Evolutionary Gaming Analysis of Path Dependence in Green Construction Technology Change

doi:10.4236/ib.2012.43024

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iBusiness, 2012, 4, 193-197

http://dx.doi.org/10.4236/ib.2012.43024 Published Online September 2012 (http://www.SciRP.org/journal/ib)

193

Evolutionary Gaming Analysis of Path Dependence in

Green Construction Technology Change

Xian-Feng Zhang, Chuan-Min Shuai, Pei-Song Gong, Han Sun

School of Engineering & Management, China University of Geosciences, Wuhan, China.

Email: [email protected]

Received April 22nd, 2012; revised May 15th, 2012; accepted June 4th, 2012

ABSTRACT

In the context of instigating green construction technology by changing current technology practices, evolutionary game

theory is used to solve path dependence problems that yield stable equilibrium. Replicating dynamic gaming shows that

in inducing technological change some problems concerning multiple equilibrium definitely exist and that profit is the

prime motivation to use or supply new technology. The model also shows that a lock-in of a current technology can be

broken as a consequence of players’ studies.

Keywords: Green Construction Technology; Path Dependent; Evolutionary Game

1. Introduction

1.1. Green Construction Technology

Construction is a process of building in which materials

are transformed into products, such as buildings, airports

and highways, which unfortunately by its nature leads

inevitably to some level of environmental pollution, ex-

travagant energy consumption and resource depletion.

The process is outlined in Figure 1. Because construc-

tion is a necessary activity, the question arises as to how

to minimize its detrimental effects; green construction

technology (GCT) incorporates the right choices to

achieve this goal. GCT refers to a kind of sustainable

development technology enabling consumption of less

resource, less energy and to bring lighter environmental

pollution during the entire construction cycle [1]. Despite

its green credentials, GCT promotion has not however

been satisfactory. It has been rejected by many builders

simply because giving up old technologies is not to their

liking, perhaps due to the expense, inconvenience or dis-

ruption to business. In this paper, the problem confront-

ing construction builders given their technology options

is investigated using evolutionary game theory to analyze

the path dependence to stable equilibrium.

1.2. Brief View of Path Dependence Research

Research using path dependence analysis covers a rich

variety of fields. In 1975, Paul A. David of Stanford

University developed the concept of path dependence

within the context of technological change [2]. David,

along with colleague W. Brian Arthur [3-6], systematized

this idea of path dependence, establishing it as one of the

more valuable theories finding a rapid development

within modern economics. They considered that techno-

logical change was a system which was influenced by a

“positive feedback mechanism”, and that change has

several characteristics, which are itemized as follows: 1)

Multiple equilibrium—that is to say, the result of a de-

veloping system is not singular but has more than one

outcome; 2) Close-down—this refers to one technology

which, once adopted, employs income-increasing mecha-

nisms preventing it from being displaced by other tech-

nologies; 3) Non-efficient possibility—those locked-in

technologies having a strangle-hold within the market are

no longer the best choices; and 4) Path dependence—the

path of an evolutionary system is dependent on the sys-

tem’s original state and trajectory. Leibowitz and Mar-

golis (1990,1994) [7,8] thought that there were two

methods which can break this path dependence: either by

predicting the results from the different choices present

or by provided more communication on options before

choices are made. Unless the subject of economics is

unwilling to change, path dependence is inevitable.

2. The Asymmetric Replication Dynamic

Game Model of Technological Change on

GCT

Evolutionary gaming is based on several hypotheses

summarized as follows: 1) Players who adopted higher

revenue strategies will repeat their strategy more readily,

and therefore in the long run, the fraction of players who

adopt lower revenue strategies will decrease; 2) Players

Evolutionary Gaming Analysis of Path Dependence in Green Construction Technology Change

194

Figure 1. The impact of construction on environment, resources and energy.

may usually imitate other players’ behaviors, and posi-

tive correlations may ensue between their revenues and

their imitative tendencies; and 3) When one player chan-

ges strategy, they always treat the present situation as a

known condition, and then change to a kind of corre-

sponding best strategy.

Given the above hypotheses, an asymmetric replica-

tion dynamic game model is considered to analyze the

process of instigating change to GCT. Assuming there

are two groups of players: one group comprising the

GCT (GCTs, for instance manufacturers, which we here

denote by F (we do not know a priori whether the tech-

nology used is GCT or not); the other group comprising

the technology users, for instance consumers which we

here denote by C. We assume two techniques can be

chosen in the market. The strategies of GCTs are SF =

{S1, S2}, where S1, and S2 mean those GCTs choosing

technique 1 and technique 2, respectively. The strategy

space of the technology users is SC = {S1, S2}, where the

Si denote the same as above. For this situation we can

form a matrix game by establishing pay-offs between

random pairings of GCTs and users (see Figure 2).

