From: AAAI-86 Proceedings. Copyright ©1986, AAAI (www.aaai.org). All rights reserved.
COOPERATION
WITHOUT
Michael R. Genesereth,
Matthew
COMMUNICATION
L. Ginsberg,
and
Jeffrey
S. Rosen&&n*
Logic Group, Knowledge Systems Laboratory,
Computer
Science Department,
Stanford University,
Stanford,
California
94305
ABSTRACT
Intelligent agents must be able to interact even without the benefit of communication.
In this paper we
examine various constraints
on the actions of agents
in such situations
and discuss the effects of these constraints on their derived utility. In particular,
we define and analyze basic raiionaliiy;
we consider various
assumptions
about independence;
and we demonstrate
the advantages of extending the definition of rationality from individual actions to decision procedures.
I
Introduction
The affairs of individual intelligent
agents can seldom be treated in isolation.
Their actions often interact, sometimes for better, sometimes for worse. In this
paper we discuss ways in which cooperation
place in the face of such interaction.
Previous
A.
In
recent
gence
has
called
arisen.
can take
a
sub-area
artificial
Researchers
have
in parallel
distributed
tributed
nature
air traffic
[29])
intelli(DAI)
freely help one another.
to address
those of synchronization,
efficient
(inadvertent)
interference.
attempted
or as necessitated
of the problem
control
domain
by the
(e.g.,
dis-
[30]).
contract-bid
metaphor
to model the assignment
of
tasks to processors.
Lesser and Corkill have made empirical analyses of distributed
computation,
trying to
*This
cooperation
strategies
that lead to efficient
solutions for a network of nodes [3,4,7,21].
research
has been supported
c.
by the Office
of Naval
Re-
search under grant number N00014-81-K-0004
and by DARPA
under grant numbers N00039-83-C-0136
and N00039-86-C-0033.
Issues to be addressed
destructive
Overview
1.
Smith and Davis’ work on the contract net [6] produced a tentative
approach
to cooperation
using a
discover
problem
assumptions
artificial
AI
the problems of interacting
agents so as to increase
efficiency
(by harnessing
multiple reasoners
to solve
problems
Their
B.
intelligence
of
distributed
These DA1 efforts have made some headway in constructing cooperating
systems; the field as a whole haa
also benefited from research into the formalisms
necessary for one agent to reason about another’s knowledge and beliefs. Of note are the efforts of Appelt [l],
Moore [24], Konolige
[19,18], Levesque [22], Halpern
and Moses [8,16].
Previous DA1 work has assumed for the most part
that agents are mutually
cooperative
through
their
designer’s fiat; there is built-in
“agent benevolence.”
Work has focused on how agents can cooperatively
achieve their goals when there are no conflicts of interest. The agents have identical or compatible goals and
work in Distributed
years,
Georgeff has attacked
the problem of assuring noninterference
among distinct
agents’ plans [12,13]; he
has made use of operating system techniques
to identify and protect critical regions within plans, and has
developed a general theory of action for these plans.
Lansky has adapted her work on a formal, behavioral
model of concurrent
action towards the problems of
planning in multi-agent
domains [20].
include
communication,
and
of this paper
True conflicts
of interest
The research that this paper describes discards the
benevolent
agent assumption.
We no longer assume
that there is a single designer for all of the interacting
agents,
Rather,
nor that they will necessarily
we examine
the question
help one another.
of how high-level,
au-
tonomous,
independently-motivated
agents ought to
interact with each other so as to achieve their goals.
In a world in which we get to design only our own
intelligent agent, how should it interact with other intelligent
agents?
Planning:
AUTOMATED
REASONING
/ 51
There
are a number
of domains
in which autjonomous, independently-motivated
agents may be ex-
The study of such constraints
and their consequences is important for the design of intelligent, inde-
pected to interact.
Two examples are resource management
applications
(such as an automated
secretary [15]), and military
applications
(such as an autonomous land vehicle).
These agents must represent
the desires of their designers in an environment
that
includes other intelligent
agents with potentially
conflicting goals.
pendently motivated agents expected to interact with
other agents in unforeseeable
circumstances.
Without
Our model of agent interaction
thus allows for true
conflicts of interest.
As special cases, it includes pure
conflict (i.e., zero sum) and conflict-free
(i.e., common
goal) encounters.
