Iran-Pakistan-India gas pipeline--an economic analysis in a game theoretic framework.
Asghar, Zahid ; Nazuk, Ayesha
In this paper we analyse the so-called Ivan-Pakistan-India (IPI)
gas pipeline in a game theoretic framework. The paper develops models
for cooperative and non-cooperative strategies of Iran, Pakistan, and
India. It also analyses the expected profits and the prices for the
three players. The importance of IPI gas pipeline has also been
highlighted for the economic development of the each country involved in
this project. The IPI gas pipeline is called peace pipeline in the
jargon of political language. We have discussed this mainly in the
economic perspective and not as a geo-political scenario; implicit
players like the USA are not included in our model.
JEL classification: C70, C71, C72, C78, O13
Keywords: IPI Gaspipeline, Game Theory, Cooperative Strategy,
Non-cooperative Strategy
**********
Over the last four decades world economy has experienced several
wide swings in energy prices. These swings have very serious
repercussions for countries of Asian, in general, and South Asian
regions, in particular; the latter having tremendous economic potential.
Rapidly growing economies like India, China and Pakistan will face
serious energy crisis if they do not plan well for future needs. Energy
is one of the most critical inputs to several variety of production
function. And we have very limited ability to replace it by other means
in the short run, without having serious setback to our GDP.
Energy conservation is a topic that has been discussed over a long
period of time. Energy conservation is not a local issue but a global
one, affecting the strategic planning and policy making of the
governments worldwide. Energy conservation is proving as a catalyst for
globalisation and international trade of energy.
There are number of challenges for the South Asian region. Energy
is at the forefront and has not kept pace with rapid economic expansion.
This analysis is about transporting gas from Iran to Pakistan and then
possibly to India. The so called Iran-Pakistan-India (IPI) gas pipeline
has been named as peace pipeline in the jargon of political language
because this will be the most credible confidence building measure (CBM)
between India and Pakistan. Both countries have high stakes involved in
this pipeline project.
An economically viable project might suffer due to geo-political
scenario of all the three countries involved. One of the main players of
this game is United States which is aimed at isolating Iran on both
economic and political front. How US pursue its policies for this IPI
pipeline and response of two beneficiaries Pakistan and India is not
merely an economic issue but a political issue as well but we shall not
cover this aspect in our paper.
Main objective in this paper will be on economic analysis of IPI
pipeline. We shall develop different scenarios of Iranian gas export to
Pakistan and India in the presence of different strategic behaviours on
the part of each player. We shall model both cooperative and
non-cooperative behaviour of these players.
To the best of our knowledge, this is the pioneering effort of
modelling the IPI pipeline under game theoretic framework. Many
newspaper articles have been written on the IPI pipeline but no formal
effort of modelling the whole scenario under some theoretical reasoning
has been carried out.
1. INTRODUCTION
Almost three-quarters of the world's natural gas reserves are
located in the Middle East and Eurasia. Russia, Iran, and Qatar combined
accounted for about 58 percent of the world's natural gas reserves
as of January l, 2007. Iran is the second largest producer of natural
gas with its major natural gas fields at South and North Pars, Tabnak,
and Kangan-Nar. According to Oil and Gas Journal, Iran has an estimated
974 trillion cubic feet (Tcf) in proven natural gas reserves, about 15.8
percent of world's total (see Appendix-I). Of all the natural gas
fields in Iran, the most yielding one is the offshore South Pars field,
which is estimated to have 450 trillion cubic feet of natural gas
reserves accounting for about 47 percent of Iran's total natural
gas reserves [Energy Information Administration (2007)]. Since the
discovery of South Pars field, in 1990, Iran has been proposing for a
pipeline project that can transport the Iranian gas to Pakistan and
India.
The US $7.4 billion Iran-Pakistan-India (IPI) line is expected to
transport Iranian natural gas south to the Asian subcontinent, with a
proposed 1724 miles and a 5.4 Billion cubic feet (Bcf) capacity [Energy
Information Administration (2007)]. From South Pars, a pipeline will
stretch over 1,100 kilometres within Iran before entering Pakistan,
travelling through Khuzdar. One section will run through Karachi, the
main section going through Multan to the Indian border (760 kilometres),
thereafter travelling 860 kilometres to Delhi.
Pakistan and Iran signed a preliminary agreement in 1995 for the
construction of a natural gas pipeline linking Karachi with the South
Pars natural gas field. Iran and India signed an agreement for an
overland natural gas pipeline in 1993, and in 2002 Iran and Pakistan
signed an agreement on a feasibility study for such a pipeline. Iran
later proposed an extension of the pipeline into India, with Pakistan
standing to benefit from transit fees. The pipeline would supply both
countries with gas: India with 90 million cubic meters per day and
Pakistan 60 million cubic meters per day [United Press International
(2008)]. In April 2008 Pakistani president Pervez Musharraf met his
Iranian counterpart Ahmedinejad in Pakistan; among several other issues
IPI has been a main gist. It is believed that Iran and Pakistan have
resolved all issues regarding the IPI pipeline project and the final
agreement may be inked soon. During the meeting, Iranian president
Ahmedinejad stated "Pakistan and Iran are like one soul in two
bodies". In response to Pakistani proposal for allowing China to
receive gas from the IPI from Pakistan, Iran showed a positive response,
which indicates that in case the project materialises, even without
India's participation, Pakistan can still enjoy the status of a
transit country.
