By Christos H. Papadimitriou (auth.), Burkhard Monien, Ulf-Peter Schroeder (eds.)

This publication constitutes the refereed court cases of the 1st overseas Symposium on Algorithmic video game thought, SAGT 2008, held in Paderborn, Germany, in April/May 2008.

The 28 revised complete papes offered including three invited lectures have been conscientiously reviewed and chosen from 60 submissions. The papers are geared up in topical sections on routing and scheduling, markets, mechanism layout, potpourri of video games, resolution techniques, and price sharing.

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Extra resources for Algorithmic Game Theory: First International Symposium, SAGT 2008, Paderborn, Germany, April 30-May 2, 2008. Proceedings

Sample text

In [24,8], it was shown that the PoA of non-atomic congestion games with latencies in class D is ρ(D). Next we establish the same upper bound on the PoA of symmetric congestion games on extension-parallel networks. The proof is based on the following lemma. 42 D. Fotakis Lemma 2. Let Γ be a symmetric congestion game on an extension-parallel network G(V, E), and let f be a PNE and g be any configuration of Γ . Then, Δ(f, g) ≡ (fe − ge )de (fe ) − e:fe >ge (ge − fe )de (fe + 1) ≤ 0 e:fe

For the latter we use a probabilistic model in which message lengths are random variables. We evaluate the (expected) price of anarchy of the game for two social cost functions. For total latency cost, √ we show the tight result that the price of anarchy is essentially Θ (n m/t). Hence, even for congested networks, when the traffic is linear in the number of players, Nash equi√ libria approximate the social optimum only by a factor of Θ ( m). This efficiency loss is caused by link restrictions and remains stable even under message fluctuations, which contrasts the unrestricted case where Nash equilibria achieve a constant factor approximation.

We highlight Congestion Games with Linearly Independent Paths 41 that both σi [u , u] and σi [w, w ] are included in σj and σj . In particular, σj [u , w ] = z ∪ p. e. σe ≥ σe ). The second inequality follows from (1). e. e. σe ≥ σe ). For the fourth inequality, we observe that the left-hand side is equal to the individual cost of player i on σi [u , u] ∪ p ∪ σi [w, w ] in σ, and that the right-hand side is equal to the individual cost of player i on σi [u , w ] in σ (recall that σi [u , w ] and σi [u , w ] are edge disjoint).

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