Analysis of Co-operative game theory for SMEs in a competitive Environment. If you walk down the streets of London and ask any anyone: How do SMEs operate? Some will say it is about offering the best services to customers. Others will say that SMEs are the survivors of a tough competitive market. Some will argue that it is all about good management. Some will also say it is about getting finance. However, very few will mention networking, cooperation, union, education or even the best strategy to win. SMEs contribute with a combine turnover of £3,100 million in 2012 and of all the businesses 62.7% were sole proprietorship, 28% were companies and 9.3% were partnership. (FSB, 2013) With the current UK Government invention to boost up SMEs funding, with an additional £300 million, one can assume the likelihood of an increase in SMEs in UK. On the contrary, little research has been conducted on Game theory in SMEs (Tidd et al, 1997) In Business, Game theory aims to help organisation to understand situation in which decisions can be made. (Osborne, 2000) Game Theory has provide a methodology that has brought insight into many previously unexplained phenomena by allowing asymmetric information and strategic interaction to be incorporated into the analysis. (Chalterjee et al, 2001) This research proposal will look into how game theory could help SMEs in different sectors to achieve a higher payoff by cooperating with competitors while there is excess demand in the market. In addition, this research will educate SMEs about the market, opting for opportunity cost, introducing SMEs networking in their particular sector. Moreover, this research could help SMEs to grow through Mergers and Acquisitions.

1. 1
Proposal for Ph.D. Thesis
Area of Study
SME’s in London
Proposed Title:
Analysis of Co-operative game theory for
SMEs in a competitive Environment.
Proposer: Mahen Gangiah
Email: alvingangiah@googlemail.com
Tel: 07799291899

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Content
Page
1. Introduction ---------------------------------------------------- 3
2. Background of Study ------------------------------------------- 4
3. Statement of Problem ------------------------------------------- 5
4. Research Question ------------------------------------------- 6
5. Research Objectives ------------------------------------------- 6
6. Literature Review ------------------------------------------- 7
7. Research Methodology ---------------------------------- 8
8. Data Analysis ------------------------------------------- 11
8.1 Data Collection Method ---------------------------------- 11
9. Proposed Development ---------------------------------- 11
10. Original Contribution ------------------------------------------- 12
11. References ------------------------------------------------------- 17

3. 3
1. Introduction
If you walk down the streets of London and ask any anyone: How do SMEs operate?
Some will say it is about offering the best services to customers. Others will say that
SMEs are the survivors of a tough competitive market. Some will argue that it is all
about good management. Some will also say it is about getting finance. However,
very few will mention networking, cooperation, union, education or even the best
strategy to win. SMEs contribute with a combine turnover of £3,100 million in 2012
and of all the businesses 62.7% were sole proprietorship, 28% were companies and
9.3% were partnership. (FSB, 2013) With the current UK Government invention to
boost up SMEs funding, with an additional £300 million, one can assume the
likelihood of an increase in SMEs in UK.
On the contrary, little research has been conducted on Game theory in SMEs (Tidd et
al, 1997) In Business, Game theory aims to help organisation to understand situation
in which decisions can be made. (Osborne, 2000) Game Theory has provide a
methodology that has brought insight into many previously unexplained phenomena
by allowing asymmetric information and strategic interaction to be incorporated into
the analysis. (Chalterjee et al, 2001)
This research proposal will look into how game theory could help SMEs in different
sectors to achieve a higher payoff by cooperating with competitors while there is
excess demand in the market. In addition, this research will educate SMEs about the
market, opting for opportunity cost3, introducing SMEs networking in their particular
sector. Moreover, this research could help SMEs to grow through Mergers and
Acquisitions.

