Improved diameter bounds for altered graphs
International Workshop WG '86 on Graph-theoretic concepts in computer science
Proceedings of the twenty-second annual symposium on Principles of distributed computing
The price of anarchy in network creation games
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Bounded budget connection (BBC) games or how to make friends and influence people, on a budget
Proceedings of the twenty-seventh ACM symposium on Principles of distributed computing
Proceedings of the twenty-second annual ACM symposium on Parallelism in algorithms and architectures
The price of anarchy in network creation games is (mostly) constant
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
On a bounded budget network creation game
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
On dynamics in basic network creation games
SAGT'11 Proceedings of the 4th international conference on Algorithmic game theory
Asymmetric swap-equilibrium: a unifying equilibrium concept for network creation games
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Bounded-Distance network creation games
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
On dynamics in selfish network creation
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
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In this paper we study a generalization of the classic network creation game to the scenario in which the n players sit on a given arbitrary host graph, which constrains the set of edges a player can activate at a cost of α≥0 each. This finds its motivations in the physical limitations one can have in constructing links in practice, and it has been studied in the past only when the routing cost component of a player is given by the sum of distances to all the other nodes. Here, we focus on another popular routing cost, namely that which takes into account for each player its maximum distance to any other player. For this version of the game, we first analyze some of its computational and dynamic aspects, and then we address the problem of understanding the structure of associated pure Nash equilibria. In this respect, we show that the corresponding price of anarchy (PoA) is fairly bad, even for several basic classes of host graphs. More precisely, we first exhibit a lower bound of $\Omega (\sqrt{ n / (1+\alpha)})$ for any α=o(n). Notice that this implies a counter-intuitive lower bound of $\Omega(\sqrt{n})$ for the case α=0 (i.e., edges can be activated for free). Then, we show that when the host graph is restricted to be either k-regular (for any constant k≥3), or a 2-dimensional grid, the PoA is still $\Omega(1+\min\{\alpha, \frac{n}{\alpha}\})$, which is proven to be tight for $\alpha=\Omega(\sqrt{n})$. On the positive side, if α≥n, we show the PoA is O(1). Finally, in the case in which the host graph is very sparse (i.e., |E(H)|=n−1+k, with k=O(1)), we prove that the PoA is O(1), for any α.