Practical Value of Game Theory - Research Paper Example

Business Information Game theory: Game theory has evolved out of the complexities and complex behaviour of business systems. It helps in the determination of economic behaviour, where business marketplace is the game, and the players are the different parties, entering business transactions with each other. In essence, “game theory is a part of (applied) maths that describes and studies interactive decision problems (Neel 2004). The games theory is important because business involving the mental attitudes of different players and their behaviour patterns, whether aggressive or co-operative. In a two player game, the strategies are less complex, and the assessment of opposing, or conflicting players are better understandably, than when the number of players start increasing. The more participants say n-persons, the more complex, the adoption of the business strategies would become, since different behavioral aspects of the different persons among themselves, and the business has to be assessed, before decisions are to be taken. In this connection, it is seen that participants in the market may adopt an aggressive posture, or a conciliatory posture, depending upon their assessment of the situation. When the postures are conciliatory or co-operative, there is no problem for the opposite side; it is only when their positions are aggressive, that counter -strategies have to be evolved for one party to get the maximum benefits from the business deals and increase individual firm profits. There are several aspects to games theory and they flow from the following assumptions: Individualism is a striking feature of each firm as each one tries to maximise their own profits The economic feature of judicious and logical thinking which takes into account the fact that most people may be self centered and geared in order to meet their own outcomes The aspect of mutual interdependence in that one firm’s action may have repercussions on other firms or in the market. The main aspects of Games Theory lays on payoffs or the rewards and profits accruing to the firm, which may depend upon the strategic decision making of the firm and how well it synthesizes with competing or conflicting firms. Since the market forces to a large extent, determine the payoffs for each participating firm, it is important that adequate strategic planning and decision making are envisaged and executed by individual firms in order to maximise their respective market shares. There are two aspects of games, static and dynamic. When one firm enters into a strategic deal without knowing the strategy of the others, it could be termed as static; and if one firm enters fully well aware of the strategy of the other, it is known as dynamic. There is another aspect when a firm chooses two or more strategies; it could be termed as a mixed strategy; the zero sums refer to the fact that total of positives of the winning firm is set off against the negatives of the losing firm, and therefore, the end result would be zero. However, it is seen that not all strategies end up in zero; it is also possible that there are non-zero constant sum games, in which the end result does not add up to zero, but something differently, which would take other connotations, depending upon the action taken up by the players. Game: Prisoner’s dilemma: In this exposition of Games Theory, the idea is that one firm, or player, needs to consider the impact of influence of action of other firm, or unit, upon the final decision of the course of action of the firm. Therefore, what is meant here is that it is not only one’s own strategic decision making that is significant, but, it is necessary to assess the strategy of the opposition which impacts one’s strategic decisions or plans. The concept relates to two prisoners, A and B, who are lodged in different cells with no means of communication. The theory is that a person who confesses would receive no sentence, and a person who does not confess would get 20 years imprisonment. However if both confess they would get 10 years each and also if both don’t confess they would be get 1 year each. A confess don't B confess 10,10 0,20 don't 20,0 1,1 A diagrammatical representation would be as above. Thus it is seen that the foundations of the game theory was laid down by John Von Neumann in 1928 and has received a overwhelming response not only in defence and strategic management but also in other spheres where decisions are dependent on the actions or non-actions of other parties.” Since then, Game Theory has become an enormously important discipline because of its novel mathematical properties and its many applications to social, economic and political parties.” (Morton). It is necessary that different strategies are utilized for different decision making situations which would significantly impact upon the rewards and profits of the firm in the long run. Pareto’s Optimality: This is to ensure that the values of the rewards should be balanced and it is not possible that everybody would win or nobody should lose. Pareto advocates the judicious division of the share in terms of related factors in terms of the individual’s level of competence, the people involved and the magnitude of the problem. It is considered as application of certain economic practices by which products or services could be made available to an individual or group of individuals without jeopardising, the interests of the other remaining individuals, or groups. It is necessary to note that a system may be Pareto compliant, but may fail to meet empirical standards of application in strategic decision making process. Therefore, it becomes necessary not only to consider the subjective aspects of Pareto Optimality but also its implementation and usage in needed context. There are instances when the Pareto optimality may be quite different in its exclusivity context. Two countries may have Pareto optimality within their own countries, but may not be able to utilize it, between themselves. (Kicks 1975). Nash considered value equilibrium in non zero sum game also. According to this theory, players would get more benefits by use of co-operative efforts, and espoused the cause of negotiation. In other words, the Nash Equilibrium presents that “If there is a set of strategies with the property that no player can benefit by changing her strategy while the other players keep their strategies unchanged, then that set of strategies and the corresponding payoffs constitute the Nash Equilibrium.” (Game Theory. 