4. 4
2. Background of Study
This research will help to promote effectiveness, profit maximisation in a competitive
environment3 for SMEs. Since little research has been carried on game theory in
SMEs and the current government intervention to boost up Entrepreneurial in the UK,
the study will focus on how co-operative game theory could help Micro, Small and
medium enterprise in the UK to maximise their profit by co-operating together as
opposed to Sum zero Game where there is one loser and one winner. In addition,
Game theory would help players5 to facilitate decision-making for further expansion
through Mergers and Acquisitions.
Proposed
Game
SCENARI
O DETAILS
INDUSTRY
SECTOR SIZE
EMPLOY
EES
1 CAB RENTAL COMPANY SERVICE MICRO <10
2 SECOND CAR PARTS SERVICE MICRO < 10
3
MANUFACTURING
COMPANY furniture
MANUFACTURI
NG MEDIUM < 249
4 FOOD /RESTAURANT MAN/SERVICE SMALL < 50
At this preliminary proposal stage the research will focus on four different industry
sectors in the market. These sectors would be described as scenario 1, 2, 3 and 4where
scenario 1 would be based a Cab rental company. Scenario 2 would be based on a
second hand car parts supplier followed by scenario 3 would be based on a medium
size furniture manufacturing company and lastly Scenario 4 would be based on
Food/Restaurant industry sector. However, Scenario 4 is yet to be defined at this stage
due to the fact that most customers prefer taste rather than location, brand and price.
(O'Boyle, 2011) These four different scenarios have a complete different customer
based and the possibility that the outcome might vary might still be questionable at
this stage.

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3. Problem Statement
Game theory has been widely used in larger organisations to promote successful
strategies but on the other hand there has been lack of research made on strategic
management for SMEs. (Fierro et al, 2007) As of 2012, there was an estimation of 4.8
million businesses in the UK, which create jobs for 23.9 million people. (FSB, 2013)
It is believed that there will be more SMEs in the coming years due to the fact that the
UK government injected £ 300 million for SMEs loan. (Guardian, 2013) On the other
hand the Guardian, 2013 cited that the UK government would also help SMEs to
grow. In addition, one of the growing concerns in SMEs is that most businesses act in
their self-interest to achieve a larger proportion of the market size or to maximise
profit. (Fierro et al, 2007) The ideology to “beat your competitor” is challenged and
put to question in this research proposal.
Based on the above problem statements, this study is undertaken to fill this knowledge
gap and test the co-operative game theories on how SMEs cooperate with their
competitors and still maximise their profit. It is also to be noted that based of the
game theory SMEs could have the advantage to grow through Mergers and
Acquisitions. (M & A)

6. 6
4. Research Questions
a) What is the extend of the application of co-operative theory in a competitive
environment for proposed scenarios in terms of
- Current economic conditions
- New players entering the market
- Existing players exiting the market
- Experience, maturity, training of the players
- Sustainable growth strategies
b) How to measure competitiveness in the market when all players want to
achieve higher payoffs?
c) How does factors such as size, location, availability, and negotiation skills
have an impact in the degree of adopting the co-operative game theory?
5. Research Objectives
The main objective in this study is to examine the co-operative game theories in a
competitive market for SMEs in London. In doing so, the study will seek:
a) To investigate the extent of which co-operative game theory could be applied
in different sectors in the market.
b) To see how factors such as size, location, availability, negotiation skills,
maturity of players have an impact on the game.
c) To see the best possible scenario where most players would win in their own
sectors.
d) To highlight the findings those are of interest towards co-operative game
theory.
e) To ascertain that players understand the rules and boundaries of the game by
implementing proposed strategies.
f) To investigate the possibilities of growth through M&A in SMEs
g) To Educate Players on game theory and strategic management