By allowing conflict of interest interactions, we can address the question of why rational
agents would choose to cooperate
with one another,
and how they might coordinate
their actions so as to
bring about mutually preferred outcomes.
No
2.
such an analysis,
a designer might overlook powerful
principles of coooperation
or might unwittingly
build
in interaction
techniques
that are nonoptimal
or even
inconsistent.
Section 2 of this paper provides the basic framework for our analysis. The subsequent sections analyze
progressively
more complicated
assumptions
about interactions
between agent.s.
Section
3 discusses the
consequences
of acting rationally
and exploiting
the
rationality
of other agents in an interaction;
section
4 analyzes dependence
and independence
in decision
making;
and section 5 explores the consequences
of
rationality
across situations.
The concluding
section
discusses the coverage of our analysis.
communication
Although
communication
for accomodating
interaction
is a powerful instrument
(and has been examined
II
in previous work [28]), in our analysis here we consider
only situations
in which communication
between the
agents is impossible.
While this might seem overly restrictive,
such situations
do occur, e.g., as a result of
Framework
Throughout
the paper we make the assumption that
there are exactly two agents per interaction
and exactly two actions available to each agent.
This as-
commmunications
equipment failure or in interactions
between agents without
a common
communications
protocol.
Furthermore,
the results are valuable in the
analysis of cooperation
with communication
[28,27].
sumption
substantially
simplifies our analysis, while
retaining the key aspects of the general case. Except
where indicated to the contrary, all results hold in gen-
Despite the lack of communication,
we make the
strong assumption
that sufficient sensory information
is available for the agents to deduce at least partial
information
about each other’s goals and rationality.
For example, an autonomous
land vehicle in the battle-
The essence of interaction
is the dependence of one
agent’s utility on the actions of another.
We can characterize this dependence by defining the payoff for each
agent i in an interaction
s as a function pi that maps
every joint action into a real number
designating
the
resulting utility for i. Assuming that M and N are the
field may perceive
the actions
of another
autonomous
land vehicle and use plan recognition techniques [9] to
deduce
its destination
or target,
even in the
absence
eral [10,11,14,27].
sets of possible moves for the two agents
we have
(respectively),
of communication.
3.
Study
pf ; A4 x l?i --+ R.
of coristrairrts
In this paper we examine various constraints
on the
actions of agents in such situations
and discuss the
In describing
specific interactions,
we present the
values of this function in the form of payoff matrices
effects of these constraints
on the utility derived by
agents in an interaction.
For example, we show that it
can be beneficial for one agent to exploit information
[23], like the one shown in figure 1. The number in the
lower left hand corner of each box denotes the payoff
to agent J if the agents perform the corresponding
ac-
about
tions,
the rationality
is interacting.
for an agent
and other
tions
of another
agents,
except
where such similarity
nonoptimal
52 /’SCIENCE
agent
with which
it
We show that it can also be beneficial
to exploit the similarity
between itself
action.
in certain
symmetric
situa-
leads to indeterminate
or
denotes
and the number
in the upper right hand corner
the payoff to K.
For example,
if agent J per-
forms action a in this situation and agent Ii performs
action c, the result will be 4 units of utility for J and
1 unit for Ii’. Each
its own utility.
agent
is interested
in maximizing
the term A;((m)
denote the action that agent K will
perform in situation s if agent J performs action m:
WI&) = &(W.r(s)).
In what follows we call AL the reac2ion function
IC. Then the formal definition of dominance is
1: A payoff matrix
Figure
Although the utilities present in a payoff matrix
generally take on any value, we will only need the
dering of outcomes in our analysis. Therefore,
we
only be using the numbers 1 through 4 to denote
utility of outcomes.
An agent’s job in such a situation
can
orwill
the
In the remainder
of agent J.
III
M.
WJ here is a function
*
predicate
3
‘R:(m)
Even if J knows nothing about K’s decision procedure, this constraint
guarantees
the optimality
of a
analysis. According
decision rule known as dominance
to this rule, an action is forbidden if there is another
action that yields a higher payoff for every action of
the other agent, i.e.,
that designates
rationality
Proof: A straightforward
of rationality.
