The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Network design with weighted players
Proceedings of the eighteenth annual ACM symposium on Parallelism in algorithms and architectures
An O( lognloglogn) upper bound on the price of stability for undirected Shapley network design games
Information Processing Letters
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
On the Value of Coordination in Network Design
SIAM Journal on Computing
On the Inefficiency Ratio of Stable Equilibria in Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Designing Network Protocols for Good Equilibria
SIAM Journal on Computing
Improved lower bounds on the price of stability of undirected network design games
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On the price of stability for designing undirected networks with fair cost allocations
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Non-Cooperative Multicast and Facility Location Games
IEEE Journal on Selected Areas in Communications
Improved bounds on the price of stability in network cost sharing games
Proceedings of the fourteenth ACM conference on Electronic commerce
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In this paper, we consider undirected network design games with fair cost allocation. We introduce two concepts Potential-Optimal Price of Anarchy (POPoA) and Potential-Optimal Price of Stability (POPoS), where POPoA is the ratio between the worst cost of Nash equilibria with optimal potential and the minimum social cost, and POPoS is the ratio between the best cost of Nash equilibria with optimal potential and the minimum social cost, and show that The POPoA and POPoS for undirected broadcast games with n players are $\mathrm{O}(\sqrt{\log n})$. The POPoA and POPoS for undirected broadcast games with |V| vertices are O(log|V|). There exists an undirected broadcast game with n players such that POPoA, $\mathrm{POPoS} = \Omega(\sqrt{\log\log n})$. There exists an undirected broadcast game with |V| vertices such that POPoA,POPoS=Ω(log|V|).