Human organizations that have begun to rely on networks for collaboration are already proli c. Networked collaboration is highly bene cial in many group activity including mixed teams of humans and agents. The prospect of understanding complex interactions on network organizations has prompted us to develop a paradigm serving as a reference model for organizations of networked individuals. In this paper we present a few salient components suggested to comprise network organizations. Network properties are central for incorporating a spectrum of collaboration styles that is outlined in our paradigm. We have introduced synergy as a speci c network e ect that embodies collaboration, which in turn has the potential to enhance performance at various levels of an organization as well as the overall productivity of it.
When the agents dwell inside an organization, they form
repeated patterns of interactions that in result shape the
structure of their network. There are many existing
patterns to describe interactions within organizations, which
a ect their performance features. Horling and Lesser [
Definition 1. Network Organization (NO) are large, semiautonomous, ad-hoc networked individual entities with the aim of automating command and control of distributed complex tasks.
We aspire to generalize the concept of NO and introduce
a novel paradigm that is the best t to model agents'
actions in an NO that we call Network Organization Paradigm
(NOP) [
Evolving in the last thirty years, network organizations
have produced signi cant impacts on formation and
functioning of human organizations. Recent advances in social
networking media have accelerated impromptu formation
and adaptations in human populated network organizations
with bene ts from collective pool of human knowledge and
skills. Furthermore, cohesion in human NO is due to
common human social traits such as trust and bene cence. We
have embarked on modeling arti cial, agent based network
organizations that no doubt will possess features inspired by
human NOs [
Earlier studies that focus on the traditional form of
organizations was moved by a homologous structure formed
from continuous cooperative interactions among di erent
organizational entities [
Since the NO is a ected by the structure of its network,
one possible e ect of the network of interest in this paper is
synergy among agents. Synergy is instrumental in
increasing agents' e ciency on di erent tasks by allowing them
to collaborate with each other in an NO. Network e ects
on the performance of a group have been demonstrated in
several recent works. Liemhetcharat and Veloso [
The remainder of the paper is organized as follows. In Section 2, we give a brief introduction to the NOP and focus mainly on one of its key concepts, which is the problem prole, and describe the parameters that fall within it. Section 3 introduces one of the important properties that are inherited from the network and a ects agents' behaviors called synergy. Section 4 describes the process of an NOP and how the problem pro le plays an important role in navigating among agents when assigning tasks. Finally, we conclude this paper and describe some of the future possibilities of this work in Section 5. 2.
There are many actual groups that rely on networks to organize their activity. Arab Spring and Science Teams are two examples. The modeling at a more generalized level cuts across domains to extricate the model from limited requirements of speci c domains. A perspective that would model a generic network organization came to be considered as a paradigm. NOP can model many NO operations that are applied to open multi-agent systems. Examples are systems of river dam control, factory cells, electrical power grids, organized labor unions, and tra c control on land, sea, and space. As a paradigm, it does not functionally alter the operations to which it is applied. The paradigm can be understood in terms of the ways it permits arrangement of command and control regimes. Invariably, NO relies on the network in which it dwells. Thus, a pro le of an NOP network residence is essential. NO member-nodes (i.e., agents) are critical constituents and will be delineated in separate pro les. Target problems (i.e., operations) modeled are important and will be separately pro led. For simplicity, we would care about ow of data, control, and coordination. The organizations may represent one or more parent institutions that govern its normative patterns of behavior and we will include distinct pro les for them. Broadly speaking, functioning of an NOP can be objective- (i.e., charter-) driven or pattern driven. Charter-based organizations seek to achieve speci c goal(s) such as solving speci c problems whereas pattern oriented organizations seek to maintain a state such as a ight formation pattern. Either of these organization types could be captured in the governance component/pro le of the NOP. At this very high level, we summarize an NOP in De nition 2 followed by subsequent description of each component.
Definition 2. An NOP is a conceptualized tuple consisting of h networks-pro les, agents-pro les, problems-pro les, governance-pro les, institutions-pro les i.
Pro les in De nition 2 are key concepts in characterizing
the NOP{i.e., the paradigm de nes speci c NO as pro les
change [
The network pro le is a graph of nodes (i.e., individuals) and links among them. The number of links will change as a result of not complete graph. The links might richly or thinly capture ties among individuals because they are most likely to be assessed when a mutual event occurs.