Cl
As
payoff
for J
(since
n’))
implies
application
3
W(s)
dominance
# m.
analy-
of the definition
an example of dominance
analysis, consider the
matrix in figure 2. In this case, it is clearly best
to perform action a, no matter what K does
4 and 3 are both better than 2 and 1). There is
the action perabove.
which actions
we need to further
Basic
n) < p:(m’,
K
as described
to judge
p;(m,
no way that J can get a better payoff by performing
action b.
WJ(S) # m.
by J in each situation,
order to use this definition
nality
> P~(mA;((m)).
rationality
predicate.
An
if there is another action
(3m’ D~(m’,m))
Theorem
sis.
Basic Rationality
however,
p$(m’, 4&n’))
We can now define the
action is basically irrational
that dominates it.
(3m’hVn’
lR”,(m)
rational,
++
of the paper we take the viewpoint
We begin our analysis by considering
the consequences of constraining
agent J so that it will not
perform an action that is basically irrational.
Let Ri
denote a unary predicate over moves that is true if and
only if its argument is rational for agent i in situation
s. Then agent J is basically
rational if its decision
procedure does not generate irrational moves, i.e.,
formed
m)
is to decide which
action to perform. We characterize
the decision procedure for agent i as a function W; from situations
(i.e.,
particular
interactions)
to actions.
If S is the set of
possible interactions,
we have
Wi : S +
D;(m’,
for
In
are
J
define the ratio-
R”, .
Figure
An action m’ dominaies
an action m for agent J
in situation
s (written
D;(m’,
m)) if and only if the
payoff to J of performing
action
m’ is greater
than the
payoff of performing action m (the definition for agent
I< is analogous).
The difficulty in selecting an action
stems
from lack of information
agent
will do.
about
If such information
to perform.
dominance
analysis
Problem
does not always ap-
ply. As an example, consider the payoff matrix in fig-
the
ure 3. In this situation,
an intelligent
agent J would
probably select action a. Rowever, the rationale for
this decision requires an assumption
about the ratio-
Let
nality
what the other
were available,
agent could easily decide what action
Of course,
2: Row Dominance
of the other
agent
Planning:
in the interaction.
ALJTOMATED
REASONING
! ii
The
main
consequence
rule commonly
known
of
independence
is a decision
If for every %xed
as case analysis.
move” of K, one of J’s actions is superior to another,
the latter action is forbidden.
The difference between
then
case
analysis and dominance
analysis is that it allows J to compare two possible
actions for each action by K without
considering
any %ross terms.”
Figure
3: Column
Dominance
Problem
As an example,
In dealing with another agent it is often reasonable
to assume that the agent is also basically rational. The
formalization
of this assumption
of mutual rationality
is analogous to that for basic rationality.
consider
the payoff
J gets 4 units of utility
(for J) of the outcome
rather
than
implies
Iterated
dominance
iterated
ad is less than the payoff of bc.
domi-
of several
following
tionality of K, we can show that action d is irrational
for K. Therefore,
neither ad nor bd is a possible outcome, and J need not consider them.2 Of the remaining two posrible outcomes, ac dominates be (from J’s
perspective),
so action b is irrational for J.
_
Action
Theorem
offers
several
with
Dependence
different,
but
rationality
Problem
and independence
By combining
inconsistent,
the independence
rationality,
we can also show
version of case analysis.
Theorem
erated
case
imply
Mutual
assumption
with mutual
the correctness
rationality
of an iterated
and independence
imply
it-
case analysis.
As an example
action.
c.
tion
Basic
of iterated case analysis, consider the
5. J cannot
use dominance
analysis,
situation
in figure
iterated dominance
Unfortunately, there are situations that cannot be handled by the basic rationality assumptions alone. Their
weakness is that they in no way account for dependencies between the actions of interacting
agents.
This secto dealing
4: Case Analysis
analysis.
dominance
analysis
handles
the column
problem in figure 3. Using the basic ra-
IV
3, and if K performs
J
Figure
Proof:
For this proof, and those
theorems, see [lo] and [ll]. III
4.
agent
c, then
K
Using this assumption
one can prove the optimality
of a technique called iterated dominance
analysis.
rationality
in figure
action d, then J gets 2 units of utility rather than 1. Dominance analysis does not apply in this case, since the payoff
lRk(m)3 W&s)#m
Theorem
Basic
nance analysis.
matrix
Given independence
of actions, a utility-maximizing
J should perform
action a: if K performs
action
However,
With
this
analysis,
nor case analysis
information
and
to select
K can exclude
using case analysis
mutual
rationality,
an
action
J can
exclude action Q.
