The Price of Anarchy

130 Pages·2005·0.37 MB·English

by  Tim Roughgarden

The Price of Anarchy
Tim Roughgarden
UC Berkeley + Stanford University
also featuring some slides contributed by
Christos Papadimitriou (UC Berkeley)
The Price of Anarchy
OR, a rendezvouz of computer science and game theory
Tim Roughgarden
UC Berkeley + Stanford University
also featuring some slides contributed by
Christos Papadimitriou (UC Berkeley)
The Price of Anarchy
OR, a rendezvouz of computer science and game theory
OR, how free food can lead to a thesis topic
Tim Roughgarden
UC Berkeley + Stanford University
also featuring some slides contributed by
Christos Papadimitriou (UC Berkeley)
(Very) Brief Overview
• basic object of study: noncooperative games
• widespread phenomenon: selfish (or
“rational”) behavior is inefficient
– could improve natural objective functions by
dictating behavior
• price of anarchy -- “competitive analysis for
noncooperative games”
– when does noncooperative behavior lead to an
approximately optimal outcome?
Example: Load-Balancing
• setup: 4 jobs self-schedule on 2 machines
– each wants a lightly loaded machine
• with coordination, can achieve the following
“good” outcome (makespan = 5)
1
2
4
3
m m
1 2
Example: Load-Balancing
• if they cannot be centrally scheduled?
Example: Load-Balancing
• if they cannot be centrally scheduled?
• e.g., the following outcome is “stable”
– no job has incentive to switch machines
2
1
4
3
m m
1 2
Example: Braess’s Paradox
• setup: traffic (e.g., many cars or packets)
pick s-t paths to minimize travel time
• travel time increases with congestion
c(x)=x c(x)=1
s t
c(x)=x
c(x)=1
Example: Braess’s Paradox
• setup: traffic (e.g., many cars or packets)
pick s-t paths to minimize travel time
• travel time increases with congestion
c(x)=x c(x)=1 ½ of traffic
s t
c(x)=x ½ of traffic
c(x)=1
• at “equilibrium”: travel time = 3/2 for all
Braess’s Paradox
Initial Network:
½ ½
x 1
s t
½ ½
x
1
Travel time = 1.5