2007). Nash’s equilibrium proposes an efficient work of the co-operation that the Noah’s model serves to accommodate all the players or firms. If there are more number of firms involved, the degree of complexity also increases. This is because coping with n number of firms is more difficult with 2 or 3, since the aspect of consensus, after participative deliberations with all the partners are required in order to enforce a cartel decision. If there are misunderstandings between the players, it could vitiate the decision making process, and delay the task of collective decision making. This is the reason why the Nash Model advocates co-operation, consultation and decision making through rational deliberations taking into account, the interests of all the players and their perspectives on the various issues which need to be sorted out. Rather than create avenues for conflict and misjudgment, it advocates the use of co-operative efforts from all the parties. The various methods in which the Nash Model could be used is that the cartel sets up the prices below which the individual members may not be able to sell. The allotment of sales volumes and profits are dictated by the cartel and the members are perforce to obey it. Coming to the question of Prisoners dilemma, it is seen that the actions or inactions of one party could affect the other party. Therefore, it is best if both the players do not confess, in which case, each of them get only 1 year sentence. Another factor is that if both confess, their terms could be 10 years, so it is in the interests of both the parties that they do not confess their alleged guilts. The n person game is when there are more than 2 players involved. This theory is not so well developed as the other 2 player case. So far, it has been seen that only the subjective parts of this theory has been considered and no operative analysis has emerged. The N-person could take the form of the following: 1. Coalition: “Coalitions formation, widely studied in Game theory” (Chalkiadakis et al). Where a main player situation is developed and through this, coalitions emerge. In the case of cartels, where one firm is able to dominate the rest, the incentive to make and use cartels may be difficult because of the costs involved. In such a case, it would be difficult to sustain a coalition and the game thus ceases to be important. The game would only gain significance if and when the individual constituent members derive some benefits from them. 2. Side Payments: Sometimes, it may become necessary to give unofficial payments to member in order to get their co-operation and agreement to the coalition. 3. Imputation : Rewards made out to the players are termed as imputations as long as it meets the following two criteria : (a)Each member must get as much profit for himself where the other players are not co-operative. If this is not done, then some members may leave the coalition. (b)The net sum of the total rewards or profits to all the members is equal to the maximum they would receive by the formation of the Great Coalition, which has the membership of several individual members. However, one of the pre-requisites is that the Pareto Optimality be used: 1. Core : Each member receives its security level – by playing as a coalition they should receive a larger reward and receive the largest reward that would available e for individual distribution honouring the Pareto optimality 2. Characteristic function: the worst scenario would be if the constituent members turn against the coalition. However, if one were to infer Pareto Optimality, this could become a constant sum 2 member collation game. 5. Domination : If Imputation I dominates Imputation J and there is a coalition C , it could be said that rewards to the members of Imputation I if every member of coalition C were to receive more from Imputation I than from Imputation J. 6. Solution: An N game could be said to have a solution if the following can be proved 1. If I and J are two imputations, if neither I dominates J nor J dominates I 2. A solution consists of set of imputation none of which dominates any other imperatives within the solution set which among them dominates excluded importance Thus from the above it is seen that the theory of Game is a complex and intricate procedure which depends to a very large extent, upon the variable and other considerations governing the problem under review. It is first necessary to find out regarding which type of games the problem falls under- whether it is co-operative or non-co-operative, symmetrical and asymmetrical, etc before decisions regarding its application and decision making could be made. Therefore, it could be seen that to a very large extent, the solutions to the game theory would lie in the fact that its applications have to be considered and applied in each level of activity and the solutions could be derived accordingly. Analysis and interpretation of the Game Theory: In what has been imbibed from the above, it is seen that the Games Theory has several applications in business