K
approaches
this deficiency.
J
The simplest case is complete independence.
The independence assumption states that each agent’s choice of
action
agent’s
is independent
reaction
of the other.
function
one of the other agent’s
we would
yields
actions.
In other
the same
words,
value
each
Figure
for every
For all m, m’, n, and n’,
then have
Note
dent,
2We
write
if two decision
the independence
procedures
assumption
=
A&(m’)
results.
A;(n)
=
A”J(n’).
“paradox.”
An alien
one marked
“!I?’ and the other
mn to describe
/ SCIENCE
that,
Case Analysis i Problem
A&(m)
the situation
where
J has chosen
action m, and K has chosen action n; we call this a joint
54
5: Iterated
action.
lope
tains
As an example,
contains
the same
some
consider
approaches
number
number
the following
you with
marked
of dollars,
of cents.
are not indepen-
can lead to nonoptimal
The
‘)?“.
well-known
two envelopes,
The first enve-
and the other conalien is prepared
to
V
Alien
General
General
nality,
J
difference
to decision
procedures
We introduce
define general
Figure
6: Omniscient
Alien
rational
In an attempt
to discourage
greed
on your
part,
you pick the envelope
alien
has decided
marked
#. Bearing
on the contents
you pick one, which
envelope
in mind
that the
of the envelope
should
before
you select,?
payoff
of $10.00.
reaction
function
The
straint.
and
by describing
abandoning
appropriate
the alien’s
the independence
axioms
A&($)
are
con-
=
1 and
A%(+‘) = 1000.
These
hand
constraints
corner
J’s attention
limit
and the upper
right
to the lower
hand
corner
#. Although
cal, there
are real-world
of independence
trated
above
the example
encounters
is unwarranted,
must
and where the effect illus-
enter the rational
agent’s
analysis.
we of course
not only
uation
the current
are reversed.
behavior
same
situation
An agent
of the interacting
(3P’ DJ(P’,
as that
of agent
J in the permuted
situation
as good
behavior
be insupportable
tion among
same design.
like, except
is a strong
agent K will take in situation
P. Then the formal definition
in general,
artificial
agents,
Unfortunately,
when
3This constraint
tion in [28,27].
combined
it is reasonable
especially
While
The
advantage
for interac-
those built from the
it is not as strong
with general
is similar to the similar
as we would
rationality.
bargainer.9
common
lows
us to eliminate
if and only if it yields
and a better
denote
payoff
in at
the action
that
behavior
actions
rationality
(defined
joint
actions
for all agents,
is that,
together
in the last section),
that
it al-
are dominated
a technique
by
called
domi-
and common behavior
imply
nated case elimination.
rationality
Let, s be a situation
Proof:
with joint
actions
uv and zy
such that psJ(u, v) > psJ(z, y) and p;((u, v) > p;C(z, y), and
let, P be a decision
procedure
such that P(s)
= z and
=
y (where
s’ is the permuted
positions
have
and Q(s’)
Under
agents
a different
informal
situation,
reversed).
J
where
Let Q be a deci-
to P except
the common
behavior
that
Q(s)
= u
assumption,
J and K and, therefore,
P for both
irrational.
In other
been
that is identical
= v.
Q dominates
erally
both
assump-
are
the rationality
s if agent J uses procedure
of dominance
is:
of general
with
case elimination.
it may
above.
actions
nl(P’, P) vspdJ(P’(s),dR(~‘
2))pd,(P(s)AON
A 3sp:(P’(s),&&“)) > pdJ(P(s)A#‘)).
and K’s
constraint.
which
dzJ(P).
another
game
General
= WJ(~‘)
*
Let the term dk(P)
sion procedure
Common
in every
least, one game.
P(a’)
Va WK(a)
dominates
a payoff
Theorem
s’.~
the ac-
as described
to judge
P))
dominated
J and an agent K have common
of K in situation
s is the
that designates
RJ.
sit-
if and only if the action
# P(s)).
need to define further
agents
s but also the permuted
s’ in which the positions
to
predicate
The definition
of rationality
for a decision procedure
is
analogous
to that for individual
actions.
