilibria: hard and easy games
Proceedings of the 9th conference on Theoretical aspects of rationality and knowledge
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Structure and complexity of extreme Nash equilibria
Theoretical Computer Science - Game theory meets theoretical computer science
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Nashification and the coordination ratio for a selfish routing game
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Facets of the Fully Mixed Nash Equilibrium Conjecture
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Total latency in singleton congestion games
WINE'07 Proceedings of the 3rd international conference on Internet and network economics
Hi-index | 0.00 |
In this work, we introduce and study a simple, graph-theoretic model for selfish scheduling among m non-cooperative users over a collection of nmachines; however, each user is restricted to assign its unsplittable load to one from a pair of machines that are allowed for the user. We model these bounded interactions using an interaction graph, whose vertices and edges are the machines and the users, respectively. We study the impact of our modeling assumptions on the properties of Nash equilibria in this new model. The main findings of our study are outlined as follows: – We prove, as our main result, that the parallel links graph is the best-case interaction graph – the one that minimizes expected makespan of the standard fully mixed Nash equilibrium – among all 3-regular interaction graphs. The proof employs a graph-theoretic lemma about orientations in 3-regular graphs, which may be of independent interest. – We prove a lower bound on Coordination Ratio[16] – a measure of the cost incurred to the system due to the selfish behavior of the users. In particular, we prove that there is an interaction graph incurring Coordination Ratio ${\it \Omega} \left( \frac{\log n} {\log \log n} \right)$. This bound is shown for pure Nash equilibria. – We present counterexample interaction graphs to prove that a fully mixed Nash equilibrium may sometimes not exist at all. Moreover, we prove properties of the fully mixed Nash equilibrium for complete bipartite graphs and hypercube graphs.