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Agent based modelling of technological diffusion and

network influence

May 14, 2013

Martino Tran, D.Phil.(Oxon)

Senior Researcher, Environmental Change Institute, University of Oxford

1

Outline

Outline

1. Study motivation

2. Analytical framework & model description

3. Sample results (agent & systems behaviour)

4. Discussion & next steps

2

Techno-behavioural dynamic framework

4. Techno-behavioural

Dynamics

• Strategic decision-making and

adoption behaviour as a

mechanism for behavioural

change.

• Technology performance and

behaviour as co-evolving

coupled dynamical system.

3. Behavioural change

• Focuses on changing individual

behaviours and lifestyles

(consumption, practices , norms)

• Partly reactionary to the

conventional focus on

technological solutions without

social context.

1. Status Quo

• Extrapolation of current macro

and micro level trends in demand

and supply.

• Conservative policy deployment

leading to incremental change.

2. Technological-optimism

• Radical departure from current

trends led by accelerated

technological diffusion

• Backed by government and

industry investment.

Demand Low

Supply

High

Supply

Low

Demand High

3

Implementing the approach – general model description

Agent Behaviour

A = ƒ (P, N, Ψ)

Technology

Change

T = ƒ (Ω, λT, X)

Decision

Analysis

P = ƒ(X, β, N)

Network

Influence

N = ƒ (Q, K)

System Behaviour

S = ƒ (Φ, λ, T, P)

4

Conventional technology diffusion models – mean field approaches

𝑑𝑃(𝑡)

𝑑𝑡 = αP(t) (1 –

𝑃(𝑡)

𝐾 )

Feedback key but no other explanatory variables

d𝑛(𝑡)

d𝑡 = M− 𝑛 𝑡 p +

q

M 𝑛 𝑡 , 𝑛 0 = 0

Additional parameters important but need to disaggregate, p & q

5

Diffusion = ƒ(A, T, P, N)

ABM derivation – need to account for variation in individual behaviour and

balancing between internal and external influence

ABMs with a general binomial form*:

Prob(t) = 1 – (1 – p) * (1 – q) ^ k(t)

t(0) = no adopt

t + 1 = prob(t) > U adopt

Re-specify model to account for technology trade-off behaviour i.e. index into matrix of

options, j and influences (P, Q, K) specific to each individual, i :

Prob(t) = 1 – (1 – Pij) * (1 – Qij) ^ Kij(t)

*Source: Goldenberg & Shapira, 2009

6

= Monte Carlo simulations used for assessing unknown individual preferences (Pij )

7

Dynamic approach,

Pni θ = Lni β ƒ β θ) d β ,

+∞

−∞

Lni β = exp(β′xni)/ exp(

j

β′xni)

Accounts for heterogeneity, better approximation

Static approach,

Pni = eβ′Xni

eβ′XnjJ

j=1

HEV’s outcompete ICE’s, survey bias?

Co-evolution of technological performance and agent behaviour

• Feedback effect between technological change and agent preferences over time

• How do different feedback effects scale up to impact the larger technological system?

8

Simple assumptions made on network influence (Qij, Kij)

9

Indirect influence, Qij, based on value estimate, V of previous adopters, nk out of a local

population, n,

Qij = V(pk), pk = nk/n

Direct influence, Kij based on previous adopters out of personal contacts, wij that has

influence, yi on an individual,

Kij(t) = ∑wijyi/∑wi

Therefore the master function is,

Prob(t) = 1 – (1 – [1

R ∗ LijRr=1 (

r)]) * (1 – [nk/n]) ^ (∑wijyi/∑wi)

See Tran, 2012 for full derivation

Technology data and assumptions

Technologies Purchase

Price

(2011 USD)

Fuel Price

(USD/

160 km)

Fuel

Consumption

(L/100 km)

Performance

(Acceleration

0-100 km/hr

in seconds)

Range

(Km on 1

tank/charge)

Environment

(Annual WTW

GHG CO2-eq

emission,

metric

tonnes)

Refuelling

Availability

(%)

Petrol 16640 12.9 8.1 6.5 567 5.9 100

Diesel 20180 11.5 6.9 8.7 714 5.7 100

HEV 26155 8.45 4.7 10 862 3.9 100

PHEV 40280 7.63 4.5 12 764 4.0 30

BEV 32780 3.74 2.4 11 117 3.6 1

FC 100000 5.00 3.9 12 384 3.2 1

Sources: See Tran, M. 2012 for full references

Rewire for random and small world network influence and sensitivity analysis

Simulations P Q K

1 0.1 0.1 0.1

2 0.9 0.1 0.1

3 0.1 0.9 0.1

4 0.1 0.1 0.9

5 0.1 0.9 0.9

1

0

Captures heterogeneous behaviour, distribution and trend effects over time

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time steps

Pro

babili

ty

Petrol

Diesel

HEV

PHEV

BEV

FC

A

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time steps

Pro

babili

ty

Petrol

Diesel

HEV

PHEV

BEV

FC

B

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Time steps

Pro

babili

ty

Petrol

Diesel

HEV

PHEV

BEV

FC

C

0 5 10 15 20 25 300

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Time steps

Pro

babili

ty

Petrol

Diesel

HEV

PHEV

BEV

FC

D

A) Mass market (price, reliability), B) Early adopter (CO2 , fuel economy) C) Trade-offs (performance

vs. environment) D) Exogenous effects (refuelling infrastructure)