A procedure
is
irrational if there is another procedure
that dominate8 it:
other joint
Another interesting
example of action dependence is
common behavior. The definition requires that we consider
a unary
by J in each situation,
rational,
left
the assumption
33 (W&J)
to use this definition
of the ma-
given here is whimsiwhere
ac-
and functions
is true if and only if its argument is
rational agent can use a
In order
trix. Since the payoff for selecting
the # envelope is better
than the payoff for selecting the $ envelope, a rational agent
will choose
Let IRi denote
*
One procedure
We can easily solve this problem
than to individual
that WJ here is a function
Recall
tion performed
predicate
The payoff matrix for this situation
is shown in figure
6. Since the payoff for $ is greater that, that for # for
either of the alien’r option@, cma anallyair dictatea chooring
the % envelope.
Assuming
that the alien’s omniscience
is
accurate,
this lead to a payoff of $1.00.
While selecting
the envelope marked # violates case analysis, it leads to a
rather
ratio-
rationality
i. A generally
-%(P)
he
has decided to put one unit of currency in the envelopes if
you pick the envelope marked $ but one thousand
units if
of basic
that general
only if it is rational.
give you the contents of either envelope.
The catch is that
the alien, who is omniscient,, is aware of the choice you will
make.
that
for agent
procedure
version
being
a new set of relations
rationality.
over procedures
Problem
is a stronger
the primary
applies
tions.
rationality
Rationality
P is gen-
q
words,
if a joint
in an interaction,
action.
arguments
This
action
is disadvantageous
at least
conclusion
one
for
will perform
has an analog
in the
REASONING
/ 55
of [5] and [17].
Planning:
AUTOMATED
No-conflict
this
situations
result.
The
joint action
interaction,
are handled
best plan
as a special
rule states
that,
that maximizes
the payoff
then it should be selected.
Carallary
Gnatal
ply best plan.
rationality
case
if there
to all agents
of
is a
in an
J
and common
bshuvior
imFigure
Proof:
Apply
alternatives.
dominated
case
elimination
common
in figure
dominance
applies.
of best
7.
None
analysis,
plan,
case
However,
action
c (under
common
consider
the situation
of the preceding
analysis,
techniques
iterated
UC dominates
and so J will perform
tions,
of the Sexes
Cl
As an example
tured
9: Battle
to each of the
case
the assumptions
a and K
of general
(e.g.,
analysis)
all of the other
action
pic-
joint
behavior
conflict
such
as that
the constraints
situations.
situation,
in figure
Neverthe-
the resolution
9 remains
of a
undetermined
by
we have introduced.
ac-
will perform
rationality
to non-symmetric
less, in a no-communication
VI
and
Conclusions
behavior).
1
C
d
4
J
1133
Figure
of this approach
There are 144 distinct interactions
between two agents
with two moves and no duplicated
payoffs.
Of these, the
2
4
b
]
2
IE
a
Coverage
A.
K
techniques
presented
remaining
27 cases
here cover
117.
are unclear,
e.g.,
The
solutions
to the
the situation
in fig.
10.
7: Best
K
Plan
Generlll rationality
and common
behavior
also handle
difkult
rituationr
like the prisoner’s
dilemma [2,512ti] pica
tured in figure 8. Since the situation
is symmetric
(i.e.,
s=a
‘, using our earlier notation),
common
behavior
requires that they both perform the same action; general rationality eliminates
the joint action bd since it is dominated
by ac. The
agents perform
each receives
dictates
that
to a payoff
actions
a and c respectively,
3 units of utility.
By contrast,
case analysis
the agents perform actions b and d, leading
of only
2 units
Figure
for each.
For a discussion
be used to handle
contrasting
theory,
K
Unfortunately,
ior
are not
the battle
uation
both
general
always
agents
actions
consistent.
of the sexes
is symmetric,
perform
on the ac/bd
rationality
problem
and common
As
an example,
in figure
and common
the same
action.
diagonal
are forbidden
behavconsider
9. Again
behavior
the sit-
dictates
However,
that
both joint
by dominated
case elimination.
