Meaning of Games Theory:
Oxford Concise Dictionary of Politics defines game theory in the following words: “A game is any situation in which the outcomes (pay offs) are, the product of the interaction of more than one rational player. The term therefore includes not only games in the ordinary sense, such as chess and football, but an enormously wide range of human interactions”. Another scholar defines it as “a body of thought dealing with rational decision strategies in situations of conflict and competition, when each participant or player seeks to maximise games and minimise losses”.
“The mathematical study of strategies for dealing with competitive situations where the outcome of a participant’s choice of action depends critically on the actions of other participants” (COD). Theory of games is therefore a type of mathematical study to deal with competitive or sometimes conflicting situations.
The outcomes and strategies are interdependent which means that what strategy one participant will adopt will depend upon the strategy of another man or participant and in this way games proceed from one strategic point to another strategic point. Game theory is associated with human interaction and at the same time an objective to maximise profit or to rationalise the decision.
Thus, profit and decision are both crucial parts of the theory. To sum up, the theory of games has got maximum relevance in economics and substantial importance in political science in general and international politics in particular.
Origin of the Concept:
In the thirties and forties of the last century the idea of applying games to social science particularly in economics and politics originated in the minds of people. In 1932 P. G. Cambray published, The Game of Politics: A Study of the Principles of British Political Strategies. Perhaps this is the earliest and most methodical work about game theory. In 1943 Neumann and Morgenstern published Theory of Games and Economic Behaviour.
After Neumann and Morgenstern large number of scholars dealt with the subject and some of them are—Schelling, Riker, Kaplan, Raiffa etc. Game theory was being used with increasing frequency since 1960s. When the theory of games was used to study the power games or strategy of each big or superpower to counteract the move of another power or rival the game theory earned wider popularity and use.
It has been observed by many that the theory was originally used in chess game, parlour game or poker game. It is known that in all these games there are two or more players or parties and each party decides its own strategy so that it can maximise benefit. But the strategy of a party or player depends upon the decision-making, cooperation or strategy of another party. Thus, the theory of games is never a one way traffic.
One party cannot take any decision unilaterally. Profit or loss of the game depends upon the selection of strategy or decision making or cooperation. There is also a place of intelligence. After the Second World War the theory of games became, in fact, a strategic policy used for the analysis of international politics particularly the power politics between the two superpowers—USA and USSR.
Assumptions of the Theory:
The theory of games is based on certain assumptions which are to be stated for a clear understanding of the subject:
1. In the first place, it has been assumed that there must be at least two players because for any game this is the minimum requirement.’ The number of players may be greater than two and this depends upon the nature of game and willingness of the participants.
2. Here the word player is used in special sense. Player means decision-maker. The players of the game are concerned with the strategy or decision. Each player of the game is exclusively interested in arriving at a decision which will be beneficial to him.
3. The dictionary meaning of strategy is a plan designed to achieve a particular long term aim and the player of the game decides this type of strategy. Without deciding this strategy the player is not capable of playing. The theory, therefore, assumes that in every game there is a strategy and it is decided by the player of the game.
4. Rationality is still another assumption. It is assumed that the players of the game are guided by rationality which means that they always act rationally.
5. Another assumption is the player is quite aware of the alternatives which exist before him and he selects one or more than one alternatives from them. The rationality of the player enables him to select the alternatives.
6. While he selects the alternative/alternatives he adopts the rule of priority which means that in order of preference he arranges the alternatives and he selects one or two which he thinks would give him maximum pay-off.
7. Since the player is interested in pay-off he, it is quite natural, will make all sorts of attempts and apply the strategy to maximise the benefit and minimise the loss from the game. This approach of maximisation and minimisation is the core of game theory and it is called the strategy.
8. The pay-off received from the game will be in full conformity with player’s own interests or what he ardently desired. Naturally any amount of pay-off or any kind of pay-off will not be acceptable to the player.
9. The player is quite aware that in the game there are both loss and gain or profit or loss. So the player will decide the strategy and the strategy is what way or technique he will adopt that will give him maximum pay-off. It means that the player is not only rational but also intelligent.
10. In the game certain amount of uncertainty is involved. Although the player adopts strategy, rationality and intelligence in the game all these do not guarantee that his loss will be zero and gain will be maximum. This can never happen because of the fact that both gain and loss are involved.
11. The strategy is an undefined term. What type of strategy is to be adopted cannot be decided before hand. It depends on the progress of the game, attitude of other competitors and other, factors. We have already noted that the objective of the player is to maximise the pay-off.
