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this way, each member of the organization may have
his own representation of the resources that are the
basis of his relationships with others. This makes it
possible to describe how a resource impacts the au-
tonomy of an actor in a more general way.
2 FORMALIZATION OF A
FRAGMENT OF SOA
In the following, we briefly describe the basic social
game formalization, as given in (Sibertin-Blanc et al.,
2006).
Within an organization, the actors are the active
entities that process the inputs and produce the out-
put and, by doing so, adapt their behaviours to the
behaviour of the other actors. On the other hand, the
resources (the UZs in SOA) are the means necessary
for the actors to properly behave and to reach not only
their own goals but also those of the organization. In
this formalization, every resource is mastered by a
single actor and every actor is assumed to master at
least one resource.
The state property of a resource characterizes how
this resource is managed by its controller, usually
rather to his own advantage or to that of a few cho-
sen actors. The characterization of how important a
resource is to an actor is done by allowing each actor
to distribute a limited amount of stakes among the re-
sources in the game. The amount of stakes an actor
puts on a resource is determined by how intensely he
needs this resource to reach his goals, in other words,
he puts more stakes on the resources he depends most.
When an actor depends on a resource, the effect
function determines the impact of the actual state of
the resource on his action capability. As a result, each
actor both controls some others, by means of the re-
sources he controls, and depends on others, by the re-
sources he needs. The overall state of an organiza-
tion is characterized by the composition of the states
of the resources it contains, and this characterizes the
behaviour of each actor with regard to others.
Let R be a set of resources, let stake(a,r) denote
the amount of stakes an actor a puts on resource r and
let e f f ect
r
(a,s
r
) denote the impact an actor a suffers
when resource r is in state s
r
. The global capacity of
action of actor a when the organization is in state s is
defined in this formalization as
payo f f (a,s) =
∑
r∈R
stake(a,r) ∗ e f f ect
r
(a,s
r
).
Within this setting, the actors of an organization coor-
dinate their respective behaviours while playing the so
called social game. An action of actor a on a resource
r that he controls is a move act
a
[r] to be applied to
the current state s
r
of r. A step of the game occurs
when each actor a has chosen a move act
a
[r
i
] for each
resource r
i
that he controls, and the game then goes
from state (s
r
1
,s
r
2
,...,s
r
M
) to state (s
0
r
1
,s
0
r
2
,...,s
0
r
M
),
where s
0
r
i
= s
r
i
+ act
a
[r
i
].
The game is repeated until it becomes stabilized,
or stationary: each actor has a satisfying payoff and
plays the null action, i.e., he no longer changes the
state of the resources he controls. Such a state of the
game is considered a social equilibrium, a regulated
situation that is satisfying and accepted by all the ac-
tors in the game. This state depends on the strategy
of each actor, i.e. how he adapts his behaviour (by
changing the state of the resources he controls) ac-
cording to the payoff he receives from others. In most
human organizations, social games are positive sum
games: each actor obtains some gain from being co-
operative, because others will also be cooperative in
return. Thus, typical social equilibria are Pareto max-
ima: any increase in an actor’s satisfaction would en-
tail a decrease of the satisfaction of another actor, and
thus produce a situation that would not be accepted
by all the actors.
3 THE EXTENDED
FRAMEWORK
The formalization of the coordination among the ac-
tors of an organization as shown above has some lim-
itations that do not allow it to handle some complex
organizations.
There exist cases in which the actors that are mem-
bers of an organization have different views on the set
of resources handled in that organization. Some ac-
tors may view a set of several resources as a single one
because they are unable to identify or to distinguish
the elements of such a compound resource, whereas
others may view each of those resources individually.
Also, a resource may be a substitute for another
one (having a good access to a resource makes it need-
less to have a good access to the other one), two re-
sources may be complementary (good access to one
resource is useful only if it goes together with a good
access to the other one), or they may have interactions
of some kind (if there is a good access to r
1
then r
2
is more important than r
3
, and the converse holds in
case of a bad access to r
1
). Moreover, these interac-
tions among resources may be different for different
actors.
The additive way used to compute the payoff of
actors as given in Section 2 is very restrictive; there,
the impact that the state of a resource has on an ac-
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