Authors: Aryan Soni (21BCL005) and Dev Shroff (21BCL009)
Institution: Gujarat National Law University
Game Theory is essentially a mathematical field that aims to explain optimum strategic behaviour in social games, as well as economic and political circumstances. The theory is normative in the sense that it gives guidance; it is descriptive in the sense that it demonstrates social and economic events to be exactly identical with proper games of strategy.
Mathematicians John von Neumann and John Nash are creators of game theory. Business competition, political campaigns, animal and plant survival struggles, and so on can all be viewed as a type of ‘game’ in which individuals compete against one another. Game theory provides a framework for describing and analysing how people act in strategic circumstances. Any social problem can be formulated as a mathematical model of a game.
This paper explains why we all play a Nash equilibrium and why it is crucial. It also highlights the distinction between what is logical for society and what is rational for individuals. The paper goes on to discuss how game theory may be used to produce more efficient results in society. It also explains the features of game theory as well as its limitations.
KEY WORDS: Game theory, Nash equilibrium, Rational, Behaviour, Sociology
Initially, game theory was a mathematical and economic theory that predicted that human interaction will have game-like characteristics such as strategies, winners and losers, rewards and punishment, profits and expenses. It was designed to help people understand a wide range of economic activities, such as business, market, and consumer behaviour. The use of game theory to political, sociological, and psychological behaviours has risen in prominence in the social sciences since then.
Matching young physicians to hospitals for on-the-job training is a notable example of the application of game theory to reality in terms of constructing effective social institutions. Doctors receive their medical degrees after graduating from universities. However, before they may practise, they must first complete a residency programme, which lasts for a set number of years. The difficulty is how to pair such physicians with hospitals. There are both excellent and awful matches. Game theorists applied their understanding of game theory to create an ideal process for matching young doctors with hospitals.
Mathematicians and economists created the area of ‘game theory’ in the previous century as a tool for analysing both economic competitiveness and political conflicts. The following is how two famous game theorists, Robert Aumann and Oliver Hart, explain the attraction: Game Theory may be thought of as a kind of umbrella or ‘unified field’ theory for the rational side of social science, where ‘social’ is taken broadly to encompass both human and non-human participants (computers, animals, plants) … It does not make use of ad hoc constructions… It creates approaches that, in theory, may be applied to any interactive situation (Aumann and Hart, 1992, P. 3)
Some definitions of game theory are below:
1. Game theory is 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. [Lexico]
2. Games theory is an abstract and deductive model of policy-making. It does not describe how people actually make decisions, but rather how they would go about making decisions in competitive situations if they were completely rational. Thus, game theory is a form of rationalism, but it is applied in competitive situations where the outcome depends on what two or more participants do. [– Thomas Dye]
3. Game theory provides a fairly general framework to analyse a situation to tell you what kind of behaviour is observed in such strategic situations. Game theory has been applied through a number of fields, including economics, political science, philosophy, psychology, sociology, biology, and computer science. Is it possible to analyse a wide variety of social and economic problems using a unified framework? Any social interaction can be formulated as a mathematical model of a game which specifies players, strategies and payoffs. The question is if we can find a unified general theory to find the solution to all of those social problems. Is there any single solution concept which can be applied to all those social interactions? John Nash has found a unified principle which can be applied to all social problems – the Nash equilibrium.
iii. WHAT IS NASH EQUILIBRIUM?
According to Nash equilibrium, a game theory concept, the optimal finish of a game occurs when there is no reason to vary from the initial strategy. The Nash equilibrium is a game theory concept that asserts that the ideal outcome of a game is one in which neither player has an incentive to deviate from their chosen strategy after reviewing an opponent’s plan. Overall, changing acts will bring no extra benefit to a person if the techniques of the other participants stay unaltered. In a game, there might be numerous Nash equilibria or none at all. When other players’ decisions are taken into account, each player’s strategy is optimal in the Nash equilibrium. Every player wins since they all get the desired outcome.