Definition 3. A network pro le is presented in a tuple hN ; Resource; Pi, where
N is a set of agents' pro les who are members of an NO.
Resource is the available resources that an NO provides to the agents in order to achieve an organizational charter that is C.
P is a set of protocols to govern the activity of an NO that includes norms, rules, and roles.
Since the entire network pro le might be far larger than an NO, members of an NO are required to possess pro les. Each agent will have a public pro le that contains all pertinent agent attributes including their allegiances with respect to an NO, capabilities, tness etc. to be compared with other agents. This agent's pro le is presented in De nition 4.
Definition 4. Each agent pro le, i 2 fN g, is a tuple of hA~i; Sk~iill; Relation; f~iit; Prieference; Aautonomyi.
i ~ i The agent i allegiance to all things it cares about is presented in A.
Skill is a set of skills that agent i has. It includes the capacity of the agent to handle tasks.
Relation is the agent i's relations with other agents or organizations. fit is the set of initial tness values for di erent types of tasks based on previous experiences.
Preference is a set of agent i's preferences for certain activities.
Aautonomy is the agent's autonomy-level at which it can perform tasks independent from other agents.
There are many reasons that compel agents to connect with each other. The most pertinent reason for our formulation is to gather in an NO in order to solve a common problem. The problem can be large or small based on the goal that agents aim to achieve. Each distinct goal will correspond to a distinct associated problem pro le that is used in selecting best- t agents to perform certain tasks. A problem pro le must contain task decomposition detail that provide task precedence and coordination requirements. With enough problem details, a plan can be retrieved from storage of prior plans. If no plans match, a new plan is conceived. Most often, problems will have corresponding plans that will be retrieved from a case history. When assuming that we have x set of problems and i 2 fxg, problem i will have its own problem pro le presented in De nition 5.
Definition 5. A problem pro le, i 2 fxg, is considered a tuple of hControl; Coord~ination; Gi; Precedence; Independencei, where
Control stands for controlling participants and available positions (i.e., roles).
Coordination is a set of coordination rules for each agent or an agent group based on an agent pro le for a possible assignment.
Gi is the goal that the problem pro le i exists to point out, which includes a set of tasks and set of plans that should be followed to achieve this goal. More details about G are presented in an upcoming de nition.
Precedence is the precedence of the problem domain comparing with others (i.e., the priority level of this problem to be addressed next, must be lesser or equal to 1, where 1 is the highest priority.) Independence stands for the independence of Gi in the problem-pro le from other competing goals that can be executed at the same time.
The goal G in the problem pro le is generated through the governance pro le of an NOP. Each goal generated will have di erent parameters presented in De nition 6 fxg, there is a tuple: hPlan; IE; EE; ; ~; p~erf i, where Definition 6. For Every goal Gi 2 fGg ! C where i 2 Plan is a set of plan(s) needed for the Gi to be achieved. It will be described in detail later on.
IE is the set of internal events that is a set of planned status to be achieved.
EE is the set of external events that a giving NO generates reactions based upon in order to address certain IE.
is the mapping function to perceive the relevance of 8eei ! iej, where eei is the ith external event of the set EE and iej is the jth internal event of the set IE. It helps an NO to decide on which reaction it should perform as a result of a certain outside action.
is a set of tasks agents need to handle for executing a plan, which is a set of h 1; 2; : : : ; mi, where m is a unique independent number of tasks. Each task will have its own pro le presented next. perf is an optimal performance threshold for each 2 ~. If, at a certain time, performance is lower than these expected performances, the agents can be evaluated and reassigned.
The comparison of perf with an actual task's performancelevel is used for two purposes: (a) it allows agents to report problems that they may face as well as (b) it allows assignment and in some cases reassignment. perf does not only depends on the type of task but also on the problem pro le provided, the plan to achieve them as well as the agent's level of tness.
Definition 7. Each task m 2 f g has a tuple of hPrecedence; Independence; MinFitness; currenti, where
Precedence is the temporal order of this task among all other tasks in the next set of tasks to be assigned to agents.