[FIGURE 1 OMITTED]
Pakistan has always been enthusiastic to start IPI project but
India has whether explicitly or implicitly shown reluctance to join the
project. The IPI project has been pending due to many geo-political,
geo-strategic and geo-economic factors, but concentrating on the
geo-economic ones, mainly due to the transit fee issues. Pakistan has
been demanding transit fee of US 50 cents per million British Thermal
Units (MBTU), while India wants it to be US 15 cents per MBTU.
It is interesting that other countries especially China has shown
interest in joining this IPI project. China told Pakistan that Beijing
is keen on importing 1.05 billion cubic feet of gas from Iran through
the pipeline if India does not participate in the project [Press TV 11
February (2008)]. Indian officials did not attend the last few meetings
on the pipeline, citing their problems with pricing.
Rapidly growing countries; China and India have great dependence on
energy import and it continues to be an issue of immense importance for
the sustainable growth rate of 7-9 percent for both the countries. The
question is that, how Iranian gas reaches Pakistan and India? In the
case of the former, issue of gas import from Iran is not a serious
problem because the two countries have their common borders. For India
it's an issue economic-cum geo-political. India can import Iranian
gas through Pakistan the most viable economic route but politically
fragile one given the past history of both the countries. Both countries
lack confidence in each other. Nevertheless, many assume that Pakistan
will never sabotage this project because it has its own economic
interest in form of transit fee of about $700 million per year.
Iran seems to be interested in gas exports mainly because of its
transition economy where unemployment is rising and budget deficits have
been a chronic problem. About 18 percent of the Iran's population
lives below the poverty line and unemployment rate is about 11 percent
[CIA world Factbook (2007)]. Iran has abundant resources of natural gas
and crude oil, oil and natural gas meet 40 percent and 49 percent,
respectively, of the Iran's energy demands (Energy Information
Administration). Beyond the geo-economic factor another geo-political
point of view is that Iran can make India and Pakistan, and possibly
China as its allies in the South Asian region and thus the so called
monopoly of the US, in the region, can be endangered. US has been
opposing the materialisation of the IPI project mainly because it fears
that Iran can play a vital role in South Asia once it becomes a gas
supplier for the two major countries of the region i.e., India and
Pakistan. Iran has been working to develop nuclear weapons and is
supporting international terrorism; that is what believed by the US
government. Iran has been assuring on several occasions that it is
interested in IPI pipeline for general economic development and not for
consolidating its nuclear weapons.
India is also facing energy crises that may catch momentum if not
addressed timely. Regarding natural gas, in the International Energy
Outlook 2007 (IEO) reference case, natural gas consumption in the
non-OECD countries grows more than twice as fast as in the OECD (Organisation for Economic Cooperation and Development) countries. Led
by demand in China and India, natural gas consumption in non-OECD Asia
is projected to expand by 4.6 percent per year on average from 2004 to
2030. India's natural gas consumption is projected to rise rapidly
in the midterm, growing by 6.2 percent per year on average from 2004 to
2015 [Energy Information Administration (2007)].
In economic horizon Pakistan's Interest in IPI is vivid as it
is an energy deficient country, though not as much as is India or China.
Energy consumption in Pakistan has grown significantly over the last few
decades due to a rapidly growing economy. Energy shortfall seems to be
one of the hurdles in the quest towards economic growth of Pakistan. In
its second quarterly report for fiscal year 2006, State Bank of Pakistan indicated that the energy demand-supply gap was 47 percent in 2006.
Major gas fields are very mature and supplies will decline from 2010.
Energy shortage is badly affecting the economic growth of Pakistan. It
is expected to moderate to 6.3 percent in financial year 2008 and then
pick up slightly to 6.5 percent in financial year 2009, underpinned by
consumption expenditures. These forecasts are lower than the average 7
percent growth rate of recent years, as the ongoing power and gas
shortages caused by an aging energy infrastructure, chronic
underinvestment in expansion and maintenance, and unsustainable pricing
regimes slow production and constrain domestic and foreign investment.
[Asian Development Bank (2008)].
Natural gas and oil meet 51 percent and 28 percent, respectively,
of the Pakistan's energy demand [Pakistan Energy Yearbook (2006)].
The total production of natural gas is 1.40 Trillion Cubic Feet (Tcf) at
the rate of 900Btu. If Pakistan has to decrease the energy demand-supply
gap then it has to devise its energy policy efficiently.
In the presence of such conditions, Pakistan is bound to streamline
the issue of natural gas and electricity shortage. There may be various
courses of action, while considering the gas import. Gas reserves are
not expected to meet the supply shortfall and IPI project may prove a
doorstep in converting Pakistan as economic tiger of the region.