Nash equilibrium is named after its founder, American mathematician John Nash. It is one of the most fundamental principles in game theory, and it seeks to define mathematically and logically what actions participants in a game should do in order to get the best possible outcomes for themselves. Expose each player’s strategy to the other players in order to quickly identify the Nash equilibrium or to determine whether one exists at all. If no one alters their method, the Nash equilibrium is proved.
One of the reasons Nash equilibria is considered as such an important concept in game theory is its applicability. The Nash equilibrium may be applied to a wide range of disciplines, including economics and social sciences.
iv. WHY ALL OF US MIGHT PLAY NASH EQUILIBRIUM?
There are various reasons why a Nash equilibrium could be used by players. There are three key causes, in my opinion:
1. It’s possible that players are really reasonable, and that all rational players calculate what they should do. They can sometimes achieve Nash equilibrium. This is the first and most important reason.
2. Reason number two is that before to starting the game, participants talk on how to play the game. Players gather and discuss how they should play the game. People are established in a certain Nash equilibrium as a result of this type of pre-play conversation.
3. The third reason is that participants may not be as sensible as they appear, and they may not have the opportunity to communicate with one another. They simply play the game, and the conclusion may or may not be Nash equilibrium. Then they play the same or a similar game again, and as they gain experience, they finally converge to a Nash equilibrium. That is the logic behind trial-and-error modification.
v. CHARACTERISTICS OF SOCIOLOGICAL GAME THEORY (SGT)
1. Game rules as social rules: In SGT, there is an explicit game rule complex that structures and regulates action and interaction, together with physical and ecological restrictions; there is an intricate theory of rules and rule regimes.
2. Diverse types of actors in varying roles: Actors as creative, interpretive, and transformational entities (with a ‘bounded’ level of reason). Additionally, because they are susceptible to normative and institutional environments, they have the capacity to be moral creatures.
3. Games are socially embedded: Games are socially entrenched, with normative, relational, and institutional settings defined and considered. Actors’ social ties have a significant impact on how they interact with one another.
4. Possible game structuring and transformation: External actors with sufficient power and/or game participants can reorganise and even alter a game, such as transforming a zero-sum game to a coordination game or a coordination game to a competitive or zero-sum game.
5. Communication actions: The rules governing action opportunities in a game define the circumstances and channels of communication. Different types of communication, as well as their uses and functions, have an impact on game processes and results, such as giving information or influencing others’ opinions and judgements. Deception and fabrication may be used in communication.
6. Limited capabilities of cognition, judgment and choice: Multiple values and norms, as well as other standards, can lead to inconsistency, incoherence and difficulties when they do not always fit together in a particular circumstance. Consistency and coherence are social constructs that are vulnerable to change.
vi. DIFFERENCE BETWEEN WHAT IS RATIONAL FOR THE SOCIETY AND WHAT IS RATIONAL FOR EACH INDIVIDUAL
One of the most essential themes of game theory is that collective rationality differs from individual rationality. It frequently differs from individual rationality. That is, what is good for society is not always or even frequently equal to what is beneficial for each person. We must work together to achieve what is best for society. However, each individual may have an incentive to avoid. For example, keeping the park clean is beneficial to society. As a result, we must work together to maintain the park clean. However, you may have an incentive to leave some waste behind, so what is good for society may not be the same as what is beneficial for each person.
Another example is that the Earth’s temperature is rising. It’s known as global warming, and it’s quite dangerous. It is better for our civilization if all countries work together to combat global warming. This is in the best interests of society. However, every country has an incentive to pollute. Again, what is good for society as a whole is not always the same as what is beneficial for each individual.