Here we let A, C denote profits to be gained when sup-

pliers choose technique 1 while E, G denote the same

when technique 2 is chosen. The benefits to users are

denoted as B, D, F and H as above. In addition, we as-

sume technique 2 can gain more profit than technique 1,

that is to say, A < B, C < D.

At the start of the Game, the fraction of suppliers

adopting technique 1 is p while the difference 1 − p

represents those adopting technique 2. Similarly, the

fraction of technology users adopting technique 1 is q,

while 1 − q corresponds to those adopting technique 2.

Let uf1 be the expected revenue when the GCTS choose

technique 1 and uf2 the expected revenue of those choos-

ing technique 2. The average revenue is denoted by

User

1 S

S1 A, B C, D

GCTs

S2 E, F G, H

Figure 2. Pay-off matrix of user-supplier.

We then have the following set of consistency relations:



uqA qC



(1)



uqE q (2)





ff f

upu pu

EpqC Gpq







(3)

Similarly, revenues for the technology users satisfy a

set of like relations:



upB pD





upF pH







 

cc c

uqu qu

BFpq DHpq







From evolutionary gaming theory, we can develop the

replicated dynamic equation for both groups associated

with the two positions. This leads to the GCTS’ repli-

cated dynamic equation:



 

ppu u

ppAEqGC qFy











(4)





qBAB



, then ddpt will always be 0, that

is to say, all the p are stable. If



qBAB, then

Evolutionary Gaming Analysis of Path Dependence in Green Construction Technology Change 195

*0q

1p

and are two stable states of p, for which

is an evolutionary stable strategy. If

*1p





qBAB,

then and are still the two stable states

of p, but for which now becomes the evolution-

ary stable strategy.

*0p*1

*0p

Likewise, the replicated dynamic equation of the tech-

nology users group is:







qqCDp D

t 



qu



q



(5)

If pDCD , then dd 0pt; that is to say, all

values of p are stable. If



ppDCD , then *0q



and are two stable states of q, with

q11q



being

the evolutionary stable strategy. If





ppD CD,

then and are again two stable states of p,

with the evolutionary stable strategy. The pro-

portional change and replicator dynamics are shown in

Figure 3.

q0

*0

q1

From Figure 3, we find that this game will converge

to points (0, 0) and (1, 1). These two points correspond to

two equilibrium points: respectively, one is *0p



and

, the other and . In Figure 3, the

graph is divided into four regions by lines L1 and L2. The

analysis is as follows: 1) When the initial state falls

within the left inferior region, that is to say, the fraction

of GCTs less than

*0q*1



p*1q



DC D and the fraction of tech-

nology users less than





BAB that have changed

choice to technique 1. In this situation the Game will

eventually converge to the evolutionary stable strategy

and , and technique 1 will eventually not

be totally adopted; 2) When the initial state falls within

the right superior region, the fraction of GCTs is greater

than

*0p*0q



DC D and the fraction of technology users is

greater than



BAB, and both groups begin to

choose technique 1. As a consequence the Game will

eventually converge to the evolutionary stable strategy

and q, and technique 1 will eventually be

adopted in total; 3) When the initial state falls within

either the left superior region or the right inferior region,

the Game will converge to point (0, 0) or (1, 1). The final

*1p*1

Figure 3. The connection between proportional change and

replicator dynamics of the two types of groups.

equilibrium state is dependent on the speed that the

groups learn and adjust. When the state falls within the

left superior region and the evolution dynamics passes

through line L1 arriving at the right superior region first,

the final equilibrium will be and

*0p*0q



; in

contradistinction, if the evolution dynamics passes

through line L1 and arrives at the left inferior region first,

the final equilibrium will be and

*1p*1q



; in re-

gard to the right inferior and left superior regions, the

evolution dynamics are just mirror opposites.

By the above model analysis, we can see clearly that

different initial states will lead to different equilibrium.

At the initial stage, the probability bias in adopting one

of several techniques compels the process of technologi-

cal change or locks the process of GCT changes towards

an equilibrium point of game. Evolution has several po-

tential outcomes based on multiple equilibriums.

3. Game Analyses on Breaking Technology

Lock-In

Although the asymmetric replication dynamic game

model above explains the reason of multiple equilibrium

and tells us why subdominant option technology can be

used during technological changes, however, the model

needs to be modified to pay more attention to several real

world issues which we now present.

3.1. The Situation of New Players Joining

When a new player adopting technique 2 is added to the

original technology users group, the total population will

increase. The addition may make the proportion adopting

technique 2 exceed





BAB, which in turn makes the

group that had adopted technique 1 opt for technique 2.

Likewise, when a new exotic player opting for technique

2 is added to the original technology supplier group, and

the fraction adopting technique 2 now exceeds





DC D



the technology suppliers group that had adopted tech-

nique 1 will also convert to technique 2 with similar

consequences.

