my thesis- game theory

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Critical Studies Paper

Vijay Raghavan 07969363

Table of contents

Introduction 2

A Game in Practice 7

Eliminating Dominating Strategies 9

Strategies Available 9

Position of Mixed Strategies 13

Mutual Appreciation 14

Observations and Conclusion 16

References 17

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Introduction

“Game theory is a mathematical and logical analysis to investigate the strategic interaction

between different players. It is a theory of decision making and modeling of dynamic and

flexible economic relationships.” (Alenka Krek, Analysis of Geo-information pricing using game

theory)

The ‘Game’ is all about the assumption and assessment of a strategic competitor using

mathematical and statistical references. The knowledge that a company/ organization holds

about its competitors game (The moves the opponent is capable of (or not) making) is a major

factor determining the risks involved in making a move or for determining payoff’s.

All players in the game (corporations) have a common ground of two choices. Each player

by tactic is ‘selfish’. This means that all players operate for profitability as their first choice.

Secondly, they can assume an equilibrium state.

The “payoff is defined as the profit made out of the choice taken.”

“The equilibrium state is the point at which neither of the players can make a profit from

making any choice unilaterally.”

(Source: Decision Making using Game Theory (An Introduction for Managers) Anthony Kelly, »

University of Southampton)

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In this study the discussion will focus on such a competitive analysis of Europe, Israel and

South East Asian markets involved in arms trade. Also to discuss the factors that have made

the US and Russia the largest dealer and emergence of France and Israel as strong emergent

competitors.

The UK statistically stands only next to the USA and Russia as being the biggest arms dealer

in the world. France, though an old player has not been able to establish a niche in the region

because of strict regulatory policy as an entry deterrent. Israel on the other hand has only been a

recent recruit in the trade and is desperately trying to place itself in the OPEC region and Asia.

Worldwide Arms Transfer Agreements, 1999-2006 and Suppliers’ share with Developing World (in

millions of constant 2006 U.S. dollars)

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China 10.860 3%

The European powers are seeking out to eliminate their competitor as they previously held a

monopoly in a few zones. They are also trying to outperform each other. Israel on the other hand

is holding a key geographical advantage over its competitors and hence able to supply at a much

lesser delivery cost.

United States 123.543 39%

Russia 54.316 17%

France 26.915 8%

United Kingdom 17.628 6%

Germany 16.073 5%

Isreal 6.506 2%

Others 20.274 6%

Devoloping Countries

Industerlised Countries

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“France had to redirect its sales from the Middle East and the third world countries to Eastern

Europe and the industrialized world in the early 1980’s. The dependence on traditional markets

made France vulnerable to the political climate in the third world and new competitors

challenged French arms export.” (Ballistic Missiles in the Third World, Aron Karp)

The dependence on US for the supply of sophisticated armaments is evident from the following

statistics. Major West European arms suppliers, such as France and the United Kingdom, have

concluded large orders with developing countries over the last eight years, based on either long-

term supply relationships or their having specialized weapons systems they can readily provide.

Germany has been a key source of naval systems for developing nations. Despite increased

competition between the United States and the other major arms suppliers, the U.S. appears

likely to hold its position as the principal supplier to key developing world nations, especially

those able to afford major new weapons. Because the United States has developed such a wide

base of arms equipment clients globally it is able to conclude a notable number of agreements

annually to provide upgrades, ordnance and support services for the large variety of weapons

systems it has sold to its clients for decades. Thus, even when the U.S. does not conclude major

new arms agreements in a given year, it can still register significant arms agreement values

based on transactions in these other categories. Need based supply is further taken care of by

other competitors.

India and china recently have grown into a humongous arms import zones and almost all of the

trading nations want a share in the Southeast Asian Market. Israel has been cleverly successful

to enter the Indian market along with the USA and Russia, but France has not bee able to

penetrate.

“Last year Israel supplied India with $1.6 billion worth of military equipment and is India’s

second-largest defense supplier after Russia. Sales are only going to rise. Indian defense

procurements from Israel in the period 2002-07 have touched the $3 billion mark. India has

also procured electronic warfare systems and advanced radars from Israel.”