One of the most significant lessons of game theory is that collective rationality, or what is desirable for society, differs from individual rationality. Nash equilibrium, which arises from individual rationality, is frequently inefficient. However, in the absence of strategic or game theoretic thinking, we prefer to believe that collective rationality occurs in society. This huge misunderstanding previously occurred in economics, owing to Adam Smith’s magnificent hypothesis:
Adam Smith said, “Rational pursuit of individual happiness leads to a socially desirable outcome in competitive markets. If each individual seeks to his or her own happiness, in competitive market wonderfully those selfish behaviour leads to socially optimal outcome.”
vii. HOW TO ACHIEVE EFFICIENT OUTCOMES THROUGH GAME THEORY? T
here are three broad approaches to achieving efficient societal results; (i) The first is simply to alter the game’s rules and create social institutions. Create optimum trade rules such that the Nash equilibrium is efficient in the first place. (ii) The second method involves the use of legally enforceable contracts. (iii) The third approach is to use long-term relationships.
Game theory informs you that if the rules of the game are given, and the game is supplied, game theory predicts what sort of behaviour will occur. This is the fundamental prediction of game theory. The kind of outcome is observed under a given set of rules is described by game theory. You can answer this question backwards using your understanding of game theory. As a result, you get off to a strong start. Now the issue is, what are the game rules that result in such a positive outcome? You may use your understanding of game theory to create the rules of the game such that the outcome is favourable. You may carefully build the system, institution, or trade rules using game theory expertise so that individuals have an incentive to attain a desirable end.
The second approach to get a desirable outcome in society is that the system itself may be inefficient, in which case participants may lack an incentive to cooperate. People can compel an efficient conclusion by forming a legally enforceable contract. You can enter into a legally enforceable contract to compel a good outcome in situations where individuals have a motive to deceive. An employment contract, for example, defines the terms and conditions. The employer or employee may break the terms and conditions if the contract is not in place.
What alternative means of preserving collaboration may there be? You may make use of long-term relationships. This is a less expensive and more flexible option than a legally binding contract. Individuals may be motivated to cheat at efficient points or cooperate if there is a positive reward from cheating. So, in a long-term partnership, it is beneficial if individuals cooperate. However, because he may cheat and get anything today, each player may have an incentive to stray. However, if he cheats now, the worth of your future connection in the long-term partnership is ruined.
viii. LIMITATIONS OF GAME THEORY
1. Game theory, like other economic theories, is based on a variety of assumptions, one of which is that the participants are rational and intelligent. Game theory ignores a player’s social context, on which his behaviours are highly dependent. As a result, these assumptions are severely faulty.
2. Another issue in this theory is that it ignores the reality that in order to make logical conclusions, all accessible evidence must be available. The players do not have firsthand knowledge of the situation. In this worldview, norms, morality, and ethics have no place.
3. Another disadvantage of game theory and Nash equilibrium is that they require knowledge of one’s opponent’s strategy. If a player is aware of their opponent’s strategy, a Nash equilibrium can only occur if they choose to stick with their current strategy.
4. In most situations, such as a conflict, whether military or commercial, an individual has limited information about the opponent’s strategy or planned outcome. Unlike the dominant strategy, the Nash equilibrium does not always result in the optimal outcome; it just signals that a person chooses the best approach based on the available information.
Game theory has been hailed by social theorists from many different fields as a framework that can unify the social sciences on a bedrock of mathematical reasoning, relegating all previous attempts to provide a unifying framework for economics, political science, anthropology, organisation theory, and so on to social science’s pre-history. Game theory provides a dependable set of social science concepts and tools for defining, analysing, and understanding a wide range of interaction events. The techniques have previously shown beneficial for exploring and modelling a wide range of interaction processes such as cooperation, conflict, and negotiation.
Game theory has been applied in a variety of circumstances where the choices of the players interact to impact the outcome. The theory supplements and extends the traditional theory of probability by emphasising strategic decision-making aspects or characteristics controlled by the players rather than pure chance. It has been used to forecast the formation of political coalitions or business conglomerates, the best price to sell products or services at in the face of competition, the power of a voter or a bloc of voters, who to select for a jury, the best location for a manufacturing plant, and the survival behaviour of certain animals and plants.
It would be astonishing if any one theory could cover such a vast array of “games”, but there is no single game theory!
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