But if the player is certain that this objective will never be achieved he will adopt the policy of damage control which means to minimise the loss. The assumption of the game is minimax policy. The term minimax may be briefly stated. By adopting strategy the player tries to lower the quantum of loss and keep the amount gain.
Application in Economics:
We have noted that the theory of games was originally devised to solve certain chronic problems which tormented the economy. We know that in the thirties of the last century USA was faced with an unprecedented crisis which is commonly known as Great Depression. Though according to Marx and his followers such sort of crisis is not uncommon in capitalism because capitalism suffers from contradictions which ultimately make way for crisis.
The capitalists were fully serious about the crisis and set themselves to the task of combating the crisis. At that juncture of time the theory of game was formulated by Neumann and Morgenstern. The economists were concerned with policy-making decisions which will save the country from devastating effects of trade cycle and depression and by doing this will ensure a smooth way for development. Marx was quite right in declaring that capitalism could not be separated from imminent crisis.
But he was perhaps not aware that the capitalist economy or liberal political system is capable of controlling the crisis. “The continuing crisis required immediate policy recommendations … but there are no agreed statement in the economics text books about the axioms of economic thought”. The tangible consequence of the new thought was the theory of games.
The propounders of the theory believed that since there were problems there were solutions. In other words, the theory of games is an important device to show the way how to come out of the crisis and depression which engulfed the economy.
Two Important Pillars:
The entire structure of game theory is buttressed by few pillars and two of them may be discussed here. There are also other pillars but they are not so crucial so far as the application of the theory in economics is concerned. One such pillar is rationality. We have already mentioned that rationality of the player plays a very vital role in the strategy of games.
In fact, the maximisation of gain largely depends on the rational handling of situation. A. Downs in An Economic Theory of Democracy has variously defined this concept because he believes that rationality practically controls the major part of the game.
A. rational man is one who behaves as follows:
(1) He can always make a decision when confronted with a range of alternatives.
(2) He arranges all the alternatives in the order of preferences.
(3) His preference rank is transitive.
(4) A rational man will choose those alternatives which will give him best results.
(5) In the new course of action a rational man will try to follow the previous experience.
(6) Rationality also implies that before taking any decision the person makes a thorough comparison of alternatives and situations.
Here it is to be noted that the concept of rationality is associated with consistency. In other words, when a man at one time acts rationally he will follow the same course of action. The supporters of this theory are of the view that economics highly thinks of rationality or of a rational man. During the period of economic crises the rational man takes cautious step and before he takes any decision he applies his rationality.
We shall now deal with maximisation which constitutes the core of the theory of games. Neumann and Morgenstern believed that when a rational economic man is faced with economic crisis his first objective would be to find out ways of how to tide over the crisis. There are number of alternatives laid before him and he will adopt one or two or combination of them, he will proceed cautiously and rationally and his attention will always be focused on the objective of the maximisation of profit/ pay-off/benefit.
While the rational economic man proceeds to maximise pay off, he may not achieve success because the economic problems are complex and their solution requires the interference of several elements or-factors which are not under the control of the rational economic man.
Under such circumstances the apprehension may occupy his mind that his maximisation of pay-off may not be successful and in that situation will he abandon the attempt? The exponents and interpreters of the theory are of the opinion that the rational economic man will try to see that if gain is not maximised the loss could somehow be minimised.
This is definitely an important strategy. The rational economic man or investor will see that when the maximisation of gain is becoming unattainable then the correct strategy would be to minimise the loss. Neumann and Morgenstern have arrived at this conclusion. It is to be noted here that the minimisation of loss is never the objective of player. It is the last resort.
Types of Game Theory:
The propounders of game theory have devised different types of theory of games and the most common form is zero-sum games of two persons. The game is played by two persons and this is a very simple type of game. Chess, bridge and poker fall in this category. In the two-person game it is played by two men only. Naturally, if one person gains the other person will incur loss. So what is gain to one may be loss to the other.
If one person launches an assault upon the other person and achieves some advancement, it means the loss to the other man. Niccolo Machiavelli (1469-1527) in The Prince advised the prince that it was the primary duty of any ruler to ensure the unity and integrity of the nation and to that end the prince must make all efforts which include to launch the first attack against his enemy and when he does ft he gets benefit and the other party loses. Let us take an illustration of recent time.
After the Second World War (1939-45) the world was divided into two camps—one was led by the United States and the other by the erstwhile Soviet Union. The advancement of the Soviet camp was tantamount to the loss of the American camp, and vice versa. This happened during the Cold War period from fifties to the mid-seventies of the last century. After the collapse of the Cold War the game of power died a natural death.
