My Thesis- Game Theory

Critical Studies Paper

Table of contents Introduction

2

A Game in Practice

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Eliminating Dominating Strategies

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Strategies Available

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Position of Mixed Strategies

13

Mutual Appreciation

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Observations and Conclusion

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References

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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

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. Devoloping Countries Industerlised Countries United States

123.543

39%

54.316

17%

26.915

8%

17.628

6%

Germany

16.073

5%

China

10.860

3%

Russia



France United Kingdom

Isreal Others

6.506 20.274

2% 6%

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Critical Studies Paper

“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 longterm 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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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

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.

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.

0

3

1

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Critical Studies Paper

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

3

1

2

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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Critical Studies Paper

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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Critical Studies Paper

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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Critical Studies Paper

“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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Critical Studies Paper

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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Critical Studies Paper

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

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