Information flows, embedded Information flows, embedded coordination, and competence coordination, and competence

building networks: an explorative building networks: an explorative modelmodel

Leonardo Bargigli, Mauro LombardiLeonardo Bargigli, Mauro Lombardi

Department of Economics, University of FlorenceDepartment of Economics, University of Florence

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Starting-pointsStarting-points

The co-evolution of technology and organizational The co-evolution of technology and organizational patterns (e. g. modularity and modular networks): patterns (e. g. modularity and modular networks): emerging patterns and co-ordination mechanismsemerging patterns and co-ordination mechanisms

Exploration strategies of economic units within a Exploration strategies of economic units within a phase-space which exceeds agents’ foresight phase-space which exceeds agents’ foresight possibilities (“walking on rugged landscapes”)possibilities (“walking on rugged landscapes”)

Towards an evolutionary theory of production:Towards an evolutionary theory of production:• Micro-diversity Micro-diversity versus versus the “representative agent” the “representative agent”

paradigmparadigm• Structural change Structural change versus versus growthgrowth• Quality preservation Quality preservation versusversus quantity reduction quantity reduction

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Basic conceptsBasic concepts

Economy as chemistry: endogenous structural Economy as chemistry: endogenous structural change is the normchange is the norm

Production cycle as an evolving sequence of phasesProduction cycle as an evolving sequence of phases Dynamic creation and exchange of information Dynamic creation and exchange of information

and knowledge as a metaphorical “glue” between and knowledge as a metaphorical “glue” between economic agentseconomic agents

Production as a multi-layered and multi-agent Production as a multi-layered and multi-agent problem solving activity within a problem solving activity within a multiple search multiple search space space

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Micro- and Macro-diversity with constraintsMicro- and Macro-diversity with constraints

Population of competing rules within the design Population of competing rules within the design space of a product space of a product

Product development is the exploration of a Product development is the exploration of a combinatorial space generated integrating combinatorial space generated integrating heterogeneous information packages in the phase heterogeneous information packages in the phase space of production sequencesspace of production sequences

Different combinations must be tested in order to Different combinations must be tested in order to match sub-component specifications, product match sub-component specifications, product parameters and demand requirementsparameters and demand requirements

Evolutionary emergence of constraints on admissible Evolutionary emergence of constraints on admissible rules (technological regime) [multiple selection rules (technological regime) [multiple selection enviroment]enviroment]

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The evolving dynamics of productionThe evolving dynamics of production

The decomposition and recomposition of phases and The decomposition and recomposition of phases and sub-phases: how activities of physical transformation sub-phases: how activities of physical transformation and information processing are combined and and information processing are combined and distributeddistributed

that isthat is How rules are combined How rules are combined Grouping rules for phases: routinesGrouping rules for phases: routines Grouping routines: modules and hierarchiesGrouping routines: modules and hierarchies Mapping routines and modules onto economic agentsMapping routines and modules onto economic agents

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A world of symmetryA world of symmetry

Molecular production cycle: n self-contained and homogeneous entities

Rules and routines are individually embedded No hierarchy, no evolving modules Limited degree of variability: they absorb

random shocks and bouncing environmental signals (technology, market)

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Breaking the symmetry

Technological discontinuities, market radical Technological discontinuities, market radical changes, producing rugged landscapes,changes, producing rugged landscapes,

can trigger:can trigger: Decomposition of compact sequencesDecomposition of compact sequences Multiple interactions and task divisionMultiple interactions and task division Complex exploratory activitiesComplex exploratory activities

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The broken symmetry

Cycles of repeated feedbacks emerge in P-S Cycles of repeated feedbacks emerge in P-S activitiesactivities

Networks of cycles of interactions Networks of cycles of interactions (hypercycles) (hypercycles)

Product development is the complex result of Product development is the complex result of decomposed sequences distributed over decomposed sequences distributed over dispersed unitsdispersed units

Coordination problems emerge: many Coordination problems emerge: many organizational form appear (evolving modular organizational form appear (evolving modular hierarchies)hierarchies)

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A model of production as a directed A model of production as a directed transformations’ sequencetransformations’ sequence

