- Game theory is based on an abstract form of reasoning arising from a combination of mathematics and logic. Nearly all game theorists agree that the theory with which they deal is addressed to what is rationally correct behavior in situations in which actors engage in interaction in the form of a game with specific strategies, goals and preferred outcomes.
- Here the actors are trying to win or maximize gain or minimize loss. Game theory in modern time is also applied to other social sciences, not only in psychology and economics.

## Game Theory

- Game theory provides a number of advantages for the analysis of international relations. It requires that a conflict situation or decision process
**be examined from the point of the utilities and disadvantages that alternative courses of action are offered to each participant.** - Since it postulates a setting in which both sides make rational calculation of their own self-interest, game theory offers the opportunity of viewing one’s antagonist as a competent contender. Advocates of game theory have tended to argue that if a problem is genuinely understood it can also be represented by a mathematical model. But its opponents have countered by saying that such reduction of a problem results in
**oversimplification and sterility.**

### Exponents

- The theory of games was primarily propounded by mathematicians and economists.
**Neumann and Morgenstern**developed this theory in the sphere of economics. Later on it was applied to many fields of social science including international relations with modifications.**Shubik, Schelling, Rapoport, Deutsch, Riker**etc. take recourse to this theory for explaining international politics.

### Assumptions

- Game theory is mathematical and deductive in form and tenor. It relies on some axioms and assumptions. Conflict situations are treated as games and strategies are chosen logically using these axioms and assumptions. Solutions are derived from deductive reasoning.
**The game theory assumes these five elements**:**STRATEGY**– A skillful plan of the previously decided set of moves to be taken as and when the expected moves of the other side requires them. The strategy takes into account the potential behavior of opponents and assumes that within limits of particular situations the range of strategy is not unlimited.**PLAYERS**The game theory assumes an opponent and no game can be played without the players. Political games cannot be played single-handedly.**RULES**that regulate any game.**PAY-OFFS**It refers to what the game is worth at the end. There is usually always a pay-off. Each player tries to maximize his own payoffs while keeping in mind the fact that he must act in the presence of other players with conflicting or at least divergent interest whose choices will partially determine the outcome and pay off of the game.**INFORMATION**The amount of information available and the mode of signaling would significantly influence the strategies of rival players.

- The purpose of the game theory is first to formulate principles which could specify what is rational behavior in certain social situations and second to formulate on the basis of those principles the general characteristics of that behavior. The theory develops mathematical formulations about choice making among alternative courses of action when it is impossible to control all the factors which govern the outcome because of the actions of others.

### Kinds of Games

- There are different kinds of games on the basis of number of players and pay-off structures. Game of two players is called
**zero-sum game**whereas game of more than two players is known as**n-person game.**Then, there are**variable-sum games or non-zero-sum games or mixed motive games.** - The variables-sum games are further divides into two sub categories.
- Game of’chicken’
- Prisoner’s dilemma’.

#### Zero-Sum Games

- In situations in which the total of the
**‘pay-off**is fixed, clearly the gain of one player must be at the cost of the other. These are the so called fixed-sum games’. The player decides on the basis of**MINIMAX or MAXIMIN**concept Each player aims at the highest possible gain at the cost of the highest possible loss of the opponent but will accept the smallest possible gain if he knows that this is likely to be the most that he can obtain. - Conversely; if a player cannot avoid losses be will naturally seek the relatively smallest loss and his opponent will have to limit his expected gain accordingly. If the two players rationally choose the worst of the best and the best of the worst respectively, a stable solution called a
**‘saddle point’**is occasionally found.

#### Chicken Game

- The game of mutual threats in situation in which two drivers drive fast cars directly at each other. Each driver has two choices: to swerve or not to swerve and the one who swerves is disgraced as
**‘chicken’.**While the winner is acclaimed as a hero; if both continue; they clash; if both swerve simultaneously; neither wins but both avoid disgrace.

##### Applicability to International Relations

- The Chickph game is analogous to crisis confrontation between America and Russia. The decision to swerve could be thought of as stepping back from the brink of nuclear war. While refusing to swerve can mean pursuing a given policy with total resolution even at the risk of nuclear war.
- The dominance of the swerving strategy within the game of Chicken offers an aid to understanding why a nuclear peace has been maintained between the two super powers in the post-war period. It also illuminates the kind of logic that may haw applied at the time of1962 Cuba crisis. When after their eyeball to eyeball confrontation with the United States, the Soviets gave in, suffering a certain loss of face but avoiding nuclear war.

