By Christos H. Papadimitriou (auth.), Lars Arge, Michael Hoffmann, Emo Welzl (eds.)

This publication constitutes the refereed complaints of the fifteenth Annual ecu Symposium on Algorithms, ESA 2007, held in Eilat, Israel, in October 2007 within the context of the mixed convention ALGO 2007.

The sixty three revised complete papers awarded including abstracts of 3 invited lectures have been conscientiously reviewed and chosen: 50 papers out of one hundred sixty five submissions for the layout and research music and thirteen out of forty four submissions within the engineering and functions song. The papers tackle all present topics in algorithmics achieving from layout and research problems with algorithms over to real-world functions and engineering of algorithms in numerous fields.

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Additional info for Algorithms – ESA 2007: 15th Annual European Symposium, Eilat, Israel, October 8-10, 2007. Proceedings

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We show that every ESS is a Nash Equilibrium, and we show that, to evaluate evolutionary stability, we have to consider only best replies to the current strategy. Then we establish that in an ESS, we not only have link group uniqueness, but also the probability distribution with which links of the same group are chosen by tasks has to be unique. In fact, an ESS requires treating two Evolutionary Equilibrium in Bayesian Routing Games 31 links with equal speed exactly the same. This result establishes the uniqueness of ESS.

U −1 be the distinct facilities chosen by k players in a strategy profile f with ≤ k, numbered according to the orientation of the cycle. For every j ∈ Z , let cj ≥ 1 be the number of players who choose the facility uj and let dj ≥ 1 be the length of the directed path from uj to uj+1 following the orientation of G. Now the strategy profile is defined by these 2 numbers, up to permutation of the players. We decompose the distance into dj = 1 + 2aj + bj , for 0 ≤ bj ≤ 1, where 2aj + bj is the number of vertices between facilities uj and uj+1 .

2 Basic Models and Concepts We first introduce Bayesian Parallel Links Games and show some simple observations concerning link load and utilities. We then introduce population games and define evolutionary stable strategies (ESS). 1 Bayesian Parallel Links Games We examine an extension of the original routing game called Bayesian parallel links game. Our definition below is a special symmetric case of the definition in [8]. Harsanyi [9] introduced the notion of a Bayesian game to analyze games with incomplete information where players are uncertain about some aspect of the game such as what preferences or options the other players have.

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