economics, philosophy, statistical data making and other applications. The applications are wide ranging and they offer solutions based on the multivariate options available to the players in different situations and scenarios. When confronted with several business options with corresponding risks factors and benefits, it is needed for the firm or its players to choose the best option under the circumstances and get the maximum profits, or payoffs. It is also necessary that the different options need to be fully assessed and quantified, along with the relevant datas available in order to arrive at the optimum solution based after considering not only the strategies of the individual firm, but also the perceived strategies that may be adopted buy the rivals or competitors. This is because the options of the competitors have also got to be considered before any decision is taken. After considering the Pareto optimality, it is necessary to utilize this, as much as possible for achieving the maximum results. The aspects become more difficult since there are aspects of multivariate factors when more than 2 players are engaged. Therefore, in such cases it is necessary that necessary steps are taken for building strong and reinforced strategies that could be implemented on a long term basis for the optimum benefit of the players and also the firm. The idea behind Game Theory is that after considering all the risk factors and the optimization of the gains, rewards or payoffs the selected strategy, after considering the perceived strategies of the opponents or business rivals are operationalised for the benefit of the firm and its total profitability studies. (b)Discuss the implications flowing from the solution to an "n-person", "n-strategy", Non-constant sum game. Before attempting to answer this question, it is first of all necessary to know about n person, n strategy and non- constant. N person means any number of persons or players in the strategic game, that is more than 2 . The term n strategy means more than 2 or in other words, more than 2, or in other words, any number of strategies over 2. A constant sum game or zero game is when, the total positives of the winning player, is equalized to 0, due to the negatives of the losing player, and thus the positives and the negative tend to negate each other, and become 0 or no value. Since the total of all the plus values and the totals of all equal minus values negate each other, it is termed as constant or zero game. But if may happen that sometimes, due to the peculiar strategies adopted by the players, in different circumstances or situations, the sum game would be non –constant or not zero. Therefore what is being considered is any number of players, in any number of strategic games, with any number of strategic demands. Nash equilibrium is the most significant solution concept for games and under the mixed strategies; neither player has the urge to change his probability to match that of the opponent. A lot of research has been done that considers the solution to the determination of equilibrium. Therefore, it has become necessary to find such algorithm based on mixed problem for the determination of the equilibrium (Sandholm et al). There are four MIP formulations for finding out the Nash’s equilibrium and although in certain cases, the equilibrium may not be readily available, it is possible to arrive at a close approximation of the equilibrium point the four MIP are: Only equilbria are practicable Fines are imposed on strategies that are played with positive probability Fines are imposed on strategies that are played with positive regret Fine either the regret or the probability based on the strategy.( Mixed Integers Programmable method for finding Nash Equilibrium : Thomas Sandholm et al) The aspects of n person and n strategy is that there should b at least one Nash Equilibrium if one allows the mixed strategy. In such cases it is seen that they are not as easy or determinable as the 2 player theory. The implications are that in such cases, there is no random action to the strategic deployment of the other rival or competitor. Another factor is that there is a general tendency for lack of interest or application, in these kinds of mixed strategies. In such cases, in equilibrium, the Government is not concerned about whether it provides child care or for that matter, its choice of p. And similarly, the poor person, the n factor is not concerned about the level of its poverty or choice of q. (Game Theory. 2002). Nash’s equilibrium proposes an efficient work of the co-operation that the Noah’s model serves to accommodate all the players or firms. The degree of complexity increases if number of firms increase. This is because dealing with n number of firms is more difficult with larger number of firms participating, since the aspect of consensus, after participative deliberations with all the partners are required in order to enforce a cartel decision. The decision making and independence of the players could be jeopardized if there are misunderstandings between the players. This could lead to lowered degree of decisions making and delay in its implementation since the acceptance of all the parties are not there. This is the reason why the Nash Model advocates co-operation, consultation and decision making through rational deliberations taking into account, the interests of all the players and their perspectives on the various issues which need to be sorted out. Rather than create avenues for conflict and delayed responses and lowered decision making process, it prophecies the use of co-operative efforts from all the parties. The functioning of cartels are an excellent example of n situations, since the factors involved are not only the decision making of the parties among themselves