1

1

High variability during early phases of diffusion, better approximation to empirical evidence

Battery electric vehicle preferences: A) Mass market (price, reliability), B) Early adopter (CO2 , fuel

economy) C) Trade-offs (acceleration) D) Exogenous effects (increasing refuelling). Network effects

held constant

0 20 40 60 80 100-1

0

1

2

3

4

5

6

7

Time steps

Tota

l

y = 1.1e-006*x4 - 0.00022*x

3 + 0.014*x

2 - 0.2*x + 0.57

Data

4th degree

Norm of residuals = 6.16

A

0 20 40 60 80 1000

2

4

6

8

10

12

14

16

18

Time steps

Tota

l

y = - 4.9e-007*x4 + 8.4e-005*x

3 - 0.005*x

2

+ 0.34*x - 0.99

Data

4th degree

B


0 20 40 60 80 1000

1

2

3

4

5

6

7

8

Time steps

Tota

l

y = - 6.7e-007*x4 + 0.00014*x

3 - 0.01*x

2 + 0.34*x - 0.71

Data

4th degree

C


0 20 40 60 80 1000

5

10

15

20

25

30

Time steps

Tota

l

y = - 1.7e-007*x4 + 3.7e-005*x

3 - 0.0032*x

2 + 0.41*x - 1

Data

4th degree

D


1

2

ABM can capture a range of outcomes – more consistent with empirical evidence showing

multiple trajectories

0 5 10 15 200

500

1000

1500

2000

2500

3000

3500

Time steps

Tota

l

LNG

A

0 5 10 15 200

1

2

3

4

5

6x 10

4

Time steps

Tota

l

ELE

B

0 5 10 15 202

4

6

8

10

12

14x 10

4

Time steps

Tota

l

CNG

C

0 5 10 15 200

1

2

3

4

5x 10

5

Time steps

Tota

l

E85

D

Cumulative adoption for A) Liquefied natural gas (LNG), B) Compressed natural gas (CNG), C) Full

battery electric, D) Ethanol-85 (E85), US 1992 – 2008 (DOE, 2008)

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3

B

C

Accounting for evolving social network influence – clustering effects for indirect and

direct network influence

A) Increasing indirect influence (Q), direct influence held constant (K=0.1), low individual preference

(P=0.02) held constant

B) Assume personal contacts (K) reflect local population behaviour and exerts influence on individual

Combined influence can have non-linear effects on individual adoption

QA = 0.4 QB = 0.5 QC = 0.6 QD = 0.70

50

100

150

Tota

lA

KA = 0.4 KB = 0.5 KC = 0.6 KD = 0.70

100

200

300

400

500

600

Tota

l

AB

1

4

Sensitivity analysis on all parameters

100

101

102

103

100

101

102

103

Time steps

Tota

l

Parameters S1 S2 S3 S4

S5

P 0.1 0.9 0.1 0.1 0.1

Q 0.1 0.1 0.9 0.1 0.9

K 0.1 0.1 0.1 0.9 0.9

Cumulative

adoption

range

100 - 150 850 - 950 250 - 300 150 - 200 850 - 950

S1 = Ref, S2 = Pref, S3 = Indirect, S4 =Direct, S5 = Combined

• High variability in short term but clear diffusion pattern over longer term

• Combined network effects can have as much influence as individual preference

• Indirect influence can have greater effect than direct personal contacts (‘influence

through numbers effect’)

• Indicates a mechanism to change risk averse behaviour?

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5

Discussion and next steps

Constraints:

• Lack of network data (esp. on high investment technologies e.g. energy technologies)

Potential:

• Framework has wide ranging applications for technological and behavioural interactions

• ABM can give a distribution of possible outcomes instead of locking into single trajectories ( ‘magic

number solutions’), can deal with future uncertainty rather than prediction

• How do agents balance internal strategy/preferences (profit maximization for service provision) and

external influence (networked behaviour of competitors, changing consumer preferences, macro-

level signals e.g. investment climate, policy incentives, etc.)

• How do personal (or firm-level) networks evolve with population level behaviour (larger network of

service providers)? What is the direction and magnitude of the feedback effect?

• Can individual behaviour (habits, risk aversion, preferences, etc.) be outweighed by external network

influence over time?

• What network topologies amplify behavioural signals at the individual, local and population levels?

How does agent behaviour scale up to impact the larger system e.g. disruptive technological

change?

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Thank you!

Questions?

Contact: [email protected]

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