7. 7
6. Literature Review
Cooperation games
Cooperation games are those in which the other players are no longer treats as
opponents, but also as partially becoming partners, cooperators, etc. These are players
with similar goals.
Noble (1995) argued that the co-operative game theory has some flaws. One of the
main drawback would be that the “Players” have different perceptions of the world
and that might affect the game. The author also citied that co-operative game theory
was intuitive and commonsensical. However, other noble scholars and authors did not
share his views. Brandenburger et al (1995) opposed Noble’s argument and cited that
co-operative game theory allowed players to look for a win-win as well as win-lose
opportunities. By keeping both strategies in minds, the authored claimed that knowing
both possibilities were important because win-lose situation often backfire. In
addition Brandenburger et al (1995) also pointed out that most common and
dangerous strategic move a player can make is to lower prices to gain market share, as
a result this would only be beneficial in the short run and the wins would evaporate if
competitors would match up the price. Thus, creating a lose-lose scenario.
Brandenburger and Nalebuff (1997) suggested that co-operative game theory creates a
solid relationship among players and players can set rules. On the other hand, in a
non- cooperative game, all players had to follow strictly to the rules of the game and
posit equilibrium behavior as the norm. Osborne (2000) argued that all players think
rationally towards their goals. In a non- cooperative game, as per Osborne, players
would face a fiercer competition, stressful environment and less room for growth as
opposed to a co-operative game. Similar views are shared by Erhan and Keskinocak ,
(2003) the authors explained using the prisoner’s dilemma that firms have to fight
harder to get a bigger portion of the market in a rational non- competitive game.

8. 8
Terms Explained ( Turocy. T & Stengel . B, 2001)
Common knowledge
A fact is common knowledge if all players know it, and know that they all know it,
and so on. The structure of the game is often assumed to be common knowledge
among the players
Dominating strategy
A strategy dominates another strategy of a player if it always gives a better payoff to
that player, regardless of what the other players are doing. It weakly dominates the
other strategy if it is always at least as good.
Extensive game
An extensive game (or extensive form of game) describes with a tree how a game is
played. It depicts the order in which players make moves, and the information each
player has at each decision point.
Game
A game is a formal description of a strategic situation.
Nash equilibrium
A Nash equilibrium, also called strategic equilibrium, is a list of strategies, one for
each player, which has the property that no player can unilaterally change his strategy
and get a better payoff.
Player
A player is an agent who makes decisions in a game.
Rationality
A player is said to be rational if he seeks to play in a manner which maximizes his
own payoff. It is often assumed that the rationality of all players is common
knowledge

9. 9
Zero-sum game
A game is said to be zero-sum if for any outcome, the sum of the payoffs to all
players is zero. In a two-player zero-sum game, one player’s gain is the other player’s
loss, so their interests are diametrically opposed.

10. 10
7. Research Methodology
7.1 Proposed Research Design
Research design would be carried for each scenario and would be treated as
independent case.
a. Literature Review
b. To determine and define research question
c. Apply research question on field
d. Prepare to collect data on the field
e. Evaluate and Analyse data
f. Prepare Report
g. Literature Review and Comparison of Data to different Scenarios
7.2 Research Methods
Research would be carried in both Qualitative and Quantitative methods for the
duration of this research.
Qualitative Research would be based on Face-to-Face Interviews, Anecdotal Data
Observation, Industrial Placement and Customer focus group.
Quantitative Research would be based on Experimental design such as surveys tracker
sheets, design contracts.

11. 11
8. Data Analysis
Scenario 1. Car Rental: Data would analyse demand and supply through telephonic
record tracker sheets, sales receipts, emails, clicks on website. Alternatively, analysis
of contract would be able to determine the effectiveness of the theory.
Scenario 2. Second hand Car Parts: Data would be analysed through Cards design
with barcode number that will register effectiveness of the theory.
Scenario 3. Restaurant: Analysis data from voucher collected would help to determine
the end results.
8.1 Data Collection Methods
- Market Research: To determine Demand and Supply Models
- Questionnaires: To understand the limitation of the Game
- Experimentation: Scenario 1: To design a Contract
Scenario 2: Design a Bar Code credit card type
Scenario 3: To design Vouchers
- Observation: Short training placement of 2 months to understand the structure
- Customers focus group
9. Proposed Development
Year 1. Research training, Market Research, Literature Review, Research Questions,
e- learning, deigning game adaptation.
Year 2. Application of Game theory, Main Empirical phase, Analysis of Data (Start),
Finalising literature review. Experimentation phrase and data collection
Year 3. Data Collection, Finalisation of Analysis, complete writing.