Independence is to indicate that the task can be achieved alone without any other requirement of prior tasks or in overlapping task completions.
MinFitness is the minimum tness value required from an agent for this task to be achieved. It will include minimum values from agent's skills and autonomy-level. current is the current task performance measure to be compared with the optimal performance (i.e., perf ) presented in the goal pro le.
In general, we consider a plan to be an and-or graph of
tasks. Naturally, mutually dependent tasks and tasks with
overlapping durations will not be independent. There are
di erent types of tasks that need to be speci ed before a
task is assigned; most importantly, the task independence
from other tasks as mentioned in the task pro le. On the
one hand, the independence of one task from others means it
does not require a prior task completion in order to complete
the current task as well as parallel achievement. This type of
tasks is assigned immediately to agents and does not require
any further classi cation or evaluation. On the other hand,
some tasks are dependent about their completion on
completion of other tasks or to be completed in parallel with
others. In such a scenario where dependence matters, we
check the performance of the agents continuously to make
sure that they are performing tasks in the expected order.
For parallel tasks assigned to three or more agents or in a
diffusion of a task to more than two agents, we will constantly
check for the network balance [
The governance pro le includes the objectives of an NO
(i.e., the organizational charters) aw well as patterns of
which those organizational charters can be achieved. It does
not interfere with both agents and problem pro les, and it
governs the network pro le. Other possible control are
inherited form other institutions trough possibly norms [
Definition 8. A governance pro le is a tuple of hC; Pattern; F ; Au; Operf i, where
C is the organizational charter adapted from the network to generate goals presented by di erent problem domains.
Pattern stands for the pattern of connecting problempro les provided to satisfy the global charter.
F is a set of tness functions for the whole NO to help in evaluating its functioning over time to make sure it follows in a proper direction.
Au is the autonomy level of an NO, where with the higher level of autonomy, the more independently the NO operates. It is self-declared and not externally determined.
Operf is an optimal organizational performance to be compared with the current performance to measure the NO progress.
As has been mentioned before, an NO lives on a network that is often far larger than its scope and there may exist one or more institutional pro le within that network environment. The network will have its own regime and control; as well institutions will provide their speci c norms, rules and roles. Common protocols will be inherited directly from the institutional pro le. However, when there is a contradiction in protocols between the institutions and network, NO will most likely stay neutral or might follow the institution's protocols for the worst-case scenario. Abstract de nition of institution is presented in De nition 9.
Definition 9. A institution pro le is a tuple of hCharter; Pattern; Regulationi, where
Charter is much bigger than C of NO to give a general idea of the institution.
Pattern is the way to link di erent NOs.
Regulation are partially inherited from the network to include a set of roles, rule, and norm that is most likely inherited by its NOs.
An NOP is intended to be a generic, meta-model that outlines prototypical NO instantiations. As such, NOP is not a direct recipe to be applied just as a set of architectural principles does not directly yield artifacts. In a later section, we describe an NOP functions via processes that connect its components in a running NO. Section 3 will focus on studying in details one type of network e ect that exists among agent living on network and helps in improving their performances and the global NO performance.
In any organization of networked agents, such as an NO,
there is a level of inter-agent compatibility in which the
agents can work together e ectively. Such a measure will
a ect the agents' performances and, as a result, the global
output of an NO. As long as there are continual interactions
between the agents inside the NO, we describe these levels as
synergy [
Synergy has a huge impact on organizational performance as a whole as well as on the agents' performances. In an NO, the current synergies are derived from the network-pro le and modi ed or controlled through the governance-pro le. The network pro le will provide a list of the agents' pro les that contains their relations with others inside and outside the NO. The synergy contribution of an agent is of a value of \0" when he rst joins an NO; then, it is derived from his relationships with others. In order to fully understand the way we derive synergy, we will describe relations in the agent pro le next. 3.1
When a group of agents form a small world to work on a
certain problem pro le, the value of their relations have a
huge impact on the formation as well as the coordination in
this world [
In order to model dynamic values of relations, we capture relations in a goal-based graph. As we described previously in the problem-pro le, there are di erent goals fGg provided by di erent problems-pro les, and each Gi 2 fGg for a problem i is equivalent to a set of tasks h 1; 2; : : : ; mi that need to be achieved in order for the Gi to be completed. The coordination and control of those goals are also provided by the problem pro le, which is generally based on the network-pro le and the agents-pro les. During task achievement, values of agent's relations ebb and ow depending on nature of interactions that forms links (i.e., edges) among them. The continual changes in inter-agent connections will be used in detailing synergies.