Iran may be one of the potential exporters of natural gas to India.
India has three options to acquire natural gas from Iran (i) in the form
of LNG (liquefied natural gas), using LNG fleets through the Arabian Sea (ii) through a deep sea pipeline or (iii) through land route. The
land-based option seems quite cheaper than all other options even after
including transit fee payments to Pakistan.
2. IRAN-PAKISTAN-INDIA IN A GAME THEORETIC PERSPECTIVE
Hirschhausen, et al. (2005) has carried out an analysis, of the
transportation of Russian gas to Western Europe. Our model is different
in structure and implications than the Hirschhausen, et al. (2005)
model. Before we specify the model of the IPI gas pipeline we identify
the fundamental difference between the cooperative and noncooperative
strategy with reference to countries involved. Let
(i) p denotes the price of imported gas in Pakistan,
(ii) [p.sub.LNG] denotes the price of liquefied natural gas in
Pakistan,
(iii) x denotes the total amount of gas exported by Iran, through
IPI pipeline, to Pakistan and India,
(iv) y denotes the total amount of gas imported by Pakistan,
(v) B denotes the benefits that Pakistan will earn from the IPI
pipeline (B = [p.sub.LNG] - p),
(vi) [c.sub.I] and [c.sub.P] denote the respective constant per
unit cost of Iran and Pakistan,
(vii) y(p) denotes the gas import function for Pakistan with y(p)
[greater than or equal to] 0 and [partial derivative]y(p) / [partial
derivative]p] < 0 [for all] p [greater than or equal to] 0,
(viii) Assume that IPI pipeline is the only way of transporting
Iranian gas to Pakistan and India.
For Iran and Pakistan we define the following strategies:
* Non-Cooperative strategy: Iran and Pakistan independently
determine the export quantity (or the final price for gas) and benefits
so as to maximise their respective profits.
* Cooperative strategy: Iran and Pakistan determine the
profit-maximising amount of imported gas and share the total benefits.
Furthermore, let us denote;
* [[pi].sup.I.sub.nc](*)= (p - [c.sub.I])x as Iran's profits
for the non-cooperative strategy and [x.sup.*.sub.nc] =
[argmax.sub.x[greater than or equal to]0] {[[pi].sup.I.sub.nc] (p)} or
[p.sup.*.sub.nc] = [argmax.sub.p[greater than or equal to]0]
{[[pi].sup.I.sub.nc](p)} as solution for Iran's profit-maximisation
problem;
* [[pi].sup.p.sub.nc](*) = (B - [c.sub.p])x as Pakistan's
profits for the non-cooperative strategy and [B.sup.*.sub.nc] =
[argmax.sub.b[greater than or equal to]0] {[[pi].sup.p.sub.nc] (b)} as
solution for Pakistan's profit-maximisation problem;
= [[pi].sub.nc](*) = [[pi].sup.I.sub.nc](*) +
[[pi].sup.P.sub.nc](*) as aggregate profits of the non-cooperative
strategy
* [[pi].sub.c](*) = (p + B - [c.sub.I] - [c.sub.P])x as total
profits of the cooperative strategy and [x.sup.*.sub.c] =
[argmax.sub.x[greater than or equal to]0]{[[pi].sub.c](x)} or
[p.sup.*.sub.c] = [argmax.sub.p[greater than or equal
to]0]{[[pi].sub.c](x)} as solution for Iran's and
Pakistan's joint profit maximisation problem.
Finally. we assume that all the above profit functions are
continuous and quasiconcave (so that [x.sup.*.sub.nc], [p.sup.*.sub.nc],
[B.sup.*.sub.nc], [x.sup.*.sub.c] and [p.sup.*.sub.c] exist and are
unique).
Then using results of Hirschhausen, et al. (2005), we have,
Proposition 1: Profits of the cooperative strategy are always
greater than or equal to aggregate profits of the non-cooperative
strategy: [[pi].sub.c](*) [greater than or equal to] [[pi].sub.nc](*).
Furthermore, the transit quantity (or the gas price) is always greater
(lesser) or equal in its level in the non-cooperative strategy:
[x.sup.*.sub.c][greater than or equal to][x.sup.*.sub.nc]
([p.sup.*.sub.c] [less than or equal to][p.sup.*.sub.nc]).