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On the contrary, the only sale France was able to manage was that of the Mirage Aircrafts and

that too in the late 1980’s. Since then the French system had to shift its focus from the Asian

market to the African one. Now it is trading heavily with Libya and Uganda.

This year, the airbus series were launched into the Indian market, which is hosted by the

French. This was followed by a US$2.7billion deal struck with the agency, the first massive

breakthrough for the French in the zone. Now negotiations are going on for the trade of

another US$17 billion for the supply of sophisticated aircraft carriers. If this is successful,

France would once again build a base for trade in the region.

In this example, there is possibly a new entrant in a diverse economic zone. Here Israel can

either choose to fight or else not compete at all, whereas France can also choose to fight or

withdraw.

Now if France doesn’t enter the market, Israel retains its position. But if France does enter, And

Israel chooses to fight, they both would lose market share. If Israel chooses not to compete,

then both the parties would gain, but Israel would end up losing a market share and also its

stronghold in the trade.

“if the government of the potential entrant considers the sector to be important, it can provide

an incentive by subsidizing the entrant and guaranteeing positive profits when it enters the

market”

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A Game in Practice:

“In 2006, the United States led in arms transfer agreements worldwide, making agreements

valued at $16.9 billion (41.9% of all such agreements),up from $13.5 billion in 2005. Russia

ranked second with $8.7 billion in agreements (21.6% of these agreements globally), up from

$7.5 billion in 2005. The United Kingdom ranked third, its arms transfer agreements worldwide

standing at $3.1 billion in 2006, up from $2.9 billion in 2005. The United States, Russia, and

the United Kingdom collectively made agreements in 2006 valued at $28.7 billion, 71.2% of

all international arms transfer agreements made by all suppliers. Developing nations from

2003-2006 accounted for 73.3% of the value of all international arms deliveries. In the earlier

period, 1999-2002, developing nations accounted for 71.7% of the value of all arms deliveries

worldwide. In 2006, developing nations collectively accounted for 73.6% of the value of all

international arms deliveries.” (Source: Conventional Arms Transfers to Developing Nations,

1999-2006 Richard F. Grimmett, Specialist in National Defense Foreign Affairs, Defense, and

Trade Division)

For the sake of the game let us assume the following. US, France and Israel are leading

exporters of cruise missile equipment to the third world, both in Africa and in Asia. Other

competing forces opt to not to participate in this game (ex. UK and Russia)

To construct a game tree let me first make the following assumptions:

The competing countries are France and Israel. The competing products are of the same

technical standards to eliminate preferences.

Assuming it takes a cost of US$ X more than the price of the product for France and Y for

Israel. Here Y is almost negligible while for France to reach a zone of mutual competition, X

is a large sum. The profitability at the zone for France is four times more than what it would

be for Israel. In other words if the value of the trade is worth 10X, at the loss of 2X for supply

and negotiation, France would gain 7X. For Israel, the gain would be around 2X, but the cost of

supply and negotiation is almost negligible.

But if both France and Israel decide to trade together, France still gets 7X but Israel gains 3X.

And if France decides to move first before Israel, its gain would be 6X, if it does not allow the

recipient to negotiate with Israel.

In case Israel waits for the recipient to make the first more, then its gain would be 1X.

Conversely to this situation, if France waits for the recipient to approach, its gains ends up

being 9X.

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What should these countries do in a real time situation to maximize their own profit? How

should they analyze the payoff’s against any of these transactions? And who decides to move

first, France or Israel?

We can call the move taken by any of the player as the strategy, a pure strategy. This maybe

influenced by sudden demand, shortages, loans etc, where behavioral or mixed strategies come

into play.

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Eliminating dominant strategies:

“A powerful way of finding the Nash’s equilibrium is by eliminating the dominant strategy”

In the above case France holds two strategies s1 and s2,(to be the first mover or to with for

the recipients move), where s2 is strictly dominated by s1. In other words, the payoff from s1

would always be greater than that from s2.