This
stricting
56
inconsistency
the
by occasionally
use of general
rationality
reand
approachs
with
paper’s
analysis
of interactions
assumptions.
have common
knowledge
of actions
of the interaction
and
their
ing utilities).
the interaction
Third,
is given
the effects
current
there
be effective
must
(otherwise,
there
choices
(i.e.,
a vari-
might
first, and the new situation
to
includ-
Second,
there
there are no miss-
is viewed
to future
in isolation
interactions
have on them).
simultaneity
are issues
matrix,
outcomes.
in the matrix
no consideration
presupposes
First, the agents are assumed
is no incompleteness
( i.e.,
those used in game
of this approach
ety of strong
and
Fourth,
in the agents’ actions
concerning
which
that then confronts
agent moves
the second
agent).
Admittedly,
can be eliminated
simultaneous
/ SCIENCE
all of these
ing choices
Dilemma
of a variety of other techniques
that can
these situations,
as well as a discussion
Suitability
This
J
8: Prisoner’s
situation
see [27].
B.
Figure
10: Anomalous
and
some
situations
example
these are serious
where
two ALVs
they
assumptions,
are satisfied.
approaching
opposite
but there are
Consider
as an
ends of a narrow
tunnel,
each having
ing one of several
the choice
alternate
of using
routes.
the tunnel
to assume that. they have common
knowledge
other’s approach
(e.g., through
reconnaisance).
unreasonable
to assume
of one another’s
route navigation,
that the agents
might be no concern
and the decisions
counters,
The
types
of analysis
to use in deciding
For
most
above
to be done
domains,
restrictive
work
in [28,27]
rently,
action
and
assumptions
more
steps
in that
on the question
needs
in turn.
Cur-
matrices
will inevitably
The existence
need
by these
to be handled
is routinely
and their
telligent
handled
automated
by humans.
extensions
agents
need to interact flexibly
of conflicting
goals will
should
The
agents,
results
successfully
for multi-agent
Decision
In Proceedings
procedures.
Workshop,
1985.
Between
Ira P. G o Id s t ein. Bargaining
ing Paper 102, Massachusetts
Intelligence
plan-
121-125.
Laboratory,
A. I. Work-
Goals.
Institute
of
pages 43-
of Technology
Ar-
1975.
Joseph Y. Halpern
and Yoram
Moses.
Knowledge
and
Common
I(nowledge
in a Distributed
Environment.
Research Report
IBM RJ 4421, IBM Research Laboratory,
San Jose, California,
October
1984.
[17]
D. R. Hofstadter.
Metamagical
themes-computer
tournaments of the prisoner’s dilemmasuggest
how cooperation
evolves.
Scientific
American,
248(5):1626,
May 1983.
[IS]
Kurt Konolige.
A computational
spection.
IJCAI-85,
pp. 502-508.
[19]
Kurt
its.
Konohge.
PhD
thesis,
theory
A Deduction
Model
Stanford University,
of belief
of Belief
1984.
intro-
and ita Log-
[20] A. L. Lansky.
Behavioral
Specification
and Planning
for
Domains.
Multiagent
Technical
Note 360, SRI International, Menlo Park, California,
November
1985.
design of inin the face of
[21]
such conflict.
of action
in
[16]
as it
in this paper
be of use in the
able to function
just
A theory
pp.
M. L. Ginsberg.
tificial
is
being pursued,
so that the type of conflict
analysis presented in this paper can be applied to interactions
with
incomplete
information
[26]. Future work will focus on issues arising from multiple encounters,
such as retaliation
and future compensation
for present loss.
Intelligent agents
with other entities.
[l5]
The
direction.
of incomplete
Georgeff.
AAAI-84,
and interaction
125-129.
the Distributed
Artificial
Intelligence
65, AAAI,
Sea Ranch, CA, December
listed
work
so that each of the
can be removed
represents
research
the
clearly
Michael
ning.
Re-
(HPP-84-41),
Computer SciUniversity,
November
1984.
Communication
AAAI-83,
pp.
[ 121 Michael
Georgeff.
multi-agent
planning.
[13]
Jef-
Matthew
L. Ginsberg,
and
Michael R. G enesereth,
frey S. Rosenschein.
