TY - GEN

T1 - Optimal price of anarchy of polynomial and super-polynomial bottleneck congestion games

AU - Kannan, Rajgopal

AU - Busch, Costas

AU - Vasilakos, Athanasios V.

PY - 2012

Y1 - 2012

N2 - We introduce (super) polynomial bottleneck games, where the utility costs of the players are (super) polynomial functions of the congestion of the resources that they use, and the social cost is determined by the worst congestion of any resource. In particular, the delay function for any resource r is ofbut the degree is bounded the form CrMr, where Cr is the congestion measured as the number of players that use r, and the degree of the delay function is bounded as 1 ≤ Mr ≤ log Cr. The utility cost of a player is the sum of the individual delays of the resources that it uses. The social cost of the game is the worst bottleneck resource congestion: maxrεR Cr, where R is the set of resources. We show that for super-polynomial bottleneck games with Mr = log Cr, the price of anarchy is o(√|R|), specifically O(2√log|R|). We also consider general polynomial bottleneck games where each resource can have a distinct monomial latency function but the degree is bounded i.e Mr = O(1) with constants α ≤ Mr ≤ β and derive the price of anarchy as min (|R|, max(2β/C*(2|R|)1/α+1 ·,(2β/ C*)α/α+1 · (2β) β-α/α+1)), where C* is the bottleneck congestion in the socially optimal state. We then demonstrate matching lower bounds for both games showing that this price of anarchy is tight.

AB - We introduce (super) polynomial bottleneck games, where the utility costs of the players are (super) polynomial functions of the congestion of the resources that they use, and the social cost is determined by the worst congestion of any resource. In particular, the delay function for any resource r is ofbut the degree is bounded the form CrMr, where Cr is the congestion measured as the number of players that use r, and the degree of the delay function is bounded as 1 ≤ Mr ≤ log Cr. The utility cost of a player is the sum of the individual delays of the resources that it uses. The social cost of the game is the worst bottleneck resource congestion: maxrεR Cr, where R is the set of resources. We show that for super-polynomial bottleneck games with Mr = log Cr, the price of anarchy is o(√|R|), specifically O(2√log|R|). We also consider general polynomial bottleneck games where each resource can have a distinct monomial latency function but the degree is bounded i.e Mr = O(1) with constants α ≤ Mr ≤ β and derive the price of anarchy as min (|R|, max(2β/C*(2|R|)1/α+1 ·,(2β/ C*)α/α+1 · (2β) β-α/α+1)), where C* is the bottleneck congestion in the socially optimal state. We then demonstrate matching lower bounds for both games showing that this price of anarchy is tight.

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U2 - 10.1007/978-3-642-30373-9_22

DO - 10.1007/978-3-642-30373-9_22

M3 - Conference contribution

AN - SCOPUS:84869594035

SN - 9783642303722

T3 - Lecture Notes of the Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering

SP - 308

EP - 320

BT - Game Theory for Networks - Second International ICST Conference, GAMENETS 2011, Revised Selected Papers

T2 - 2nd International ICST Conference on Game Theory in Networks, GAMENETS 2011

Y2 - 16 April 2011 through 18 April 2011

ER -