#### Prisoner’s Dilemma

- There is another game that offers thought provoking insights into the nature of international relations but that does not provide the possibly dangerous lessons of Chicken. Prisoner’s Dilemma has been stated in a variety of forms and with differing numerical utilities but it too is a game whose essentials remain similar throughout the various descriptions.
- Two suspects are arrested and separated. The public prosecutor is certain they are guilty of a specific crime but lacks evidence sufficient for conviction in a trial. He tells each prisoner that each has two alternatives: to confess to the crime the police are sure they have committed or not to confess.
- If both do not confess then the prosecutor will book them on a minor trumped up charge such as illegal possession of a weapon and they will both get relatively minor punishment(one year in jail);
- If both confess they will be prosecuted but he will recommend less than the most severe sentence five years each.
- If one confesses and the other does not then the confessor will get lenient treatment for turning state’s evidence (three months imprisonment) where as the latter will suffer the maximum sentence (ten years).

- It is found that because each prisoner wants to maximize his own utilities, his rational strategy is to confess. The rational or dominant outcome is that both prisoners confess and both get five years.
**The rational outcome is not the best outcome.**Were they both to remain silent they both could spend only one year in jail instead of five.

##### Applicability to International Relations

- The above lesson is immensely revealing when applied to international relations because it can show how a situation may lock two participants into conflict regardless of their individual wishes and even though both may be neither evil nor stupid. A model of the US-USSR arms race provides a good analogy.
- If the US chooses low arms spending, the worst possible outcome for it is that the USSR will continue high arms spending and thus obtain a strong military and political advantage internationally. If the US chooses high arms spending, the worst possible outcome is a mutually costly arms race. If the US chooses low arms spending it will be seriously disadvantageous. Similarly USSR chooses high arms spending regardless of what US does. The dominant outcome is an arms race.

## System Theory by Morton Kaplan

- Systems approach in international politics is based on the systems approach of David Easton. It is also influenced by the general systems theory. General systems theory suggest the utilization of the concepts of different disciplines. Systems approach in international relations is based on the fundamental concepts of the system approach in general. However systems approach (in IR) is often criticized that it does not include even the fundamental features of systems approach.
**Stanley Hoffman**–**‘Systems approach is a huge misstep in right direction’.****Morton Kaplan’s objective:**He wanted to give**‘grand theory’**of international relations. A theory as universal as Newton’s law of gravity. The theory which is capable of explaining past, present and future of international politics. Hence he developed different models (total 10) to explain the past, present and future of international politics.

### Models by Morton Kaplan.

**Balance of power model.**- International politics from 17th century till the end of 1st WW can be understood through balance of power model.
**Features:**Security Dilemma, Multipolar world order, absence of international orders… (explain from billiards ball model.)

**Bipolar model (Later on named as Tight Bipolar model)**- When there are two superpowers, status of other states is like satellites. The entire concentration of power is in two poles.

**Loose Bipolar model.**- 3rd Actor emerges. It weakens the magnetic force of the superpowers

**Very Loose Bipolar model.**- Very loose bipolar suggests further loss in the power of attraction of the poles. Satellites start jumping out of the orbits.

**Universal Actor model.**- Poles vanish, world government comes into existence. All states come under the universal actor. (Hypothetical model).

**Hierarchical systes.**- When all states come under single state. e.g. USA or Unipolar world.
- It is opposite of universal actor model.

**Unit Veto Model**- It means all states posses equal capacity to destroy each other.

**Incomplete nuclear diffusion model.**- Around 14 to 15 states posses nuclear weapons.

**Detente system****Unstable block model**- It is opposite of Detente model. Detent show relaxation of tensions, unstable block model show high level of suspicion and rivalry among superpowers. Return of cold war. It symbolize a very dangerous situation.

### Critical Evaluation

- According to
**Stanley Hoffman,****‘systems approach is a huge misstep in right direction.’**It is a strange parlour game, it does not capture even the basic stuff of international politics. - The models do not have analytical of explanatory importance. Some models are hypothetical, some models are outdated and the current international politics does not resemble any of the model.
- The purpose of the discipline of international politics is to find ways to establish peace. This model has no such relevance.
- Model does not fulfill even the basic requirements of systems theory. It neither explain the environment, not structures, functions, input output processes. It does not show the role of domestic variables in international politics.