Proof: For the non-cooperative strategy, maximum aggregate profits
are
[[pi].sub.nc](*) = [[pi].sup.I.sub.nc](*) + [[pi].sup.P.sub.nc](*)
= [max.sub.x[greater than or equal to]0][[pi].sub.I](x) +
[max.sub.b[greater than or equal to]0][[pi].sub.P](x) =
([p.sup.*.sub.nc] - [c.sub.I])[x.sup.*.sub.nc] + ([B.sup.*.sub.nc] -
[c.sub.P])[x.sup.*.sub.nc] = ([p.sup.*.sub.nc] - [c.sub.I] +
[B.sup.*.sub.nc] - [c.sub.P])[x.sup.*.sub.nc] or [x.sup.*.sub.nc] =
[max.sub.x[greater than or equal to]0] [[pi].sub.I](x) +
[max.sub.b[greater than or equal to]0][[pi].sub.P](x) =
([p.sup.*.sub.nc] - [c.sub.I] + [B.sup.*.sub.nc] -
[c.sub.P])[x.sup.*.sub.nc]. However, because [x.sup.*.sub.nc] (or
[p.sup.*.sub.nc]) and [B.sup.*.sub.nc] are chosen within two separate
problems, aggregate profits cannot exceed maximum profits for the
cooperative solution in which [x.sup.*.sub.c] is directly chosen to
maximise the same expression [x.sup.*.sub.c] = [argmax.sub.x[greater
than or equal to]0]{[[pi].sub.c](x)} = (p + B - [c.sub.I] -
[c.sub.P])[x.sup.*.sub.c]. Now the regularity condition of
quasi-concavity imposed on [[pi].sup.P.sub.nc](*) = (B - [c.sub.P])x
requires that ([partial derivative]x/[partial derivative]B) [less than
or equal to] 0. Thus if Pakistan gains zero benefits from the IPI
project in the cooperative strategy and shares total profits with Iran
then [[pi].sub.nc](*) cannot exceed maximum profits for the cooperative
solution. Because if [[pi].sub.nc](*) exceeds [x.sup.*.sub.c] then
[c.sub.I] > p. Hence it is proved that [x.sup.*.sub.c] [greater than
or equal to] [x.sup.*.sub.nc] or [p.sup.*.sub.c] [less than or equal to]
[p.sup.*.sub.nc].
Now we shall extend this general result to a specific situation.
1. Non-cooperative Strategy (Two Players)
Under prevailing circumstances Iranian gas can reach Pakistan
through LNG method or through a pipeline. In geo-economic aspect the
pipeline may benefit Pakistan if B > 0. Symbolically speaking, we can
say that Iran being the main supplier of gas to Pakistan, sets an export
quantity x to maximise its profits [[PI].sup.I] = (p - [c.sub.I]) x. It
is assumed that the relationship between p and x is direct, so that the
function p(x) is increasing and [partial derivative]p(x)/[partial
derivative]x < 0. It is plain to envisage that the two players Iran
and Pakistan have almost same bargaining power;
Iran is very wholehearted to start the IPI pipeline project to pace
up its collapsing economy and to defend itself against the embargoes and
trade restriction imposed by countries like United States and United
Kingdom. It also wants to develop friendly ties with two important
countries of the region i.e. Pakistan and India. India is reluctant on
their part due to the US pressure and fears of US that Iran may become a
strong country through its nuclear energy programme. Iran has to keep an
inviting tone rather than dictating one with reference to IPI pipeline
project. Pakistan is enthusiastic for IPI because of energy shortfall
that it is facing. Pakistan is also interested because of the transit
benefits and lower cost it can enjoy (when compared with prevalent LNG
prices). All in all Iran the supplier needs foreign exchanges to support
the economy. So both Iran and Pakistan do not have much bargaining power
on the IPI pipeline issue.
The First Order Condition (FOC) for Iran's profit maximisation
problem requires that the optimal price of exported gas (x) to be so as
to ensure
[partial derivative][[PI].I]/[partial derivative]p = x + (p -
[c.sub.I]) [partial derivative]x/[partial derivative]p = 0, (1)
Pakistan problem is to enjoy maximum benefits from importing x
units of gas from Iran through IPI pipeline. Since benefits of Pakistan
are portrayed by the quantity B, which is the price differential between
price of gas through IPI pipeline and price of gas otherwise (where we
have attributed LNG to be the other source). Cetris Peribus the benefits
of Pakistan will increase as the amount of gas imported increase. The
underlying mechanism is that if the price differential is [B.sub.i]
(say) for i units of import through IPI pipeline then [B.sub.i + 1]
[greater than or equal to] [B.sub.i], where [B.sub.i] is the benefits to
Pakistan on importing i units of gas from Iran through IPI pipeline. The
highest possible benefits will be earned when Pakistan imports gas from
Iran on the minimum price. But Iran will set the price not at the
minimum but at the optimum level ensuring the optimum volume of trade x.
So benefits of Pakistan are directly dependent on x that is to say B =
B(x). With this prior setup and background information, the FOC for
Pakistan is;
[partial derivative][[P].sub.P]/[partial derivative]B = x +
[partial derivative]x/[partial derivative]B (B - [c.sub.P]) = 0,
[B.sub.opt] = - x/[sigma] + [c.sub.P], where [sigma] = [partial
derivative]x/ [partial derivative]B < 0. (2)
Assume that if quantity imported/demanded by Pakistan increases,
suppliers shall offer higher prices. Therefore the gas imports function
for Pakistan, is given by
y (p) = x + [x.sub.0] = a p, (3)
where [x.sub.0] is the gas imported by Pakistan from any other
source and a > 0 is an exogenous parameter.