3.2. The Result on Technology Compatibility

If some compatibility between techniques 1 and 2 exists,

the revenues for both GCTs and technology users will no

longer be zero when they both choose technique 2. We

need to modify the pay-off matrix in Figure 1 to that

shown in Figure 4. Here both UI and UII are less than A,

and both UIII and UIV are less than C. We had supposed

A < B and C < D previously, so we can conclude that UI

< A < B, UII < A < B, UIII < C < D and UIV < C < D.

Here, the expected revenues when the GCTs choose

either technique 1 or technique 2 are uf1 and uf2 respec-

tively. The average revenue is denoted as

u. The con-

sistency relations become:

Evolutionary Gaming Analysis of Path Dependence in Green Construction Technology Change

196

User

1 S

S1 A, B UI, UIII

Supplier

S2 UII, UIV G, H

Figure 4. Pay-off matrix of user-supplier.

 

uqA qUAqqU I



 

2II II

uqU qBqUBq



 

III

11 1

ff f

upu pu

pqpq UpqUBq



 





The replicated dynamic equation of the GCTS group

is:



 

IIII

ppu u

pABUUqUB



 





The horizontal boundary line L1 is fixed by its q-value

(seeing as Figure 3):

 



IIII

IIII I

qBU AU BU

AUAU BU

 





  





The technology users’ expected revenues are respec-

tively:

 

1IV

upCpUCp pUIV



 

2 IIIIII

upU qDdpUDp 



 

IV III

11 1

fcc

Uqu qu

Cpqq pUqpUDp



 







The replicated dynamic equation of technology users

group is:



III IVIV

qqu u

qqCDUUpUD





 

,





While the vertical boundary line L2 is determined by

the p-value (seeing as Figure 3):











IVIII IV

III III IV

pDUCU DU

CUCU DU



 





 







Clearly the more incompatible techniques 1 and 2 are,

the closer the GCTs’ profit UII is to A when suppliers

choose technique 2, and the closer the technology users’

profit UIII is to C when technique 2 is chosen.

3.3. The Breaking Mechanism

In a real world environment, every player will be gaming

with neighbors or with a correlative group. We build a

local interactive game model to examine this behavior

(as indicated in Figure 5). This model represents an ap-

plication of iterative game theory and the evolution

strategies of a few rational players. In this model, we

suppose there are five players, and in every period play-

ers will game with neighbors or with a correlative group.

This can be represented graphically by placing identify-

ing marks say numbered stars, one for each player (see

Figure 5) on a circle with each player gaming repeatedly

only with their neighbors.

Because players are assumed to be “bounded rational”,

each player in the first game will either adopt technique 1

or 2. Assume at time t, players’ strategies are (T1, T1, T1,

T1, T2). That is to say, players 1 through 4 will choose

technique 1 while player 5 will choose technique 2. All

single players will adjust their strategy simply, and this

decision is based on the strategy distribution which is

given by the players’ neighbors. If both neighbors choose

technique T1 (or T2), it is to the advantage of player i to

follow suit in the next period. If the neighbors’ strategy

distribution is (1/2, 1/2) from the previous period, player

i will choose T2 in the next period because the average

revenue of T1 is A/2, which is lower than the T2 average

revenue of B/2. Obviously, in period (t + 1), the players’

strategy distribution from period t becomes (T2, T1, T1, T2,

T1). Similarly, we learn that the players’ strategy distri-

bution becomes (T1, T2, T2, T1, T2) in period (t + 2), and

(T1, T2, T2, T1, T2) in periods (t + 3) and (t + 4). This

shows that although almost all players have chosen a

non-superior technology at period t, a better technology

will finally obtain advantaged status among all players

interacting with each other via nearest neighbors (as in-

dicated in Figure 6).

Combinatorially, we see in Figure 5 that players have

two options of either T1 or T2, so there are 25 = 32 con-

figurations possible in total for the first Game. It is easy

to prove that if, in Figure 5, there is at least player

choosing technique 2, the Game evolves to the final state

where all players will ultimately have chosen technique 2.

When the initial game distribution is (T1, T1, T1, T1, T1),

this situation is not always stable. Once one player has

chosen another technique and in a sense betrayed the

others in seeking more profit, players will within a finite

Figure 5. The game of player with neighbors or with cor-

relative group.

Evolutionary Gaming Analysis of Path Dependence in Green Construction Technology Change

197

Figure 6. GCT strategic distributions.

REFERENCES

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ploying the better technology. According to this theo-

retical analysis, all non-superior technologies will ulti-

mately be replaced by the more efficient technologies.

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4. Conclusions

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1) The model presented shows that, in instigating a

process of technological change, several problems in

regarding to multiple equilibriums definitely exist. In

competition, the final result of the dynamic evolution is

that one of several techniques either occupied the market

totally or has no market share. Which of the techniques

will dominate is however hard to predict as the results of

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of subdominant optional technology is unstable under

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[7] S. Leibowitz and S. Margolis, “The Fable of the Keys,”

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