A sociograph, as a part of the network-pro le, will be build
upon the contributing agents' pro les in order to model
interactions among agents in each task assigned. The agents
will be presented with a node and the edges are based on
their provided relations in their pro les. Other parameters
in the problem-pro le will have an e ect on the total value
and shape of the graph. By the generic assembly, the
sociograph is not active. However, when agents start to
interact over existing but not active edges, they form an active
edge through successive interaction. There are two di erent
types of interactions: (a) explicit a nities when two or more
agents have interactions with whom they have previous
experiences over an existing edge in the graph (i.e., the edges
of a graph is build upon original relations provided by the
agents-pro les). (b) Implicit a nities are the interactions
in between two agents without any previous experience
between them [
Based on the di erent structural con guration of the agents'
coordination, the interactions of a triad can be either
mutual, directed one way, directed in reverse, or null. The
classi cation of these interactions is based on the MAN
labeling introduced in [
In a network environment, con uence of individual actions
and decisions often yield collective and residual rewards for
the network that would not exist had the individuals not
been active members of the network. These rewards are post
mortem markers of successful interaction in the network.
Although we may not be able to quantify how well a network
functions during task performance, we can observe the
results from time to time whenever rewards are witnessed. The
degree of successful interaction is called synergy [
Syi!nejrgy = Beni!j + Benj!i (1) where i and j 2 N By the time an entire group bene ts from an individual action, we call that generalized benevolence. Degree of i's contribution to group g 2 fN g is denoted by GBeni!g. When a group appreciates i's benevolence, we consider the proportional appreciation of benevolence to be a synergy between i and group g. Appreciation can be measured by the importance of an group g bestows to the individual i denoted by importancei and synergy is shown in Equation 2.
Syi!negrgy = GBeni!g
where i is an agent belongs to fgg (2) fN g An important property of collaboration is timely and bene cial contribution of actions. When an individual recognizes a speci c opportunity for a timely and signi cant action by i for another individual agent j, we capture that in complementary collaboration denoted by CCj!i. Whereas benevolence is a general o ering of helpful action toward another, complementary collaborative action is much more directed and appreciated by the recipient since it is a response to a speci c opportunity (i.e. a need ful lled by the recipient). Similar to benevolence, synergy is generated when it is reciprocated.
Syi!nejrgy = CCi!j + CCj!i (3) where i and j 2 fN g A variation of complementary action is general complementary collaboration (denoted by GCCi!g) when i's action bene ts a group g 2 fN g. With group appreciation measured by the importance value we derive a measure of synergy captured in Equation 4.
Syi!negrgy = GCCi!g
where i is an agent belongs to fgg (4) fN g
To this end, it becomes clear that the value of synergy is proportional the contributor capability and relation toward another or toward a group. It is one of the major e ects of the network in an NO that determine its performance and productivity for that the previous possibilities of measures are not exhaustive.
After the NO parameters (i.e., pro les) have been determined, an NO will begin functioning by the processes where the NO will e ectively achieve problems or produce desired patterns. We focus on synergy as a predominant form of network e ect that changes performances. This change can be at the level of individuals or groups. We will brie y outline network e ects at these two levels. However, we postpone detailed discussions of processes to a latter part of this section. Figure 1 depicts a simpli ed sketch of ow in the problem pro le, as prescribed earlier in this paper.
At the individual level, process f4 (see Figure 1) will continually monitor task performances and reassign tasks to each agent as needed. In part, an agent's performance is determined by its synergy with others (i.e., a network effect). Reassignments will attempt to augment synergies over a task. I.e., positive network e ects will increase task performance. At the group level, process f5 will monitor progress on the current goal and plan in order to remedy problems with low performance on goals and plans. By initiating the process of goal re-assignment, NO will strive to increase network e ect on goal performance. By initiating proper problem selection, NO will strive to fortify network e ects on problems.