but also 1 to 1 relationship with the main decision makers and board of management of the cartel. The Game Theory could typically deal with the OPEC (Oil Petroleum and Exporting Countries) they are a powerful cartel which determines the global prices of oil in the international markets. Here there are some large players like Kuwait, Saudi Arabia, UAE etc and also certain smaller players like Iran etc. The dominance of the larger players are there and therefore, it has become necessary for the smaller countries to form a sub group to protect their business interests. Saudi Arabia is the largest producer and exporter of oil in the world, but it has over the years consistently reduced its production in order to reduce prices and remain at par with the needs of the smaller OPEC countries. This is because if Saudi Arabia increases its oil output, the demand and price of its products would also increase. By keeping its long term interests in view, the Saudi Arabian Government wished to keep prices and production lower in order to protect the interests of its other members. Smaller countries do not have the infrastructure or investment capacities to produce to full capacity and therefore, it becomes difficult for them to compete with the bigger players. If big countries like Saudi Arabia, Kuwait etc, increase their production, it would become necessary for the smaller ones also to do so, in order to avoid larger production costs in their countries. This may not be possible. Bigger countries take up a long term view in terms of strategies for next 5 or even 50 years whereas for the smaller countries, it is necessary to think in terms of recouping their investments over the short period of time, in order to reinvest and earn bigger profits. Therefore it becomes necessary for OPEC especially to devise the Game Theory taking into account the Pareto Optimality in order to ensure that the interests of the weaker and marginalized members are not sacrificed at the altar of higher production and higher profits on oil trade in the international markets. It is therefore essential that Saudi Arabia, Kuwait, Oman and UAE, among the other big members, use the cartel of OPEC to subserve the collective interests of all its members, especially the weaker and smaller countries so that their economies are not adversely affected by the actions of the bigger players. The main idea of the Game theory as advocated by Nash Equilibrium is to allow the players to choose their own equilibrium and maintain it, by a collective and Co-operative efforts sub serving the interests of their countries and also the interests of other participating countries in the OPEC. This basic idea behind the use of cartels so that the economic interests of the countries could be served by the powers of collective bargaining and consensus. In the case of oil, it is of supreme importance, since oil prices are a major determinant of economy of the world, and even small variations in $ cost of barrels could seriously determine the economy, especially of the smaller and developing countries of the world. The fact remains that a lot needs to be done for the propelling of the economy through sound decision-making and its implementations after considering the common good of the nations concerned and also the members of the Cartel or Trade community Non constant game theory is more applicable to the modern world where the solutions are different depending upon the situational effectiveness and the management decisional making process this has also been seen in the Nash Equilibrium. But it is possible that players may sometimes make decisions which may not always be rational. A firm may not be certain or sanguine about the decision of the other party or firm and therefore, if decisions need to be taken, it has to be the least risk and most profitable option. But this is not true in all cases. There are often situations when decisions may become negative and the choices limited. The exercise of either one or the other may cause unpleasant and undesired action and yet an exercise of choice is needed. In such cases, it is better to avoid exercise of choice, since it would in the best interests of the firm and with lowered punitive repercussions. The Games theory is just based to deal with such kinds of emergencies in which it becomes necessary to deal with the least risk with best payoffs and that is a decision that has to be taken with utmost care taking into account the moves and strategies of the opponent and rivals. This is where collusion is also important since through collusions, the markets risks are reduced and payoffs substantially increased. However collusions have their disadvantages in that they may not be of a permanent nature and the domination aspect of one firm over another would also subsist. The Games theory deals with the situations of conflicts relevant to business enterprise. In static game plans, there are only two aspects- Win or lose whereas in dynamic games, the situation is that the profits may differ and different types of actions need to be taken. The Nash Equilibrium shows the equitable method of the optimal strategies that could be used to reach the maximum equilibrium. The Sub game perfect Nash is where the threats and dangers are averted and the strategies are judiciously adopted. The Baynesian sub game perfect Nash equilibrium deals with the updating of corporate beliefs and the use of the theory to marginalise the risks and maximize the profits. Thus the Baynesian Subgame serves its purpose of creating the best market opportunities by suitable relevant strategies for the firm. It needs to be seen whether the Game Theory as a deterministic model serves any purpose or not. It needs to be said that no deterministic tool or model is totally reliable or correct, and