A dominated strategy s2 can never be a part of the Nash’s equilibrium because it can always be

replaced by a more dominant one.

Strategies available:

France can either seal the deal for the sake of entering into the Southeast Asian market at the

cost of the large profitability that they could have made elsewhere.

They can otherwise wait for India to find another source for the trade, and if they don’t find any

(assuming France is their only viable option left), increase the payoff margin.

When France has completely valuated the strictly dominating strategies of Israel for the trade

in the region, they can build a strictly dominating one (or in some cases a dominated one) on

its basis. But if there remains none it is then called a “dominated Nash’s equilibria.”

The dominating strategy for Israel in this case would be:

To host the trade for the carriers by procuring it from another source so that it reaffirms its

position in the region. This would mean very low profits, if any, but would maintain the sense

of monopoly. To not compete with this current business as the requirement of this good is not

generic.

Now France can also choose to make the first step. If it chooses to enter, it knows that Israel

can either fight or not compete. Since not competing would give Israel a higher payoff, it’s more

likely it would choose it. Even if France chooses not to enter, Israel would still have the same

payoff. Since the payoffs remain the same, France would rather like to choose entering the

market as there is a larger likelihood of Israel not competing.

The next step would be the elimination of the weakest strategy for both the players. Thus each

would be left with only one ‘playable’ strategy. The resulting profile would indicate the Nash’s

equilibrium.

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In the above case the players can also choose to use their weakly dominating strategies, that

is, France can choose to wait or else Israel can choose not to compete in the deal. It is possible,

but however “a Nash’s equilibrium that uses weakly dominated strategy has very poor dynamic

properties, and cannot be evolutionarily stable.”

For a game with the two players, we can predict the following tree.

In 1996 France and Israel together entered the Indian Arms market for the sale of Radar

Artillery technology (CRS report for Congress, Richard F. Grimmett). The Duration of the

tender was highly lucrative for both the countries. If either won the contract, it would give

them 8 years of stronghold in the country for the technology.

India forces a simple yet effective game system to the competing countries. The duration of the

negotiation for the tender was for a span of 1 year, and extension of another year was given in

case no deal was struck. After primary negotiations, the players have to choose to make a move.

They can either wait for the other player to move first so that a better offer can be made, else

they can wait for India to approach either of them accepting their terms. Primarily, it would be

an advantage to both of them if they move first.

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The action of both France and Israel are independent of each other. If they both choose not to

act, then they are looking at a period of five years before either of them is approached by India.

But if France chooses to act first then it is either looking at winning the contract for 8 years or

losing out to a better offer by Israel after a negotiation for two years. Israel on the other hand is

looking at the same situation.

0

1 2

3

This is the prisoner’s dilemma the countries are facing. And the waiting period of 5 years

here would be the point of Nash’s equilibrium. Theoretically the best choice for either of the

countries would be to wait till they are approached.

In reality, France chose to act first. The reason for this was that France was already involved in

the negotiation for the sale of control rods and subsidiary equipment to India. The previous

deal would have an effect on buying successive contracts. The resultant offer from Israel was

way more lucrative, and hence India chose to go for the deal with Israel.

Here France is indicated by the round figure

and Israel by the box.

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Now if both players have to reach vertex 2, neither of them have a winning strategy over the

other. However, there are two Nash’s equilibria. France can move from 0 to 3 and Israel from

3 to 2. Conversely, France can move from 0 to 1 and Israel can stay in 3. But why should Israel

stay in 3? The following was the real time answer to the game by Israel for the deal and hence

successful.

The problem arises when Nash’s equilibria ignores the sequential structure of a finite game.

(Michael Ummels, FSTTCS 2006). Therefore a player requires that the strategies are optimal

after every possible game node. Hence every sub-game equilibrium is a Nash’s equilibrium.

0

1 2

3

Now recall that this game has two Nash’s equilibrium if both France and Israel wan to reach

vertex 2. But it is now clear that this game has an unique sub-game equilibrium. Which is

France moves from 0 to 3 and Israel moves from 3 to 2. But it must be noted that stating in 3

would not have been an optimal move when France moved from 1 to 0.

