european natural gas supply: cooperative game theoretic ... · shapley value: properties it always...

motivation cooperative solutions the model new pipelines

European Natural Gas Supply:

Cooperative Game Theoretic Analysis

Franz Hubert

based on joint work with

Onur Cobanli, Ekaterina Orlova

Berlin May 2015

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Motivation I

The European gas industry largely depends on supply throughpipelines.

Gas pipes: a physical network connecting producers, transitcountries, customers.

How is the power structure in this industry affected by:

the liberalization of the gas market within EU,

the investment in new pipelines like Nord Stream, SouthStream, Nabucco,

More generally: How do we measure power in a network?

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Motivation II

Cooperative game theory appears to be well suited for analyzingpower relations in such supply networks (comprehensive contracts,free format bargaining).

But it offers several solutions: Shapley Value, core, nucleolus ...

We know a lot about the abstract properties of these solutions.

We know little about their economic implications in appliedindustry studies.

CGT has been applied in voting games, cost allocation, but not IO.

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Non-cooperative approach

Players: set of players N .

Strategies: strategy space S := S1 × S2 × ..Sn with Si denotingplayer i’s strategy set.

Payoffs: u : S → R|N |, where ui(s) is player i’s payoff (utility)given strategy profile s ∈ S.

Game: the players, the strategy space and the payoff functions:Γ := {N,S, u}.

Solution: typically the Nash-equilibrium.

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Non-cooperative approach: problems

The set of Nash-equilibria is often very sensitive to the(mis)specification of the strategy space (e.g. price matching).

In supply chains, the players usually negotiate complex contracts.

Neither the contracts, nor the bargaining process is easilyconverted to the non-cooperative format.

With strong complementaries you will typically obtain a lot ofimplausible equilibria.

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Cooperative approach

Players & Coalitions: set of players N , and S set of all subsets(coalitions) of N .

Value function: v : S→ R+ such that v(S) is the maximal payoffto coalition S ⊆ N .

e.g.: v(∅), v(a) , v(b), v(c), v(a, b), v(a, c) ... v(N)

Game: is specified by the players and the value function:Γ := {N, v}.

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Solving Coalition Games

Solution: assigns a payoff xi to each player and can be interpretedas his power index.

individual rationality: no player can improve by unilaterallywithdrawing

xi ≥ v({i}) ∀i ∈ N

group rationality: nothing is wasted∑i∈N

xi = v(N),

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Shapley Value

The Shapley Value ψ of a players i is given by his weighted(marginal) contribution to all possible sub-coalitions S ⊆ N .

ψ(v) :=∑S:i 6∈S

|S|!(|N | − |S| − 1)!

|N |!· [v(S ∪ {i})− v(S)],

The weights can be motivated by random order bargaining, with allorderings having equal probability.

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Shapley Value: properties

It always exists, is unique, and it is easy to calculate — once youhave the value function.

It is the only imputation fulfilling the axioms of symmetry &dummy player property & linearity (Shapley 1953).

It is the only imputation featuring balanced contributions (Myerson1980).

It is the only imputation featuring symmetry & monotonicity(Young 1985).

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Excess

Let x be a vector of payoffs and x(S) :=∑

i∈S xi be the totalpayment to a coalition S.

For a given x, the excess of coalition S is the difference betweenwhat it can achieve alone and what it receives with x:

e(S, x) := v(S)− x(S)

The larger the excess is, the ‘worse’ is the coalition doing under x.

If the excess is positive, the the coalition has an incentive to reject(block/veto) x, because it can do better on his own (providedthere are no cost of doing so).

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Nucleolus

The nucleolus is the imputation which maximizes ‘equality’ amongcoalitions (Schmeidler 1969).

let θ(x) be the vector of excesses arranged in decreasing order fora payoff vector x and let � stand for lexicographical smaller.

n(v) := {x ∈ I : θ(x) � θ(y) for all y ∈ I}

First excess is made minimal for the coalition, which is doingworst. Then excess is reduced for the coalition, which comessecond. And so on.

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Nucleolus - properties

The nucleolus always exists and is unique.

If the core (c(0)) is not empty, then the nucleolus is in thelexicographic center of the core (Maschler & Peleg & Shapley1979).

The nucleolus can be computed by solving a nested sequence oflinear optimization problems.

This is a ‘hard’ problem for which we use an algorithm proposed byPotters & Reijnierse & Ansing (1996).

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Application

The Economic Question: A new pipeline project will alter thevalue function from vo to v1 and consequently the solution of thegame.

φi(v1)− φi(vo) gives the gross impact of the pipeline on the

surplus of player i for the Shapley Value, which can then becompared to the investment cost of the pipeline (same for n(v)).

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The network & access

Eurasian gas network: nodes and links:

production node RP

customer node RC

transit node RT

link l = {i, j}, i 6= j ∈ R

We have 35 nodes, 40 links and 20 players, each of whom controlsonly some parts of the network.

L(S): set of links at the disposal of coalition S ⊆ N .

