Algorithmic Game Theory: First International Symposium, SAGT by Christos H. Papadimitriou (auth.), Burkhard Monien,

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

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

The 28 revised complete papes awarded including three invited lectures have been rigorously reviewed and chosen from 60 submissions. The papers are equipped in topical sections on routing and scheduling, markets, mechanism layout, potpourri of video games, answer ideas, and value sharing.

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

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General Restrictions. , the sets Aj = ∅ are not constrained in any further way. Our main result states that the price of anarchy for general restrictions behaves similarly as for clustered restrictions. Theorem 2. Under the assumptions of Theorem 1, the bounds stated therein 2 2 and ε2 = 2nm . remain valid if ε1 and ε2 are replaced by ε1 = 2nm t2 E[T ]2 We relate the price of anarchy with clustered restrictions to general restrictions. This requires an additional concept, which is closely related to clusters.

Now consider the machines with their optimum loads w1∗ , . . , wm Let M1 , . . , Mk be the groups induced by any chosen Nash equilibrium. The above observation implies that also in the optimum solution no task on any of the machines Mi can be on any of the machines in Mi+1 , . . , Mk , because the restrictions forbid it. However, it is possible that certain tasks of Mi change to the groups M1 , . . , Mi−1 . The following lemma quantifies the effect of such changes. Lemma 3. Let s∗ be an optimum schedule for an instance of the restricted selfish scheduling game with arbitrary restrictions.

67–73 (2005) 5. : Selfish traffic allocation for server farms. In: Proc. 34th STOC, pp. 287–296 (2002) 6. : Tight bounds for worst-case equilibria. In: Proc. 13th SODA, pp. 413–420 (2002) 7. : Computing nash equilibria for scheduling on restricted parallel links. In: Proc. 36th STOC, pp. 613–622 (2004) 8. : Nash equilibria in discrete routing games with convex latency functions. , Sannella, D. ) ICALP 2004. LNCS, vol. 3142, pp. 645–657. Springer, Heidelberg (2004) 9. : Structure and complexity of extreme Nash equilibria.

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