Using (3) and (1), we get
[p.sub.opt]([x.sub.0] + [c.sub.I] (a - [[sigma].sub.0])/2a -
[[sigma].sub.0]), [[sigma].sub.0] = [partial
derivative][x.sub.0]/[partial derivative]p < 0. (4)
This optimum price depends purely on the cost structure of the Iran
and the exogenous parameters of the gas import functions of the gas in
Pakistan. Finally using (4) as Pakistan best-response function (given in
(2)) the optimum benefits that Pakistan ought to enjoy are,
[B.sub.opt] = - 1/[sigma]([x.sub.0] + [c.sub.I] (a -
[[sigma].sub.0])/2a - [[sigma].sub.0]) + [c.sub.p], (7)
This solution is termed as non-cooperative as it does not assume
partnership between the two major players Iran and Pakistan
2. Cooperative Strategy (Two Players)
In the cooperative strategy, Iran and Pakistan jointly maximise the
aggregate profits (benefits) and then share it between themselves. It is
important that we can utilise the aggregate profit function under
non-cooperation, given by [[pi].sub.c](*) = (p + B - [c.sub.I] -
[c.sub.P])x. Simply maximising this aggregate profit function w.r.t x
will provide an estimate of the optimal quantity of gas that should be
exported by Iran to Pakistan.
However, another more formal approach is to use the Nash Product.
Let the joint profit (or benefit) be distributed among Pakistan and Iran
according to Nash bargaining criteria. For two players, the Nash product
is defined as the product of each player's profit under cooperative
environment after deduction of the profit under non-cooperative
environment.
Let [NP.sub.IP] denote the Nash product, when two players Iran and
Pakistan are considered. Then [NP.sub.IP] is given by,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (8)
If Iran and Pakistan play under cooperation then Iran's
profits are characterised by the function,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (9)
Where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the
fixed benefits offered to Pakistan by Iran, under cooperation agreement.
Since both Pakistan's and Iran's supreme interest is not
to stall the mega IPI pipeline so we assume that non-cooperation can
only occur if India remains reluctant to start the IPI pipeline. In that
case Pakistan may become the only potential customer of the Iranian gas
and then Pakistan can play a role of monopolistic customer. Similarly,
Iran can be a monopolistic supplier if Pakistan has no options of
imports other than that of Iran. Several other assumptions can be stated
before we assume monopoly of Iran and Pakistan, but we shall not go into
intricate geopolitical details of the issue.
Coming back to the identification of the profits of Iran and
Pakistan under noncooperation, we say that [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN
ASCII] are the respective profits of Iran and Pakistan. Therefore, the
Nash product in (8) can be restated as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Now, we shall seek the optimal benefits that Pakistan should gain,
to maximise the aggregate profits under joint venture (cooperation).
Maximising the Nash product in (10) w.r.t [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] yields;
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)
which implies that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)
Thus optimum benefits for Pakistan are 50 percent of the
profit-maximising surplus in the Nash product solution.
Now, incorporating the optimum benefits from (12) into the Nash
product (10), the Nash product can be restated as follows,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
Maximising (13) w.r.t p, yields the optimum selling price of gas
for Iran ( purchase price for Pakistan).
[p.sup.coop.sub.opt] = [x.sub.0] + ([c.sub.P] + [c.sub.I])(a -
[[sigma].sub.0])/ 2a - [[sigma].sub.0] (14)
This optimum price depends purely on the cost structure of the
players and the exogenous parameters of the gas import functions of the
gas in Pakistan and India. In cooperative strategy the optimum benefits
of Pakistan are independent of marginal impact of Pakistan's
benefits, whereas reverse is the case in non-cooperation. Furthermore,
as stated in proposition (1), the total benefits of the cooperative
strategy are always greater than the total benefits of the
non-cooperative strategy. Iran and Pakistan have relatively friendly
ties and Pakistan can plausibly cooperate with Iran.
