Paper by Erik D. Demaine

Reference:

Noga Alon, Erik D. Demaine, MohammadTaghi Hajiaghayi, and Tom Leighton, “Basic Network Creation Games”, SIAM Journal on Discrete Mathematics, volume 27, number 2, 2013, pages 656–668.

Abstract:

We study a natural network creation game, in which each node locally tries to minimize its local diameter or its local average distance to other nodes, by swapping one incident edge at a time. The central question is what structure the resulting equilibrium graphs have, in particular, how well they globally minimize diameter. For the local-average-distance version, we prove an upper bound of 2^O(√lg n), a lower bound of 3, a tight bound of exactly 2 for trees, and give evidence of a general polylogarithmic upper bound. For the local-diameter version, we prove a lower bound of Ω(√n), and a tight upper bound of 3 for trees. The same bounds apply, up to constant factors, to the price of anarchy. Our network creation games are closely related to the previously studied unilateral network creation game. The main difference is that our model has no parameter α for the link creation cost, so our results effectively apply for all values of α without additional effort; furthermore, equilibrium can be checked in polynomial time in our model, unlike previous models. Our perspective enables simpler proofs that get at the heart of network creation games.

Comments:

This paper is also available from SIAM.

Updates:

Unfortunately the proof of Theorem 5 is flawed, but the theorem is still true. Read our erratum for a correct proof.

Length:

The paper is 13 pages.

Availability:

The paper is available in PostScript (713k), gzipped PostScript (340k), and PDF (380k).

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