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Model: value of a coalition

The value function is obtained by maximizing the joint surplus of theplayers in coalition S using the gas-flows in the pipelines L(S) :

v(S) = max{xij |{i,j}∈L(S)}

∑{i,j}∈L(S), j∈RC

∫ xij

0

pj(z)dz −∑

{i,j}∈L(S)

Tij(xij)

s. t.

node-balancing:∑

i xit =∑

j xtj , ∀ t ∈ RT (S),

network capacity: |xij | ≤ kij , ∀ {i, j} ∈ L(S),

positive consumption & production: xij ≥ 0, ∀ i ∈ RP or j ∈ RC ,

xij-gas flows, kij - capacity limit for the link {i, j}, Tij(xij) - link

specific transportation cost, pj(xij) - inverse demand

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Calibration:

Parameters on pipeline capacities are obtained by aggregating datafrom ENTSOG 2009.

The model is calibrated using data on consumption in the regionsand flows between the regions from 2009 (IEA (2010))

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Geography

NS

OSNW

SW

WS

CSES

ES

TC

Nabucco

Nord

Stream

South Stream

Algeria

Balkan

Belarus

Belgium

France

Italy

Libya

Poland

Turkey

UK

Ukraine

AlgeriaIran

IraqLibya

Russia

Center

East

Center

Norway

Spain

Portugal

Nether

lands

Azer

baijan

Kazakh

stan

Russia

Turkme

nistan

Uzbe

kistan

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Three new pipelines

Nord Stream: offshore link between Russia and Germany;55 bcm/a, 12-14 bln e, completed in 2012.

South Stream: offshore link between Russia and Balkans;63 bcm/a, 18-20 bln e, planned for 2018, scrapped in 2014.

Nabucco: new southern corridor: connecting central Europethrough Balkans and Turkey with Caspian/central Asia andIraq/Iran;31 bcm/a, 17-20 bln e, planned for 2019, strongly backed by EUCommission, but European partners dropped off; recently Turkeytook the initiative for TAP.

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The Puzzle

Three huge projects but neither adequate supply nordemand!

In 2008 Europe’s

Consumption: 489.7 bcm

Production: 184.2 bcm

Net imports: 305.5 bcm(Source: BP (2009), Statistical Review of World Energy)

Nord Stream and South Stream will increase transport capacity forRussian gas from app. 186 bcm/a to 304 bcm/a (63%).

All three pipelines together will increase the European pipelineimport capacity by 150 bcm/a (47%) .

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Hypothesis & Questions

Pipelines have a strategic role in changing the balance of power inthe network.

For the pipeline consortium the gain in bargaining power mayjustify the investment cost, even if the pipeline is not needed forthe efficient supply of gas.

Who benefits in terms of bargaining power? How do the gainsrelate to investment cost?

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Shapley: Pipeline Impact [% total surplus]

Nord Stream South Stream Nabucco

Russia 3.0 0.8 -3.1

Ukraine -2.5 -0.9 -0.7

Belarus -0.8 -0.2 0.0

Norway -2.5 -0.6 -0.8

Netherlands -0.9 -0.2 -0.3

Center 1.5 0.5 0.3

Center-East 0.8 0.2 0.2

Italy 0.4 0.1 0.0

Poland 0.2 0.0 0.0

France+Belgium 1.0 0.3 0.2

Balkan 0.0 0.2 0.2

Turkey+Azerb. 0.0 0.1 3.5

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Shapley: Nord Stream

The strategic value for the initiators of the consortium, Wintershalland EON Ruhrgas of Germany and Gazprom of Russia (in ourmodel Center and Russia) is huge and clearly exceeds the project’scost.

Ukraine and Belarus are badly hurt from increased transportcompetition.

Norway and Netherlands suffer from increased supply competitionin the European markets.

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Shapley: South Stream

Assuming that the NW section from Bulgaria to Austria isexempted from EU regulation on third party access:

1.) As a alternative to Nord Stream (counterfactual), it hassimilar, but somewhat smaller effects on bargaining power. It isviable in spite of higher cost.

2.) With Nord Stream’s large capacities in place, South Streamprovides much less additional leverage and the benefit cost relationbecomes critical.

If the NW section from Bulgaria to Austria is not exempted, thenRussia has little interest in the project.

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Shapley: Nabucco

Increased supply competition harms Russia.

The lion’s share of the benefits accrues to Turkey while the impacton the EU regions is small.

The EU’s support makes little strategic sense.

South Stream has almost no impact on the strategic viability ofNabucco.

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Shapley: summary

A clear ranking of projects nicely corresponding with observedinvestments.

1. Nord Stream: the strategic value for the initiators of theconsortium, Germany (Center) and Russia, is large and clearlyexceeds the project’s cost.

2. South Stream: given its higher cost, the viability isquestionable, in particular if Nord Stream’s capacity is accountedfor. Regulatory holidays for NW section critical.

3. Nabucco: the gains for the EU are marginal and do not covercost. The eastern sections are profitable for Turkey.

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Nucleolus

None of the projects has a significant impact on bargaining power.All are strategically irrelevant.

1. Nabucco: there are small gains for Turkey and small losses forRussia — much smaller than project cost.

2. South Stream: No effects whatsoever.

3. Nord Stream: No effects, except for a tiny loss(!) for Russia.

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