A Study on Photovoltaic Internet Pricing Problem under Bargaining Game
Analysis
Wu-jun Cao1, Qi Zheng1
1
Department of Management Engineering, Zhengzhou University, Zhengzhou, China
(caowujun@zzu.edu.cn, zhengqi.zq@163.com)
Abstract - As a renewable energy, PV gradually
highlights its clean, no pollution, recycling and other
advantages. However, the high costs of production makes the
prices of photovoltaic products have been high. In this paper,
under the conditions of incomplete information, it gets the
price of the two sides quote in the negotiation process, and
analyzes the conditions they conclude the transaction by
establishing a bargaining game model between grid
company and photovoltaic enterprise. So that it makes the
parties gain more interests and promotes the rapid
development of photovoltaic industry.
Keywords - Photovoltaic Enterprise, Grid Company,
Internet Pricing, Incomplete Information, Bargaining Game
I. INTRODUCTION
At present, Wind energy，hydroenergy，geothermy
and solar energy are mainly common renewable energy
resources. Solar energy is the most available renewable
energy resource of all. Compared with wind energy, solar
energy has better stability and it is affected little by
season and monsoon；Compared with hydroenergy, solar
energy has little location limitation; geothermy and
hydroenergy are the same, which have much location
limitation .At the same time, it is hard for us to find the
places where enough geothermy can generate electricity[1].
As photovoltaic power generation matures, People’s
awareness of eco-environmental protection increases. PV
power industry is stepping into a rapidly increasing stage
with policy push by government from various countries[2].
PV generation has become main way of solving the
shortage of primary energy sources. As for the industry
which has a good prospect development, the
determination of tariff price is the key factor limiting its
development.
From the overseas development situation, the
determination of PV tariff price is primarily promoted by
governmental policy [3]. Subsidy policies abroad are
classified into 3 categories: Firstly, PV installation system
is subsidized directly, such as Japan. Secondly, setting
the tariff for photovoltaic power generation.
In
Germany, they take compulsory feed-in for PV power
generation and fix feed-in tariff. Meanwhile, the tariff
price is decreased every year. They make PV power
generation enter the market by laws and regulations and
bring in the law of market economy to better play the role
of market mechanism. Thirdly, it is subsidy programs that
mixed the two support policies in the State of California,
United States. In this scenario, the investment subsidies
imposed on small and medium-sized system, system
implementation of the tariff law [4].
In China, PV industry is still in the initial stage of
development. Relevant supporting policies need
perfecting and the photovoltaic industry chain is supposed
to cultivate. The high cost of PV industry is the important
factor of the high photovoltaic electricity price[5]. High
price may lead to enterprises’ vicious competition, which
is bad for the development of PV industry. Low price may
lead to the following situations: low cost enterprises make
high prices, high cost enterprises make low prices. As a
result, it may lead to false quotation [6]. At present, the
research on photovoltaic grid price determination in the
academic is still lacking. This article attempts to establish
a Bayesian game model of Internet pricing, which is in a
fully competitive market environment, whose objection
are grid company and photovoltaic enterprises. The
results will provide the theory of reference of Internet
pricing for us.
II. ESTABLISHMENT OF BARGAINING GAME
MODEL OF PHOTOVOLTAIC ELECTRICITY PRICE
A. Descriptions of bargaining game model
PV enterprises and grid companies realize their
transaction by signing a contract. The two parties
negotiate the internet pricing with each other in order to
realize the deal[7]. In this study, suppose that supply
power q is a constant. The two parties only bargain on
internet pricing
P . We use Pv and Pe respectively
represent quotation bottom line, which plays decisive role
in its negotiation.
Bargaining game between PV enterprises and grid
companies, if Pv > Pe which means expectation from
,
grid companies on internet pricing is lower than that of
PV enterprises. At the time, both of the parties can’t
realize their deals. When Pv  Pe , the deals can be
realized. In this study, the author discusses about
bargaining game photovoltaic electricity price between
PV enterprises and grid companies.