In an NO, the problem pro les are provided through the governance pro le. Problem pro les are mainly generated to focus on the organizational charter whereas other problems are based on a perception of an external event that requires NO attention. The governance-pro le will generate a set of goals. Each goal will have its own pro le that shows its priority among others in the set. This set should be updated continuously in order to prioritize the set before assignment. Thus, the use of f1 is not only to generate a set of goals that partly satis es the charter, it will also update this set for new generated goals, as presented in the Algorithm 1.
The governance process does not stop unless the completed goals largely satisfy the NO charter. After it generates a set of goals based on the available parameters of the NO, the problem-pro le will follow the traditional steps of planning (or selecting a prior plan) for each goal. Those goals will go through the planning phase based on the priority levels assigned to them by the generator function in the governance module. In majority of cases, the problempro le will use a case based script f2 to match and assign a plan or play. f2 may generate a plan based on the exiting agents' pro les as start up for the NO. Then, it will store them in the plan database for future reference. When a similar new goal is needed to be assigned, f2 will invoke similar a plan that has been assigned to similar previous goals and match the new goal with a best- t plan.
When the agents work on a goal, they form synergy from f ∗ 4
Given a C and Pattern of an NO from the governance pro le;
Let i be a random G 2= fGng; while C is not satis ed do
C feeg ! fGg if fGng = null then
Let Gi = fGng; else if Gi 2 fGng then
exit; end end end for i : 1 ! n do
MergeSort Gi based on a priority level in fGng; end Algorithm 1: The process of generating and prioritize goals the assortment of di erent tasks that they collaborate with each other in order to achieve. Employing those synergies will enrich the NO structure and connectively, which in turn will improve the total performance of NO. However, those synergies are not preserved and will immediately be lost by the time agents complete their current goal or depart from one goal to another. This is remedied when agents' pro les are updated continually in order to take into consideration the new formed values of synergies. As well, an NO will use the formed network of synergies to improve its performance.
After a plan has been set up for execution, f3 will assign tasks while taking into consideration agents' pro les. The process of f3 is presented in Algorithm 2. When a task has low performance, f4 is used to reassign tasks for other agents based on their level-of- tness (i.e., fit). The task will have low performance when the comparison of its performance (i.e., current) with expected performance presented in goal pro le (i.e., perf ) is low on the case based threshold (i.e., ). The status of an NO is reported through triggers. The reassignment of tasks/roles using f4 is triggered through t1. The trigger t1 will make sure that the condition ti1 : ciurrent < pierf is satis ed before reassignment (i.e., the current performance is not less than the expected once). The performance of an NO is formed through di erent stages of process. This initial performance is a domain related and can be represented in a scale of \0" as a minimum to \100" for the maximum. Using those initial performances, an agent's performance at a time interval for a random task m 2 f g is measured through Equation 5.
Perf ( m; + 1) = jNj jNj X Perf ( m; ) + X Synergy( m; ) (5) i;i0 i;i0 where i; i0 2 fN g, m 2 f g, and is a time interval.
In the case of dependent task or task assignment to more
than two agents, f4 will use balance theory in order to
examine the balance of those agents' network. The balance
of the network is the percentage of the number of balanced
cycles over number of existing cycles [
Data: TaskAssignment for assigning tasks to agents
Given agents' pro les that include Skill, Preferences and Autonomy;
Given a set of tasks Precedence and Independence; Let i be a random agent 2 fN g;
Let j be a task 2 f mg that is ready to be assigned; for j : 1 ! m do
StateOfTask j; for i : 1 ! jN j do if j 2 fPrieferenceg then fiit = Scale of(Skiill + Aiutonomy); if fiit MinFitness( j) then
Assign: j ! i;
. Refer to Algorithm 3 end end end end
Algorithm 2: TaskAssignment for agents
By the time the plan is complete and tasks need to be assigned, di erent types of tasks have di erent priority and independency levels that, in result, take more time for agents to complete them. The StateOfTask is a simple comparison function that covers tasks' Precedence and Independence and sort them for assignment. This function is used to examine the process of assigning di erent types of tasks, presented in Algorithm 3.