Focus on the “spontaneous creation” Focus on the “spontaneous creation” of production processes from routinesof production processes from routines

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ConstrainsConstrains over over TT

Inputsentry

Intermediate processes

Outputexit

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A sample set of production A sample set of production processesprocesses

•production processes of different length for the same output

• processes using different inputs and routines for the same output (redundancy)

• partially overlapping processes (degeneracy)

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Definitions & remarksDefinitions & remarks Definitions:Definitions:

• Production spaceProduction space: the set of production processes in : the set of production processes in TT• Production processProduction process: any sequence of : any sequence of t t in in TT starting with a starting with a

rrI I and ending with a and ending with a rrOO• Random PS: Random PS: PS in which PP are created through a random PS in which PP are created through a random

processprocess• Production systemProduction system: the set of units taking part to one or : the set of units taking part to one or

more PP by performing more PP by performing t t and exchancing and exchancing rr

Remarks:Remarks:• Representation of production by Representation of production by t t in in T T isis independent from independent from

the scale of observationthe scale of observation• Irreversibility is necessary (apart from physical Irreversibility is necessary (apart from physical

considerations) to maintain this independenceconsiderations) to maintain this independence• Production processes are Production processes are open open and and modularmodular

This part not considered

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Implementation of random Implementation of random production spaces (RPS)production spaces (RPS)

We start with the simplest assumption: We start with the simplest assumption: each feasible routine (i. e. the set of each feasible routine (i. e. the set of routines satisfying the constrains over routines satisfying the constrains over TT) ) has the same probability has the same probability p p to belong to to belong to T T (standard Erdos - Renyi Random Graphs)(standard Erdos - Renyi Random Graphs)

Thus Thus p p measures the “richness” of the measures the “richness” of the production space in terms of routinesproduction space in terms of routines

Two questions: Two questions: • at which conditions RPS are not empty? at which conditions RPS are not empty? • At which conditions they are saturated (i. e. all At which conditions they are saturated (i. e. all

I I and and O O are included in production processes)? are included in production processes)?

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RG definitions/1RG definitions/1 GraphGraph is the basic object of study in graph theory. is the basic object of study in graph theory.

Informally speaking, a graph is a set of objects Informally speaking, a graph is a set of objects (called points or (called points or verticesvertices) connected by links ) connected by links (called lines or (called lines or edgesedges))

Di-graphsDi-graphs (as RPS) are graphs in which edges (as RPS) are graphs in which edges have directionshave directions

RGRG are graphs or di-graphs in which edges are are graphs or di-graphs in which edges are generated by a random processgenerated by a random process

The The degreedegree of a vertex in a graph is the number of a vertex in a graph is the number of edges connected to that vertex: of edges connected to that vertex: • Degrees in Erdos-Reny RG follow the binomial Degrees in Erdos-Reny RG follow the binomial

distributiondistribution In di-graphs each vertex is characterized by an In di-graphs each vertex is characterized by an in-in-

degree degree and an and an out-degreeout-degree value value

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RG Definitions/2RG Definitions/2 A A componentcomponent in a graph is any of its connected in a graph is any of its connected

sub-graphssub-graphs A graph or sub-graph is connected when there is A graph or sub-graph is connected when there is

a a pathpath connecting each of its elements connecting each of its elements A A weak component weak component in a di-graph is any in a di-graph is any

component generated by its undirected pathscomponent generated by its undirected paths A A strong componentstrong component in a di-graph is any in a di-graph is any

component generated by its component generated by its strong connectionsstrong connections In a di-graph two vertices are strongly connected In a di-graph two vertices are strongly connected

only if there is a directed path from the first to only if there is a directed path from the first to the second and a directed path from the second the second and a directed path from the second to the firstto the first

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E-R RG main propertyE-R RG main property

E-R RG show a phase transition for E-R RG show a phase transition for increasing average degree values increasing average degree values , at , at which a which a giant componentgiant component emerges:emerges:• when when >1 the size of the largest component >1 the size of the largest component

becomes theoretically infinite, and all vertices becomes theoretically infinite, and all vertices tend to belong to it independently from graph tend to belong to it independently from graph size (Newman, 2002)size (Newman, 2002)

