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.

*0p*1

*0p

p

Likewise, the replicated dynamic equation of the tech-

nology users group is:

cc

u

d1

d

qqCDp D

t

1

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

*

q11q

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.

*

q

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:

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