3. IPI IN THREE-PLAYERS SET-UP
Now we introduce India as a third player of the mega IPI game and
develop the three players' scenario, by using following notations
Let
(i) [p.sub.PA] denotes the price of imported gas in Pakistan,
(ii) [p.sub.IN] denotes the price of imported gas in India,
(iii) [p.sub.LP] denotes the price of liquefied natural gas in
Pakistan,
(iv) [p.sub.LI] denotes the price of liquefied natural gas in
India,
(v) t denote the transit fee Pakistan may earn on transiting gas
from IPI to India,
(vi) [y.sub.PA] denote the amount of gas imported by Pakistan by
Iran,
(vii) [y.sub.IN] denote the amount of gas imported by India,
(viii) [y.sub.IO] denote the gas imported by India from sources
other than Iran,
(ix) [y.sub.PO] denote the gas imported by Pakistan from sources
other than Iran,
(x) [y.sub.tot] (= [y.sub.IN] + [y.sub.PA]) denotes the total
amount of gas exported by Iran, through IPI pipeline, to Pakistan and
India,
(xi) [B.sub.PA] denotes the benefits that Pakistan will earn from
the IPI pipeline ([B.sub.PA] = [p.sub.PA] - [p.sub.LP] + t),
(xii) [B.sub.IN] denotes the benefits that India will earn from the
IPI pipeline ([B.sub.IN] = [p.sub.IN]- [p.sub.II]),
(xiii) [c.sub.IR] and [c.sub.PA] and [c.sub.IN] denote the
respective constant per unit cost of Iran, Pakistan and India,
(xiv) [x.sub.P] denotes the demand function of Pakistan for gas
imports with [x.sub.P] [greater than or equal to] 0 and ([partial
derivative][x.sub.P]/[partial derivative]p) < 0 [for all] p [greater
than or equal to] 0, such that the inverse demand function p =
[p.sub.x] [greater than or equal to] 0 exists with ([partial
derivative][x.sub.P]/[partial derivative]p) < 0,
(xv) [x.sub.I] denotes the demand function of India for gas imports
with [x.sub.I] [greater than or equal to] 0 and ([partial
derivative][x.sub.I]/ [partial derivative]p) < 0 [for all] p [greater
than or equal to] 0, such that the inverse demand function p = [p.sub.x]
[greater than or equal to] 0 exists with ([partial
derivative][x.sub.I]/[partial derivative]p) < 0,
(xvi) Assume that IPI pipeline is the only way of transporting
Iranian gas to Pakistan and India.
For each of the three players we define the following strategies:
* Non-cooperative strategy: Iran, Pakistan and India take
independent decisions to maximise their individual profit functions.
Iran determines the final price and amount of gas that it allows to be
exported, Pakistan determines the allowable transit quantity and India
determines the quantity it imports through IPI and both Pakistan and
India set their own prices.
* Cooperative strategy: Iran, Pakistan and India determine the
joint profit-maximising values of final price, amount of gas, transit
quantity and quantity of imported gas through IPI.
Furthermore, let us denote;
* [[phi].sup.IR.sub.nc](*) = ([p.sub.PA] + [p.sub.IN] -
[c.sub.IR])[y.sub.tot] as Iran's profits for the non- cooperative
strategy and [[phi].sup.*.sub.nc] = [argmax.sub.x[greater than or equal
to]0] {[[phi].sup.IR.sub.nc](y)} or [p.sup.*.nc] = [argmax.sub.p[greater
than or equal to]0] {[[phi].sup.IR.sub.nc](p)} as solution for
Iran's profit-maximisation problem;
* [[phi].sup.PA.sub.nc](*) = ([B.sub.PA] - [c.sub.PA])[y.sub.PA] as
Pakistan's profits for the non-cooperative strategy and
[([B.sub.PA]).sup.*.sub.nc] = [argmax.sub.b[greater than or equal to]0]
{[[phi].sup.PA.sub.nc](b)} as solution for Pakistan's
profit-maximisation problem;
* [[phi].sup.IN.sub.nc](*) = ([B.sub.IN] - [c.sub.IN])[y.sub.IN] as
India's profits for the non-cooperative strategy and
[([B.sub.IN]).sup.*.sub.nc] = [argmax.sub.b[greater than or equal to]0]
{[[phi].sup.IN.sub.nc](b)} as solution for India's
profit-maximisation problem;
* [[phi].sub.nc](*) = [[phi].sup.IR.sub.nc](*) +
[[phi].sup.P.sub.nc](*) + [[phi].sup.IN.sub.nc](*) as aggregate profits
of the non-cooperative strategy
* [[phi].sub.c](*) = ([p.sub.PA] + [p.sub.IN] + [B.sub.PA] +
[B.sub.IN] - [c.sub.IR] - [c.sub.PA] - [c.sub.IN])x as total profits of
the cooperative strategy and [x.sup.*.sub.c] = [argmax.sub.x[greater
than or equal to]0] {[[phi].sub.c](x)} or [[phi].sup.*.sub.c] =
[argmax.sub.p[greater than or equal to]0] {[[phi].sub.c](x)} as solution
of for Iran's and Pakistan's joint profit maximisation
problem.
Finally, we assume that all the above profit functions are
continuous and quasiconcave.
Using Proposition 1 (stated in 3.1), in three players' setup,
the profits of the cooperative strategy will be greater than the profits
in non-cooperative strategy.
1. Non-cooperative Strategy (Three Players)
In three players setup Iran, India and Pakistan have almost equal
standings, as far as bargaining on IPI is concerned; Iran is eager to
find buyers of its gas and both India and Pakistan are amid energy
crisis. Pakistan being the transit country may have an added benefit in
the form of transit fee.