B. Hypothesis of bargaining game model
Generally speaking, there are two basic hypothesizes.
Firstly, economic man: each party involved pursues their
own maximum benefits. Secondly, perfectly rational
hypothesis: each party involved should have full analysis
ability. In this study, we make several hypothesizes based
on the basic hypothesis. The specifics are as follows:
1) Suppose both PV enterprises and grid companies
are risk neutral whose decision rule is to maximize their
expected return.
2) PV enterprises and grid companies remained
independent of each other in the other party’s bid
expectation, and obedience to evenly distribution in the
known interval.
3) The discussion is under the environment of
perfectly competitive market. The government would not
participate.
III. BARGAINING GAME MODEL’S SOLVING
PROCESS
A. Parameter establishment
During the course of dealing, one of the party bids,
the other party can accept or refuse. If the quotation is
accepted, bargaining game would come to an end; if it is
refused, the declining party would quote once again,
while the other party chooses to accept or refuse it. They
won’t negotiate with each other until one party accepts
the other one.
In the bargaining game, So-called incomplete
information refers to PV enterprises and grid companies
don’t know each other’s expectations of feed-in tariff.
Pv and Pe are personal information. PV enterprises
judge Pe is obedience to evenly distribution in [m,n];
Grid companies judge
Pv is obedience to evenly
distribution in [m,n].We think that both PV enterprises
and grid companies have strong learning capacity. They
continuously change their expectations according to the
other party’s quotation.
In the unlimited bargaining game, according to the
way put forward by Shaked and Sutton to solve the
problem of bargaining game, participants’ bargaining
game at any stage equals to the whole bargaining from the
first time[9]. Therefore, we can apply backward induction
to find bargaining game equilibrium.
Grid
Company
PV Enterprise
disallow, quotation P2
Grid
Company
accept
enterprises choose to accept or refuse. At the time,
revenues of the two sides would be consumed. Suppose
PV enterprises and grid companies’ consumption
coefficients are  v
 respectively, grid companies’
、 e
revenue is  e ( P2  Pe )q
。
If  e ( P2  Pe )q  0 , we can conclude that
(1)
P2  Pe
Grid companies would accept PV enterprises’ price,
its revenue is  e ( P2  Pe )q
.
PV enterprises’ quotation needs to be met the
condition that is to maximize its expectation revenue.
max[ v ( Pv  P2 )q  Pr ob( P2  Pe )
(2)
0  Pr ob( P2  Pe )]
In (2) ，  v ( Pv  P2 )q  Pr ob( P2  Pe ) is PV
enterprises’ expectation revenue when grid companies
accept P2
is PV enterprises’
, 0  Pr ob( P2  Pe )
expectation revenue when grid companies refuse P2
.
Estimated by PV enterprises, we can get:
P m
(3)
Pr ob( P  P )  2
2
e
disallow
Fig 1. Bargaining game structure in both sides
P1  m
Substitute (3) into (2), derivation of
P2 in (2), we
can get the optimal bid from PV enterprises.
P m
(4)
P2  v
2
Therefore, when grid companies accept PV
enterprises’ quotation, the revenue of grid companies and
PV enterprises respectively is:
P  m  2 Pe
(5)
Re  v
q e
2
Pv  m
Rv 
q v
2
quotation P1
accept
B. Using backward induction to solve
According to the three stages, we use backward
induction to solve:
1) When t=2, PV enterprises quote P2 , PV
(6)
2) When t=1, If grid companies at the first stage
quotation P1 makes ( Pv  P1 ) q  Pv  m q v ,that is
2
2 P1  m v
PV
enterprises
would
accept the
Pv 
2 v
,
quotation from grid companies, otherwise they would
refuse the quotation. Similarly, grid companies know PV
enterprises’ selective mode at the first bargaining stage
and revenue PV enterprises’ selective mode bring to both
sides[10]. Therefore, Grid companies’ quotation would
make P1 to maximize its expectation revenue.