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Position of Mixed Strategy (“Catchin’em off guard”):

It is simply the cumulative probability of one strategy happening or the other. Where both the

strategies available are assumed (both France and Israel) to be pure. France has the knowledge

about Israel’s stronghold in the region but is also aware of its weakness, that it needs a market

in this zone. Israel on the other hand knows its monopoly and success history but is also aware

of the risks of penetration of the French industry. In this case the question arises, that which of

the two countries would show the variability and the dexterity that the other hasn’t sorted out.

For instance, Israel could convince Russia to negotiate the same deal in its favor by offering it a

stake on another. Else France could subsidize another trade with India if this deal is taken.

Due to Israel’s recent handshake with Russia over arms manufacturing units, a new trend of

symbiosis has generated. The same goes for France with Sweden and the United Kingdom. Both

Russia and the UK are affected by the unprecedented growth in the number of sellers in the

region. The best way to avoid direct confrontation would be to do so using sub sellers. In this

relationship both the serving and the selling nation would benefit.

In the recent radar artillery system software transfer to India, the Israeli government made it

purposefully compatible with Russian artillery. This was to enforce a prospective deal with the

Russians in the future. In return, Russia, the biggest arms dealer to Southeast Asia, could help

Israel by selling the aircraft carrier through it. This would help maintain the iron fist over the

region.

Similarly, the United Kingdom has a huge military and arms trading zone in East Asia. It would

definitely like to extend it over the region. Thus if it helps France by either subsidizing the

product’s materials (UK supplies the bulk material for assembly in French armory), they could

proportionally reduce the selling price, and thereby lure the importing country.

A strategy that dictates following one course of action until a certain condition is met and then

following a different strategy for the rest of the game is called the trigger strategy.

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Mutual Appreciation (Bargaining Model):

This case study is about the analysis of a Negotiation Framework known as Rubinstein’s

Alternating Offers Protocol. In such a framework two agents, the Buyer (B) and the Seller

(S), bargain over an item. Players alternatively take it in turns to make an action which can

be either (i) throwing a proposal (offer), or (ii) accepting the most recent proposal. In theory

both players can keep Rejecting offers so that an agreement may never be reached (in that

case we talk about disagreement or conflict deal). However a player’s utility depends on the

value at which an agreement is reached (as well as on the time at which it is reached), hence

disagreement is the worst possible outcome for both players and it is ruled out.

Players’ offers are calculated by means of the so-called Negotiation Decision Function (NDF),

a function of time that determines a player’s strategy. Strategies can be linear or non-linear,

the latter being either conceder, if the player is willing to concede a lot in the early phase

of negotiation, or boulware if a player is willing to concede considerably only when its time

deadline is approaching. The following parameters are relevant for the characterization of a

player strategy.

T_b (Time-deadline ): player b quits negotiation if an agreement has not been reached within

T_b.

IP_b (Initial Price): player b’s first offer.

RP_b (Reserved Price): the threshold above (below) which player b will certainly reject offer

(hence also its maximum/minimum offered value, i.e. Player b offers RP_b only at time T_b).

The uncertain nature of an offer evaluation outcome is represented by making the decision

whether to accept or reject a player’s offer a probabilistic one. The will of a player (b) to accept

an offer is affected by both the offered value and the player’s reserved price (RP_b). The

following points are considered for the characterisation of players’ acceptance probability

(functions S_AP() and B_AP() below):

Any offer below (above) the S_RP (B_RP) will be certainly rejected by the Seller (Buyer).

The probability of accepting an offer (counter-offer) asymptotically tend to 1 as the offer

(counter-offer) increases (decreases).

For the sake of symmetry, players should have an equal attitude towards acceptance/rejection

of an offer, which is: players are equally likely to accept offers of equal utility (i.e. offers whose

distance from their respective RP is the same).