Pakistan's interest is to maximise with respect to benefits it
can gain through IPI. Pakistan wants to enjoy maximum benefits from
importing x units of gas from Iran through IPI pipeline. Since benefits
of Pakistan are portrayed by the quantity [B.sub.PA]. Cetris Peribus the
benefits of Pakistan will increase as the amount of gas imported
increase. The underlying mechanism is that if the price differential is
([B.sub.PA]) (say) for i units of import through IPI pipeline then
[([B.sub.PA]).sub.i+1] [greater than or equal to] [([B.sub.PA]).sub.i],
where [([B.sub.PA]).sub.i] is the benefits to Pakistan on importing i
units of gas from Iran through IPI pipeline. The highest possible
benefits will be earned when Pakistan imports gas from Iran on the
minimum price and maximum transit fee. Following the inverse demand
convention, Pakistan may charge a higher rate of transit fee if the
volume of gas transit to India is high. It implies that transit fee, and
consequently benefits of Pakistan, are dependent on the volume of trade
[y.sub.tot], that is to say B = B([y.sub.tot]). With this prior setup
and background information, the FOC for Pakistan is;
[partial derivative][[PHI].sub.P]/[partial derivative][B.sub.PA]/ =
[y.sub.tot] + [xi]([B.sub.P] - [c.sub.P)] = 0,
Where [xi] = [partial derivative][y.sub.tot]/[partial
derivative][B.sub.PA] < 0, then
[([B.sub.PA]).sub.opt] = - [y.sub.tot]/[xi] + [c.sub.PA] (15)
Now, concentrating on Iran's profit maximisation, profits are
supposed to be maximised with respect to the optimum prices of imported
gas in India and Pakistan, through IPI.
The Pakistan's gas import function is given by,
w = [y.sub.PA] + [y.sub.PO] = [bp.sub.PA] (16)
where b > 0.
India's gas import function is given by,
z = [y.sub.IN] + [y.sub.IO] = [cp.sub.In] (17)
where c > 0.
Maximisation of Iran's profit function w.r.t [P.sub.PA],
yields
[([P.sub.PA]).sub.opt] = [c.sub.IR](b - [[sigma].sub.1]) -
[p.sub.IN] (b + c - [[sigma].sub.1]) + [y.sub.PO] + [y.sub.IO]/2b -
[[sigma].sub.1], [[sigma].sub.1] = [partial
derivative][y.sub.PO]/[partial derivative][p.sub.PA] < 0. (18)
Substitution of (18) in Iran's profit function and then
maximising w.r.t [p.sub.IN] yields
[([p.sub.IN]).sub.opt] = -[k.sub.4]/[k.sub.3] (19)
[[sigma].sub.2] = [partial derivative][y.sub.IO]/[partial
derivative] [p.sub.IN], (19)
[k.sub.1] = [c.sub.IR](b - [[sigma].sub.1]) + [y.sub.PO] +
[y.sub.IN]/2b - [[sigma].sub.1],
[k.sub.2] = b + c -[[sigma].sub.1]/2b -[[sigma].sub.1],
[k.sub.3] = 2c - 2c[k.sub.2] - 2b[k.sub.2] + 2b[k.sup.2.sub.2] -
[[sigma].sub.2] + [[sigma].sub.2][k.sub.2],
[k.sub.4] = b[k.sub.1] - [y.sub.PO] - [y.sub.IO] -
2[k.sub.2][k.sub.1]b + [k.sub.2][y.sub.PO] + [k.sub.2][y.sub.IO] +
[k.sub.1]c - [k.sub.1][[sigma].sub.2] - [cc.sub.IR] +
b[c.sub.IR][k.sub.2] + [c.sub.IR][[sigma].sub.2].
2. Cooperative Strategy (Three Players)
Just like two players setup we use the Nash Product. Let the joint
profit (or benefit) be distributed among Iran, Pakistan and India
according to Nash bargaining criteria. Iran and Pakistan negotiate a
fixed value of transit fee for the quantity, [y.sub.IN], to be
transported to India through Pakistan. In this way benefits of Pakistan
are also fixed mutually by Iran and Pakistan.
Let [NP.sub.IPI] denote the Nash product, when three players Iran,
Pakistan and India are considered. Then [NP.sub.IPI] is given by,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (21)
Now, we shall seek the optimal benefits that Pakistan should gain,
to maximise the aggregate profits under joint venture (cooperation).
Maximising the Nash product in (21) w.r.t [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] yields;
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)
Now, incorporating the optimum benefits from (22) into Nash Product
in (21), the Nash product can be restated as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (23)
Using (16) and (17) and maximising (23) w.r.t [P.sub.IN], yields
the optimum quantity of gas exports to India.
[([p.sub.IN]).sub.opt] = [y.sub.IO] + (c -
[[sigma].sub.2])([c.sub.IN] + [c.sub.PA] + [c.sub.IR] - t(c -
[[sigma].sub.2])/c(1 - [[sigma].sub.2]). (24)
Similarly optimum value of Pea may easily be found.
It may be noted that, in a three player setup, under cooperative
strategy the optimum prices are dependent on the exogenous parameters of
the gas import functions of India and Pakistan, the cost structures of
the players and the amount of gas imported by India and Pakistan from
sources other than Iran.