In di-graphs when In di-graphs when dd >1 a >1 a strong giant strong giant componentcomponent emerges emerges

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How to create RPS in practice?How to create RPS in practice?1.1. Create all the possible routines from a given set Create all the possible routines from a given set

of resources of resources 2.2. Random ordering of routines Random ordering of routines 3.3. Deletion of routines until the final RPS is obtained:Deletion of routines until the final RPS is obtained:

a)a) for each routine it is controlled if it respects the for each routine it is controlled if it respects the constrains 1, 3, 4 and 5; constrains 1, 3, 4 and 5;

b)b) if the answer is negative, the routine is deleted; if the answer is negative, the routine is deleted; c)c) if the answer is positive, a number extracted from a if the answer is positive, a number extracted from a

uniform [0,1] distribution is assigned to that routine; uniform [0,1] distribution is assigned to that routine; d)d) if that number is lower (higher) than a prefixed if that number is lower (higher) than a prefixed

probability value, the routine is included in the RPS probability value, the routine is included in the RPS (deleted); (deleted);

e)e) if the accepted routine is an intermediate one (for if the accepted routine is an intermediate one (for example rexample ri rrj), the routine r), the routine rjj rri is searched from the set is searched from the set of those already included in the RPS; f) if the routine rof those already included in the RPS; f) if the routine r jj rri is in the RPS, the routine r is in the RPS, the routine ri rrj is deleted is deleted

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RemarksRemarks The algorithm for generating RPS, though The algorithm for generating RPS, though

less efficient than standard methods used less efficient than standard methods used to generate RG, works correctly:to generate RG, works correctly:• the numbers of resulting routines is in line with the numbers of resulting routines is in line with

the theoretical ones and distributed uniformly the theoretical ones and distributed uniformly across the different “regions” in T (table 1)across the different “regions” in T (table 1)

• Phase transitions of RG (emergence of giant Phase transitions of RG (emergence of giant weak and strong components) occur according weak and strong components) occur according to the theory (table 2 and graph 1)to the theory (table 2 and graph 1)

Hence, it is possible to make inferences Hence, it is possible to make inferences on the ensemble of RPSon the ensemble of RPS from samples from samples generated by our algorithmgenerated by our algorithm

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0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1,0

0,000 0,020 0,040 0,060 0,080 0,100Alpha

Fra

ctio

n of

res

ourc

esProduction process

Weak component

Strong component

Production processes exist also when the GSC includes only a small fraction of resources (dd <1 or 1), although the fraction of empty spaces in the ensemble is not negligible

The three measures converge at a critical level of =2p0.100 (dd4)

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PP is a “looser” concept than SCPP is a “looser” concept than SC

Examples of RPS for =2p0.0

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Remarkable overlapping with emerging redundancy and degeneracy

The RPS is not saturated (4 different outputs produced on the average – table 3)

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SaturationSaturation for pfor p5% and higher values, three facts 5% and higher values, three facts

occur at the same time:occur at the same time:• the WGC includes all the resourcesthe WGC includes all the resources• the SGC includes all the intermediate the SGC includes all the intermediate

resourcesresources• all routines are embedded in production all routines are embedded in production

processes (table 3), hence the RPS is saturatedprocesses (table 3), hence the RPS is saturated Saturation can be conjectured as a third Saturation can be conjectured as a third

phase transition, specific of RPS, which phase transition, specific of RPS, which could depend from a critical value of could depend from a critical value of dd

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ConclusionsConclusions

RPS are a very flexible and general RPS are a very flexible and general representation of production:representation of production:• Scale independencyScale independency• Saturated versus unsaturated RPSSaturated versus unsaturated RPS• Simple representation of the distinction Simple representation of the distinction

between internal/external environmentbetween internal/external environment• Reconciling of cyclicity and directionality Reconciling of cyclicity and directionality

in the theory of production: economic in the theory of production: economic production is an open and cyclic set of production is an open and cyclic set of directed interlinked processesdirected interlinked processes