12. 12
10. Original contribution by Researcher.
The aim of this research is to determine whether Co-operative game theory could be
applied to SMEs to maximise profit as opposed to zero sum game where player 1
wins and player 2 losses (Vice Versa). This research will also help SMEs to search for
new ventures, understanding the market, create networking, and breed a new strategy
to co-operative with competitors. In addition, little networking has been done for
SMEs and this research is believed to help SMEs to create new knowledge, problem
solving and also support to new entrance.
A few assumptions are taken into consideration at this stage of the proposal, where it
is believed that players would co-operate with competitors and in real world scenario
and this ideology could be rejected due to the fact that most SMEs players act in their
own selfishness to gain a greater proportion of the market. It is also assumed that
players would play the game in such economic condition. Due to the decrease in
demand, competitions are getting tougher and tougher.
10.1 Proposal of co-operative game theory.
Scenario 1 of the Game
Rent a Cab is a small business in London and deals with hiring PCO cars to potential
taxi drivers. In 18 months of operation, the company has now a fleet of 50 cars. Rent a
Cab London (Player A) has been experiencing an increase in demand over last 4
months. In July, Player A has more than 70 demands for Cab and due to time and
financial restrain he could not increase its fleet in the short run.

13. 13
In fear of loosing his customer, Player A turns to its competitors (Player B, C &D) for
help. Player A makes a contract with player B to supply him 22 cars and in return
Player B will provide player A with two of its own cabs and make a different contract
with player C for the remaining cabs. In return player A will gain £15 per cab as
payoff and Player B will have a payoff of £ 135 per car assuming that the average
JAN FEB MARCH APRIL MAY JUNE JULY
DEMAND 30 20 50 52 55 60 72
SUPPLY 30 20 50 50 50 50 50
0
10
20
30
40
50
60
70
80
nooftaxitorent
PLAYER A : RENT A CAB BUSINESS
ACTIVITY
PROPOSED APPLICATION OF CO-
OPERATIVE THEORYIN SCENARIO 1
£
PLAYERS LOCATION
NO OF
FLEE
T
AV
PRICE
PER CAR SUPPLY
PLAYER
A RENT A CAB EAST LONDON 50 150 0
PLAYER
B AB CAB RENTAL WEST LONDON 43 150 2
PLAYER
C LSC CAB RENTAL
NORTH EAST
LONDON 25 150 12
PLAYER
D
LONDON CAB
RENTAL SOUTH LONDON 78 150 19

14. 14
rental price of a cab is £150. On the other hand, player B can only supply 2 cabs and
has to make a contract with Player C to achieve its target. Player B payoff would be 5
x £135 + 25 x £15. Similarly is sequence is repeated among all players. Opportunity
cost of player B is to gain (win) £ 50 or gain (lose) £ 0.
Player A = α Player B = β Player C = γ Player D = δ = 15
. α = (10*150) + (20 * β + γ + δ ) s
∏ =
300
. β = (5*150)+ (15* γ + δ ) s
∏ = 50
. γ = (10*150)+ ( 5* δ ) s
L= 225
. δ = (5*150) L
= 225
(4500)
In this game, the best outcome would be to co operate with other players, Even if
player C & D are making a loss, the opportunity of earning £ £1275 and £525
respectively is consider to be a win win strategy.

15. 15
10.2 Problem with theory of Co-operation.
At this preliminary stage, this theory would not be applicable to different SMEs
operating in different sectors such as food/Restaurant. Due to the unavailability and
lack of research and customer’s personal taste it would be difficult to test this game in
the food sector.
In addition, It is also assumed that customers will not be dealing directly to player B,
C, and D. It is also assumed that the overall average price to rent a PCO cab is £150.
It is also to be noted that additional overheads such as rent of premises, valeting,
servicing would affect would also affect the decision making of Player C, D.

16. 16
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