4. CONCLUSIONS
We have explored the IPI gas pipeline benefits to Iran, Pakistan
and India under two different scenarios cooperation versus
non-cooperation. All three countries can enjoy economic growth and
prosperity by materialising IPI pipeline project. The whole scenario of
profit-maximisation has also been studied under three players setup. In
both the cases cooperative strategies are beneficial for all three
countries. We have ignored geo-political aspects of the project which
can be considered by some political economy student in some other paper.
One limitation in our paper is the lack of any data on the variables we
have included in our model and therefore, we have not been able to carry
out any simulation analysis of the results which would have helped
in finding out the magnitude of the benefits all the three countries
will reap. Last but not the least IPI gas pipeline project in no way
implies that Pakistan and India can afford to take risk of not exploring
other means of energy both domestic and international.
Comments
The paper on economic analysis of the IPI Gas Pipeline project by
Zahid Asghar and Ayesha Nazuk is an attempt to present the pricing
problem in the proposed scheme in a game theoretic framework. For the
problem at hand, game theory provides a suitable framework, provided the
assumptions and rules of game more or less accurately represent the
reality at least in qualitative terms.
This particular paper appears to be an informal analysis of the
problem and it seems to have been extracted from another work done by
the authors because its section headings and section numbers are
inconsistent. For example, the Section: "1.
Introduction" starts after one and half page written material
with no heading. This section is followed by section 3.1, which in turn
has further two sub headings both labeled as 3.2: "Non-cooperative
Strategy (Two Players)". The terms 'non-cooperative
strategy' and 'cooperative strategy' are inappropriate
and need to be replaced by 'non-cooperative game' and
'cooperative game'. The two main references on which the paper
is mostly based, namely Tongia (with no year mentioned) and
Hirschhausen, et al. (2005) are either missing from the list of
references or are incorrectly referred. The list of references in not
properly arranged as practiced in economics literature.
The analysis in the paper is based on the well-known proposition
that cooperative games yield at least as much total payoff for all
players combined as obtained under non-cooperative games. The solution
under non-cooperative game is only incompletely presented: For example,
Equation (5) shows solution for p conditional on x, which could be
solved for p, x and [pi] by using the demand Equation (3). Similarly
Equation (7) presents incomplete picture. No attempt is made to derive
algebraic expressions for payoffs and compare them under the two types
of games.
The paper does not spell out all behavioural assumptions of the
model. For example, the implicit assumption that Iran sets the price and
Pakistan acts as price taker can only be inferred from the algebra. It
needs to be written and justified explicitly. It is again inferred from
algebra that pricing problem is presented assuming that the gas pipeline
is already there.
Most importantly, the paper is presented as a typical textbook example to prove something quite obvious and no effort is made to
provide cost-benefit assessment in numerical terms. Even the numbers
quoted in introduction are based on newspapers reports, which cannot be
accepted in an academic work.
The paper needs a thorough revision if it is to be considered as
serious work having academic value and/or policy relevance.
Eatzaz Ahmad
Quaid-i-Azam University, Islamabad.
APPENDIX-I
Table 1
World Natural Gas Reserves by Country as of January 1, 2007
Reserves
(Trillion % of World
Producers Cubic Feet) Total
Russia 1680 27.17
Iran 974 15.75
Qatar 911 14.73
Saudi Arabia 240 3.881
UAE 214 3.461
USA 204 3.299
Nigeria 182 2.943
Algeria 162 2.620
Venezuela 152 2.458
Iraq 112 1.811
Turkmenistan 100 1.617
Kazakhstan 100 1.617
Indonesia 98 1.584
Norway 82 1.326
China 80 1.293
Malaysia 75 1.213
Uzbekistan 65 1.051
Egypt 59 0.954
Canada 58 0.938
Kuwait 55 0.889
Rest of World 581 9.396
World's Total 6183 100.00
Energy Information Administration, Report #:DOE/EIA-0484 (2007),
Release Date: May 2007.
REFERENCES
Asian Development Bank (2008) Asian Development Outlook 2008
Update. Asian Development Bank's Flagship Report.
Energy Information Administration (2007) Country Analysis
Brief-Iran.
Energy Information Administration (2007) India Energy Data,
Statistics and Analysis.
Hirschhausen, C. V. , B. Meinhart, and F. Pavel (2005) Transporting
Russian Gas to Western Europe--A Simulation Analysis. The Energy Journal
26:2.
State Bank of Pakistan (2006) Second Quarterly Report for Fiscal
Year. Karachi: State Bank of Pakistan.
United Press International (2008) India Won't Attend IPI
Meeting.
Worldwide Look at Reserves and Production (2006) Report of the Oil
and Gas Journal 104: 47, 22-23.
Zahid Asghar <g.zahid@gmail.com> is Assistant Professor,
Quaid-i-Azam University, Islamabad. Ayesha Nazuk
<ashcash1983@gmail.com> is Lecturer, Allama Iqbal Open University,
Islamabad.