Cooperation in Distributed Systems

1
Cooperation in Distributed Systems - Simulation
of Cooperation -
2
What is Cooperation?
1.
There exists a dual structure of goals.
Goals of individual agents

Goal of the agents as a whole
May be implicit
May be a constraint
2.
Each agent spontaneously changes course of action

when pursuing its own goal hinders achieving the
goal

of the agents as a whole.
Each agent usually pursues its own goal.

Failing to achieve the overall goal causes a
serious
problem.
3
Real-World Situations
1.
OPEC countries negotiate the amount of oil
production

every year.

2.
Competing two parties cooperate for a third party
not to

take advantage of the competing.


The Chinese government and the communist party


cooperated against Japan at the time of World War
II.

3.
The US and other countries sometimes
cooperatively


buy dollars to prevent extreme depreciation of
dollar.
4.
Trading stocks and currency by computers may
cause

a catastrophe.
4
Motivations
1.
To study the effects of cooperation
Quantitative evaluation
2.
To get new insights into cooperation
5
Pursuit Game
2-D Infinite Grid
(I)
Goal of each blue agent
(?)
X
For him/her to capture the red agent
He/She will get a bonus.
?
(II)
Goal of the blue agents as a whole
?
For one of them to capture the red agent
Otherwise they would all have their
salaries cut.
?
)
(III)
Goal of the red agent (
X

Not to be captured
The initial positions are
randomly chosen.
There is a dual structure of goals (
(I)
and
(II)
).
(I)
is a sufficient condition for
(II)
.
(I)
's are mutually incompatible.
There can be conflicts between
(I)
and
(II)
.
6
Previous Work
Pursuit game

Study on organization and control
Benda, et al. (1985)


Stephens et al. (1989)

Gasser et al. (1989)

Game-theoretic approach


Levy et al. (1992)

The agents have identical or compatible goals.

2x2 Game

Prisoners' Dilemma

Study on basic rationality

Rosenschein et al. (1985)



Genesereth et al. (1986)

The goal of the agents as a whole is not
considered.
7
Cooperative Action
Rule-Based Approach
(I)
X
X
Approach
X
(II)
(III)
X
Go round
Stay
Take action according to the positions of the
other blue agents.
Six kinds of rules were prepared.
8
Effects of Cooperation
Quantitative Evaluation
Success rate (Capture rate)
Move by each blue agent
Getting out of being
round in circles
70
Cooperative action
X
?
Effects of
?
40
cooperation
?
1
9
Introducing an Objective Function
Minimize
Combination of an individual measure and the
common measure
of overall order


is a parameter representing degree of
cooperation.
a
No cooperation when
a
0.

Dividing the second term by the distance to the
red agent causes
repulsion between the blue and the red agents.
Some repulsion works for going around.
10
Degree of Encirclement
Measure of how far the red agent is from the
center of gravity
2
2
2
-1
l
m
n
(
1/3)
(
1/3)
(
1/3)

(Degree of encirclement)
2
2
2
l
m
n



1/3
l
m
where
X


1
2
l
m
n


1
2
1
X
11
Experimental Results
Success
rate ()
Just
100
encircling
80
Going
Going
around
60
behind
40
20
0
1
3
5
7
9
11
13
15
17
19
21
23
a

Cooperation Parameter
12
Conclusion
Simulated cooperation by taking a pursuit game in
a dilemmatic
context as a problem


Evaluated the effect of cooperation
quantitatively.


Incorporated an objective function

Combines an individual measure and the common
measure of


overall order.


Includes a parameter representing degree of
cooperation.


Studied the relationship between the cooperation
parameter and

the success rate.


Obtained interesting insights


Getting out of being round in circles is
effective.


The success rate goes down for a large
cooperation parameter.

Distributed control can be as good as centralized
control
13
Future Research
Application to optimization problems with more
than one
objective function

Each agent corresponds to each objective
function.

Cooperative framework for software agents

Preventing catastrophe and making sure "fairness"

Evaluating the overall goal

Comparison with an individual goal

Adjusting the cooperative parameter by learning