The interesting aspect of the Cold War period was both the groups or parties were involved in continuous rivalry. The victory of one party could not deter the other, rather it encouraged and instigated the other party or group to take a new strategy or adopt of policy that would produce favourable results.
Theory of games also involves ideological conflict. The Cold War was characterised not only by the game of power between the two groups but also by the ideological conflict between Soviet Union and United States. Former Soviet Union and her allies of Eastern Europe which represented communism while America and other members of the group stood for capitalism or liberalism.
The move of each party was designed to stall the positive arid aggressive move of another party in respect of ideological warfare. U.S.A. used the electronic and print media’ to prove the superiority and excellence of capitalism or liberal democracy. The Soviet Union did not lag behind. She distributed the literature of Marx, Engels and Lenin among the people of the Third World either at nominal price or freely.
In the type of zero-sum game as it prevailed after the S. W. W. the main parties were two—USA and Russia. In the American group there were UK, France, Germany (then West), Canada and other capitalist states. On the other hand, the Soviet camp included the communist states of Eastern Europe. Another variation of game theory is to be found in the conflict between Moscow and Beijing and it was ideological conflict.
But Washington’s support to China was in no term an ideological support for Chinese variety of Marxism-Leninism. The main purpose of Washington was to isolate Russia in international politics and gain ascendency in the vast field of world politics.
Needless to say that in many instances America gained over Russia which meant loss for Russia. In this model of zero-sum games the parties are America and Russia and the purpose of each is to gain over the others.
There is another type of games theory narrated by Karl Deutsch in his The Analysis of International Relations. This type is variable-sum (Mixed-Motive) Games. Deutsch says that though majority of the games fall in the category of zero-sum games model but in actual situation there are numerous various variations and one of them is variable- sum games.
In the opinion of Deutsch: “These are games in which the players not only win something competitively from one another, but also collectively stand to gain or lose something from an additional player. Such games are mixed- motive games for their primary players”. Such games are generally characterized by competition and coordination. Deutsch has cited an illustration.
In many countries revolts have been found to be erupted among the prisoners. Some prisoners defy the order of the prison guards and try to escape from the prison. The prison guards, to save their services, resist this move and the prisoners remain adamant and this leads to some skirmishes. In the melee some prisoners escape and this is their gain while others fail to do this and this is their loss.
The conflict between prisoners and prison guards has been interpreted as a type of game theory. There is another side. Some prisoners may oppose the attempt of their co-prisoners and this may favourably be treated by the prison authority. Here the point is no side gains absolutely and the loss is not absolute.
Application of Games Theory in Politics:
Neumann and Morgenstern have propounded various models of theory of games and subsequently a number of writers have applied them in politics. But the genesis of games theory reveals that the relevance of this theory is more pronounced in international politics than in domestic politics. Kaplan, Schelling and Riker are the prominent personalities. Kaplan and others believe that the theory of games is a very important tool for analysis of international politics.
Particularly the post Second World War politics of most of the countries can be fruitfully explained in terms of games. Every nation, specially the big powers, is busy in finding out strategy to cope with the move adopted by the rival powers. During the Cold War period the rivalry between the two superpowers was excessively animated by the strategy of games. The strategy taken by one power was swiftly followed by another power and this process heavily surcharged the international politics for more than two decades.
So long bipolarism prevailed in world politics and occupied a major section of this politics the theory of games was a very vital tool of analysing such political situation. It is believed that today’s international politics and power politics are synonymously used.
Though the bipolarism no longer prevails the multi-polarity of world politics has a strong and crucial relation with games theory. Whenever a big power ventures to take an action or tries to adopt a strategy that automatically comes under the aegis of game theory.
Numerous recent instances may be cited in support of our contention. In the present day international politics there are several big powers such as USA, Britain, Russia, and France. There are also some emerging big powers whose influence in international politics is no less important.
Some of them are India, Japan, Germany (today’s united Germany) and China. So the move of any one country is very often faced with the challenge of another country. In a world of multi-polarism there exist continuous moves and counter moves adopted by different powers to gain ascendency or to harvest maximum benefit from the power game.
Another offshoot of the application of game theory in international politics is in order to gain more, nations (particularly big powers) form alliances or coalitions and these are called military alliances. The chief objective is to control international politics and each nation takes a strategy so that its position gets enhanced.
So the rivalry among the power groups always remains a characteristic feature of world politics and so long it is so the theory of games will continue to be a relevant factor of international politics. It has been maintained by some that in today’s situation of world politics the formation of coalition or military alliances has become a general tendency and to make it successful a aspect of world, politics strategies are being devised continuously which demands the application of games. Hence we are of opinion that the theory of games has a very important place in international politics.
