Abstract
AbstractWe analyze the convergence of the price of anarchy (PoA) of Nash equilibria in atomic congestion games with growing total demand T.
When the cost functions are polynomials of the same degree, we obtain explicit rates for a rapid convergence of the PoAs of pure and mixed Nash equilibria to 1 in terms of 1/T and $$d_{max}/T$$
d
max
/
T
, where $$d_{max}$$
d
max
is the maximum demand controlled by an individual. Similar convergence results carry over to the random inefficiency of the random flow induced by an arbitrary mixed Nash equilibrium. For arbitrary polynomial cost functions, we derive a related convergence rate for the PoA of pure Nash equilibria (if they exist) when the demands fulfill certain regularity conditions and $$d_{max}$$
d
max
is bounded as $$T\rightarrow \infty .$$
T
→
∞
.
In this general case, also the PoA of mixed Nash equilibria converges to 1 as $$T\rightarrow \infty $$
T
→
∞
when $$d_{max}$$
d
max
is bounded. Our results constitute the first convergence analysis for the PoA in atomic congestion games and show that selfish behavior is well justified when the total demand is large.
Funder
National Science Foundation
Anhui Science and Technology Department
Talent Foundation of Hefei University
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Software
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