(Source: (Alternating Offers Protocol Contributed by Paolo Ballarini, Michael Fisher & Michael »

Wooldridge)

“Game Theory is a systematic way to understand behavior of players in situations where their

fortunes are interdependent”

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“A bargaining model is a game in which two or more players stand to gain by cooperating, but

they must negotiate an acceptable procedure for sharing the gains from cooperation.” (Source:

Arms transfer in the modern world edited: Stephanie G.Neuman and Robert E.Harkavy)

When both the parties are fully aware of the choices in front of them, and have complete

assessments of the payoffs that they might receive out of a fight, non entry or allying, they

could choose bargaining as a tool for mutual benefit.

The bargainer, however, loses his potency as a dominator at this stage. But if the strategy has a

backup plan if the bargain doesn’t work, then there is a scope of stealing a higher payoff.

Usually, the wealthier of the bargainers (in scale, power or capital) has the domineering

presence in the negotiation. This is a key point in the game as both the players are completely

aware of the other’s position. But usually the one with the obvious better fallback position is

having the say.

In our case, if the situation is to reach this stage, then there can be two possibilities. France

approaching the table and negotiating for a mutually beneficial payoff, in exchange for the

market share, where Israel could bargain asking a much higher payoff than offered as the stakes

are known.

Alternatively, if Israel approaches the table, it could offer France a decent trade opportunity in

exchange for stepping back from the deal. This could leave France in a dilemma as it both lured

by the opportunity for a much profitable business, and losing a much fought for stake in the

SEAsian market. “A bargainer who becomes less risk averse receives the larger payoff.”

We could hence come to a presumptive conclusion that Israel, which holds the stronger

arm could possibly pull off the negotiation and maintain its niche. If not, it must fight the

competition as the extent of trade in India is of larger importance than any of its other

importers.

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Observations and Conclusion:

Primarily there is a need to assess the degree of requirement of a commodity by the importing

nation. This precedes strategies and game planning. In our case, France has been given a time

up to November 2009 to come up with a plan of trade. Israel is obviously using the strategy of

waiting for the while in this issue as it does not want to expose its dominating attitude to its

country of interest. France as well, would take this time frame to assess the strategies of all the

trading nations in the region before actually committing to a number.

In game theory neither the markets are fixed nor the prices. “The economy is dynamic and

evolving”( Source: Brandenburger & Nalebuff- Foreword to Co-petition). We use the prisoner’s

dilemma to breakdown the suppliers say, and urge competition, which would eventually lead

to lower prices. It can also be used to break down free trade agreements between countries, if a

monopolistic trader decides to become a protectorate.

The dictator can either choose to be competitive, cooperative or non-indulgent as the game

requires him to be. The problem with Nash’s theory is that it does not state the extent

of influence a player has if the other is holding a trump in another game involving the

same players. It restricts the choices a player could make as strategies are based on overall

dominance. In our case if Israel chooses to fight, then there is a chance of retort from the

French as well in another trade. Political and international policies also restrict the mobility of

a plan to a very large extent. And even these policies are biased towards a particular direction.

To state this with an example, when Israel was in war with the gulf, Egypt was supplied with

armaments by the Americans. But now it is supplying to Israel just to reconfirm its fist in the

region. But the same is not applicable when the transfers are done by the countries of EU and

Asia. Therefore, a real-time assessment of a game plan cannot be done without acknowledging

the region and countries in trade.

Game theory though, gives an insight of what to plan for the future when different situations

are influencing a business. My case study therefore to an extent reconfirms this by analyzing

the different strategies that can be made depending upon the system of factors influencing.

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Reference:

Books:

Decision Making using Game Theory (An Introduction for Managers)

Anthony Kelly, University of Southampton

“Caves, R. Frankel, J. and Jones, R., World Trade and Payments”

Dr MoonJoong Tcha “Interactive International Trade”

Notes by Prof. Richard B. Goldstein “game theory”

ARMS TRANSFER IN THE MODERN WORLD ( edited: Stephanie G.Neuman and Robert

E.Harkavy)

Websites:

www.globalissues.org/Geopolitics/ArmsTrade/BigBusiness.asp#Armssalesfigures

http://www.un.org/News/Press/docs/2006/gadis3335.doc.htm

my thesis- game theory

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