Solving the Prisoner’s
Dilemma.
port NO. STAN-CS-84-1032
ence Department,
Stanford
[14]
this approach
assumptions
1984.
[ll]
tool
to take.
84-36, Heuristic Programming
Project, CornStanford University, September
Report
puter Science Department,
models
are an appropriate
of course,
limiting,
in developing
most
have some
(in this case) over future enare effectively
simultaneous.
in this paper
what
far too
are
of one anNor is it
utility functions.
Finally, in the domain of
the choices are often few and well-defined.
There
HPP
or try-
It is not unreasonable
V. Lesser
and D. Corkill.
The
distributed
vehicle
moni-
toring testbed: a tool for investigating
distributed problem
solving networks.
AI Magazine,
4(3):15-33,
Fall 1983.
REFERENCES
[l]
D. E. Appelt.
Satisfy
Multiple
Planning
Goals.
[2] Robert Axelrod.
The
Books, Inc., New York,
[3]
D. Corkill.
University
Evolution
1984.
of Massachusetts,
of Cooperation.
Organizalional
Networks.
for
Problem-Solving
Amherst,
Basic
Self-Design
PhD
thesis,
MA, 1982.
[4] Daniel D. Corkill and Victor R. Lesser. The use of metalevel control for coordination
in a distributed
problem solving network.
[5]
IJCAI-83,
pp.
Davis
and
Reid
metaphor
for distributed
telligence,
20(1):63-109,
G.
Negotiation
solving.
Artificial
report.
[9] Michael
R. Genesereth.
consultation.
IJCAI-79,
[lo]
Michael
R.
G enesereth,
frey S. Rosenschein.
[26]
Jeffrey
Matthew
C ooperation
Reasons
Jeffrey
[29]
Also
published
(301
of Im-
Interaction:
Cooperation
PhD thesis, Stanford Univeras STAN-CS-85-1081
(KSL85-
of Computer
Science, Stanford University,
1985.
S. R osenschein and Michael R. Genesereth.
rational agents. IJCAI-85,
pp. 91-99.
R. G. Smith.
A F Ta4meWOTk
tributed Processing
University,
1978.
and limited
Rational
Agents.
Intelligent
Department
among
in the Presence
Ox-
Technical Report, Knowledge SysComputer Science Dept., Stanford Univ.,
S. Rosenschein.
sity, 1986.
(281
Cooperation
Press,
In preparation.
Jeffrey
40),
Clarendon
In
of
Information.
tems Laboratory,
[27]
and Persons.
S. Rosenschein.
complete
as a
In-
in automated
Games
and DeciJohn Wiley and
D. Parfit.
ford, 1984.
pp. 491-501.
The role of plans
pp. 311-319.
Survey.
[25]
October
IJCAI-85,
Raiffa.
belief.
R. Moore.
A formal theory of knowledge
and action.
J. R. Hobbs and R. C. Moore, editors, Formal
Theories
the Commonsense
World, Ablex Publishing
Co., 1985.
1983.
Belief, awareness,
and explicit
[24]
Among
Smith.
problem
[8] R. Fagin and J. Y. Halpern.
preliminary
R. Duncan Lute and Howard
aions, Introduction
and Critical
Sons, New York, 1957.
1986.
American
j’i’] Edmund
H. Durfee,
Victor
R. Lesser,
and Daniel
D.
Corkill.
Increasing
coherence
in a distributed
problem
solving network.
IJCAI-85,
pp. 1025-1030.
reasoning:
[23]
748-756.
L. Davis.
Prisoners,
paradox and rationality.
Philosophical
Quarterly,
14, 1977.
[S] Randall
Hector J. Levesque.
A logic of implicit
AAAI-84,
pp. 198-202.
Natural
Language
Utterances
to
PhD thesis, Stanford Univ., 1981.
A F ramework
in Distributed
[22]
R. Steeb,
fOT
Environment.
S. C ammarata,
Distribzlted
intelligence
port WD-839-ARPA,
Problem
Solwing
PhD
F. Hayes-Roth,
for air fleet control.
The
Rand
thesis,
Deals
in a DisStanford
and R. Wesson.
Technical Re-
Corporation,
Dec.
1980.
L. Ginsberg, and Jefwithout Communication.
Planning:
AUTOMATED
REASONING
/ 5’