1. The theory of games is not a toy but a tool. The games act always as tool for arriving at rational decisions both in economic and political fields. It can be better stated in the words of Mackenzie, “A company may ‘play games’ by computer against a competitor or ‘against nature’, but to do so it must specify exactly, the rules, the information … and the strategy. In this sense, games theory is not a toy, but a powerful and rigorous tool for computation. The application to politics proceeds by relaxing the rigour and precision of the theory and by venturing into an area where measurement of pay- offs is possible only in gross terms. It is thus possible to maintain that political gaming is a toy, not a tool”.
Mackenzie uses the games theory both as a tool and a toy. Sometimes it works as a toy and sometimes tool. However, in what form it is to be used that depends on the user as well as circumstances. He also observes that even when it is used as a toy that may be useful heuristically.
2. Game theory works upon the assumption that in a simple game there are two players and the decisions of the players are based on their rationality and a moral attitude. But this assumption is highly faulty because how could we know that players possess adequate amount of rationality and they will remain amoral in the face of any eventuality. Moreover, there is no way of ascertaining the rationality.
This considerably clouds the whole concept of game theory. The mere fact is that the theory of games is based upon a faulty concept—rationality. It can neither be measured nor its existence is ascertained. Again it is not supposed that all the players will be rational, and in that case the success of the theory of games will be followed by a question mark. It is surprising that its sponsors have not thought it fit to highlight their aspect of the theory.
3. There is another drawback of the theory. Taking of decision depends not only on the rationality of the participants but also on the information they receive and it is claimed that the information is not always up to satisfaction. The players do not get first hand or correct information. This may blur the making of correct decision.
For correct decision, an important precondition is there shall exist an efficient and honest network of communication system and in many political systems this is found to be lacking. There is also another condition and it is the decision-making process depends upon the circumstances. The theory ignores it.
4. The theory of games rules out any possibility of interference of norms, values, ethics etc. The players are primarily concerned with the final outcomes even if these are devoid of normative values and ethical considerations. They always focus their attention on the strategy taken by the rival parties. In other words, the real situation is the determiner of the moves to be taken and in this way moral and ethical norms have been ousted from the jurisdiction of the theory of games.
When the theory of games is applied in international politics it assumes peculiar dimensions. The players of the game (here the big powers) pay very scant importance to the universal values such as ideals, morality, ethics etc. Their main concern is to defeat the opposition.
Machiavelli thought of such power politics and he advised his prince to follow that type of power politics which will have no connection with morality, religion and ethics. Today’s politicians are scrupulously following this same principle. But we do not deem it fit to be the follower of this technique. So we can say that the normative character of politics and theory of games, are in opposite direction.
5. The theory of games was originally devised for its application in economics. At least Neumann and Morgenstern had that intention. But a score of political scientists applied the theory in political science. The application of a theory in a particular discipline or branch of social science may have importance or relevance but the same theory may not have the same importance or applicability in other disciplines. This is the greatest drawback of the theory of games.
6. The concept is too naive to be applied in international or domestic politics. What is the end result of the game? One player takes a strategy and the other player counteracts that and in this way the game continues to proceed to infinity. Again, there is another problem.
The consequences of the game may not be accepted by the people and the decision taken by the player may be strongly resented by the general public. The theory of games does not say anything about it. The advance of the theory to infinity cannot be a helpful method for building up an acceptable theory. Any political process must have an end and the game theory frustrates us.
We have pointed out some of the major limitations of the theory of games. But these drawbacks should not induce one to jettison the concept in toto. Since the days of Neumann and Morgenstern different models of game theory have been devised by scholars and this suggests that the theory still enjoys a certain amount of acceptability. “Game theory” writes Deutsch “is still developing, and even the eighty- seven types of two party conflicts cited by A. Rapport have not yet been explored for their possible applicability to international politics. Game theory models for conflicts among more than two parties (N-person games) still need to be developed much further but already they incorporate much more accurately the realities of multilateral international relations and conflict”.
Karl Deutsch further claims that in recent years many researchers have developed new models of game theory which deal with new strategies and situations, and these new models have considerably enhanced the acceptability and applicability of the game theory. If so we cannot be any more suspicious about its narrowness or other limitations.
Finally, we are of opinion that no model in any discipline can claim hundred percent success or applicability and in that sense the theory of games is no exception. No theory of social science can claim complete acceptance by all sections of academic circle and the theory of games is certainly no exception. If so the theory of games is no exception.