Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Near-optimal network design with selfish agents
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Non-cooperative multicast and facility location games
EC '06 Proceedings of the 7th ACM conference on Electronic commerce
Network design with weighted players
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
Convergence time to Nash equilibrium in load balancing
ACM Transactions on Algorithms (TALG)
Algorithmic Game Theory
Designing networks with good equilibria
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Nash equilibria in Voronoi games on graphs
ESA'07 Proceedings of the 15th annual European conference on Algorithms
On the complexity of pure-strategy nash equilibria in congestion and local-effect games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
Task graph pre-scheduling, using Nash equilibrium in game theory
The Journal of Supercomputing
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We prove $\mathcal{NP}$-hardness of pure Nash equilibrium for some problems of scheduling games and connection games. The technique is standard: first, we construct a gadget without the desired property and then embed it to a larger game which encodes a $\mathcal{NP}$-hard problem in order to prove the complexity of the desired property in a game. This technique is very efficient in proving $\mathcal{NP}$-hardness for deciding the existence of Nash equilibria. In the paper, we illustrate the efficiency of the technique in proving the $\mathcal{NP}$-hardness of deciding the existence of pure Nash equilibria of Matrix Scheduling Games and Weighted Connection Games. Moreover, using the technique, we can settle the complexity not only of the existence of equilibrium but also of the existence of good cost-sharing protocol.