max[( P1  Pe )q  Pr ob( Pv 
2 P1  m v
)
2 v
Pv  m  2 Pe
2 P  m v
q e  Pr ob( Pv  1
)
2
2 v
When   2( n  Pe ) , grid company and PV
v
nm
(7)
grid company. Contract would be finally written when
 Pr ob( P2  Pe )]
Derivation of
P1 in (7), then make it equal to 0;
2 Pe  n(2   v )  m v
(8)
P1 
4
C. Results of model solution
We can conclude from above, Nash Equilibrium of
grid companies and PV enterprises in bargaining game
are:
1) When t=1 in grid companies, they quote
2 Pe  n(2   v )  m v
P1 
4
.
2 P1  m v
Pv 
2 v
2)
When
is
met, that
2 Pe  n(2   v )  m v
Pv 
2(2   v )
is
. PV enterprises accept
the quotation p1 from grid companies, bargaining game
would come to an end. If it is not met, they continue to
bargain.
3) When t=2, grid companies estimate P6 evenly
Pv  m
[m, P1 ]
. Its quotation is P2 
2
distributed in
P2  Pe
4) When
, grid companies accept their
quotation, otherwise they refuse.
IV. RESULTS ANALYSIS
There are two Nash Equilibrium influence factor:
one is consumption coefficients  v , the other are
quotation bottom line estimates
When t=1, quotation P1
Pe and Pv
.
in grid company is rational,
because in order to avoid loss during the deal [9], it
would raise the price to realize the deal with PV
enterprise at a fairly high price. Its quotation wouldn’t be
higher than its quotation bottle line Pe .
That is
P1  Pe According to (8), we can get:
.
P1 
2 Pe  n(2   v )  m v
 Pe
4
(9)
Solving (9), we can get:
2(n  Pe )
 v 1
nm
enterprise make a deal when t=1, grid company
quotes P1  Pe , PV enterprise accepts quotation made by
(10)
If PV enterprise accepts the quotation from grid
company when t=1，then the following must be met:
2 Pe  n(2   v )  m v
(11)
n  Pv 
2(2   v )
2( n  Pe )
(12)
0  v 
nm
From （11)and （12）
，we know:
P  Pe
.
When
2(n  Pe )
  v  1 , grid company quotes
nm
Pe  n
P1  Pe , but at the time it is
, which clash
m

P

n
e
with
. Therefore, bargaining game steps into
the second stage. When t=2, PV enterprise quotes
P2 
Pv  m
2
, grid company accepts its quotation, the
contract finally written when
P 
Pv  m
2 .
2( n  Pe )
n  m , grid company and PV
When
enterprise can’t make a deal.
0  v 
V. CONCLUSION
In this study, the author establishes bargaining game
model of grid companies and PV enterprises, analyzing
the quotations and the final deal condition between the
both sides. We can make a conclusion: 1) When
2( n  Pe ) , grid company and PV enterprise make
v 
nm
a deal when t=1, grid company quotes P1  Pe ,
contract is finally written at
P  Pe . 2) When
2(n  Pe )
  v  1 , bargaining game steps into the
nm
second stage, PV enterprise quotes
P2 
Pv  m ,
2
contract is finally written at P   Pv  m . 3) When
2
2( n  Pe ) , grid company and PV enterprise
0 
v
nm
can’t make a deal.
This is a study on bargaining game of photovoltaic
electricity price under the environment of complete
competitive market. The author gains the equilibrium
solution by the model only providing the lead-in tariff
with theory analysis. It also supplies reference to
various enterprises. Moreover, with the further explore,
we develop the bargaining game between a PV power
industry and an grid company into that of two PV power
industries and an grid company or into a bargaining game
among PV equipment supply ,PV power industry and grid
company, which we will complete in the future.
ACKNOWLEDGEMENT
This work is supported by the Education
Department’s Natural Science Research Program of
Henan Province (2010A630004) and the Program for
Science & Technology Innovation Talents in Universities
of Henan Province (2011HASTIT002).
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