In Algorithm 3, the \Sort" function applies a traditional sorting style to prioritize tasks based on their precedences. The functions \End" and \Start" are for the time intervals for each task that are used to make sure there are no overlapping in tasks achievements when assigning them. Algorithms 2 and 3 are complimentary to each other, and the functions, \TaskAssignment" and \StateOfTask" help to easily navigate between them.
The problem pro le should be informed about the status of the goal assigned. When the tasks/roles have di culties even after the reassignment, t2 will trigger f5 to report the current status and ask for possible change in the current plan. In a case where the goal is taking longer than expected, f5 is used to update the status and to see if an extra time can be allowed for this tasks to be completed or assign a di erent plan. For the possibility of a goal failure, f5 will add the goal to OLDGoal set, and f2 is required to perform the comparisons of the priorities between the two goal sets and assign the goal with the highest priority. Each goal will have a history added to its pro le so that when f2 tries to nd a plan for a previously assigned goal, it will avoid using a similar plan as assigned before and entering into an in nite loop. f5 will also inform the problem pro le when the goal has been achieved.
Di erent tasks will have di erent performance levels. The cumulative value of those task performances present the performance values of the goal, which is also calculated through f5 , helps in evaluating the process of the goal assigned. The performance of each goal is determined using Equation 6.
Assume a level of Precedence of f0; 1:0g, where 1:0 is the optimal precedence of a task to have the highest priority among others and 0 for the complete opposite;
Assume another scale of Independence of f0; 1:0g, where 1:0 for a complete independence of one task to be achieved independently from others and 0 for a total dependent on others; if Precedence = 1.0 then if Independence = 1.0 then
TasksAssignment j; . Refer to Algorithm 2 else if Independence =1.0 then
Sortf g; TasksAssignment j; while count : 1 ! j do if End( count) Start( j) then
TasksAssignment count; end count + +; end TasksAssignment j; Sortf g; for count : 1 ! j do if End( count) Start( j) then
TasksAssignment count; end count + +; end
TasksAssignment j; else end else end end Algorithm 3: StateOfTask based on tasks pro les Giperf = m1 X Perf ( m) m (6) where i is the problem pro le and 8m 2 f g f5 will compare the current value of tasks performance with the optimal performance showing the goal pro le, and report it to the problem pro le. The status of completion or failure of a goal are reported to the NO through outside triggers that are out of the scope in this paper.
When the current performance passes the threshold of
the minimum performance, we can consider the
organization productive. Thus, the improvement in the performance
will improve the productivity of an NO. Synergy helps in
improving NO productivity since it improves the
performance of the goals through existing network e ects among
its agents. Low productivity level forces an NO to adopt or
plastically transform with di erent pattern to perform
better, which may require an update to all NO pro les. The
plastic transformation of an NO,addressed in [
An NO can be a small team of two or more agents working on a common, quick goal that is possibly faster than human perceptual threshold (e.g., aerial coordination at high speeds) or a large collection of agents made up of thousands of people (i.e., possibly swarms) working on long term objectives that are possibly beyond a single human's cognitive capacity (e.g., detecting climate change). I have brie y introduced a paradigm to best model organizations dwelling on socially connected networks. This paradigm is a collection of principles, layouts, and interaction protocols that obviate the network nature of group activity as an organization. The salient properties that set an NOP apart from other organizational paradigms are: a. Openness, b. Evolving structure, c. Sel sh allegiances and community social power, and d. Impromptu network topology.
Given the volatility of networks, an NOP will allow for rapid depiction and analysis of emerging and evolving networked organizations witnessed in our connected world. An NOP has introduced modular components capturing essential units to be modularly combined to de ne NOs. An NOP replicates many properties and features of virtual working groups. A speci c salient phenomenon is how working together in networks a ects their individual as well as collective productivities. Synergy is one of the main types of network e ects featured in our paradigm to enhanced performance of agents and the organization.
Our plans include analyses of naturally occurring network
organizations that illustrate principles indicated in our
proposed paradigm as well as designs for novel applications
that illustrate exibility of our modular paradigm. We have
shown by a case study that the NO paradigm is
applicable for modeling real world organizations [