a lot depends upon the surrounding corporate environment on which it is operationalised and the desired results evolved and determined. A lot would depend, not only on the tool of Game Theory as such, but on how suitable and efficiently and user-friendly manner in which it has been used for the operational gains of the firm or the players. All deterministic and statistical tools are as good as the operational effectiveness and the method of its usage. A scientific tool needs to be in sync with the environment and also should serve utility to its users. In the case of Game Theory, it is necessary for the management to be able to diagnose the various options available to it , vis-à-vis its competitors and rival firms , the assumed strategies they may be following and how well this could be neutralized and used for the company’s ultimate advantage. In this case, it is seen that many companies adopt a standby strategy, leading its rivals to believe that this would be the strategy that they would be following in the future. Suddenly, the leader changes its strategy completely, leaving the rivals lurching and unable to decide what to do next. A simple example would drive home the point. Company A decides to launch its Consumer product in the market and works out a massive advertisement and publicity plans. The business rivals get wind of it and they also decide to launch rival products to cut down the market share of Co A and try to eliminate them from the marketplace, however, within a month or so, Company A withdraws from the market and immediately launches another product once the market has been captured by them. The business rivals do not know what to-do next, in such circumstances and are forced to retreat, and thereby, a major part of the market now falls in the hands of Company A which it exploits to good use. Having market savvy is not only the prime criteria. It is also necessary to be able to put it into good use and that is what Company A has just been doing in order to waylay the competitors and establish a dominant market image and market share. All these and other strategies could be accounted for in the Game Theory, including an in depth coverage of the risks, threats, profits rewards and payoffs each strategy entails. It is all the more important in the present context since geographical barriers are a thing of the past and there are competitive onslaughts in all major product or service lines. With the advent of globalization, the accent has been on delivery systems and the use of market opportunities for the best competitive advantages. Game Theory is important but it also needs to be cost effective and have distinct utility value. The market information that Game Theory is able to generate should justify its costs and efforts and also should be able to contribute to the term strategy of the company’s operations in the long run. It is also necessary that game theory should be able to disseminate market information and competitor’s plans and policies, but in these matters extreme care needs to be focused regarding the accuracy and reliability of the said information. It often happens that decisions are taken on wrong or inaccurate information, which creates more damage than good by the application of the Game Theory. Therefore the management needs to take into account the aspects of reliability of the source of information, its operational effectiveness and the fact that the said information could be utilized or modified or refined for detailed analysis regarding the future profitability and development of the firm and its market standing and future prospects. As has been earlier detailed the Game Theory basically deals with choosing between different supervening risks and attendant rewards, or payoffs. It is necessary that the management should evaluate the surrounding aspects governing the implementation of the Game theory, its suitability for the gains of the firm and the major players, and also initiate action for its implementation after considering all the relevant factors. The idea of Game Theory lies in the fact that it should be able to substantiate and reinforce management decision making to a large extent and should also be able to judge, with a reasonable degree of accuracy and genuineness, the effects of certain strategies, whether relating to production, pricing, quantum of sales and sale networks, besides a host of other critical areas where it could yield satisfactory results. It would be useful if it is able to aid and effectuate the decision making process and by and large, contribute to the economic well being and growth and development of the firm, especially in the fiercely competitive markets with rival firms making constant forays into its market shares and profit standings. Through the use of scientific tools and analysis, it is possible for present day firms to alleviate, if not eliminate, the high risks and stakes involved in present day market information collection and decision making, involving risks and uncertainties in the market place where each decisions is as decisive as it is challenging for the present day management practitioners. Bibliography CHALKIADAKIS, Georgios et al. Introduction. Coalition formation under uncertainty: Equilibria & the Bayenesian Core Stability Concept. Last accessed 29 November 2007 at: http://www.cs.toronto.edu/~gehalk/Papers/nonCoopJustBC.pdf Game Theory. (2002). How should we interpret mixed strategy equilibrium? Last accessed 29 November 2007 at: http://www.colorado.edu/Economics/morey/6808/game-lect.pdf. Game Theory. (2007). An Introductory Sketch: “Solutions" to Nonconstant Sum Games. [online]. Last accessed 29 November 2007 at: http://williamking.www.drexel.edu/top/eco/game/game.html KICKS, John (1975). 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