What Is a Zero-Sum Game? Definitions and Examples for Students
Based on true logic and analytical decision-making, the theories and steps of Game Theory are applied to various sources in real-life. Both mathematical and non-mathematical fields make use of Game theory to acquire relevant information and make the event a success. Sounds a bit vague but let’s take a deeper look at the concept of Game theory with suitable examples in the following sections.
Game Theory - Definition and Important Pointers to Learn
Game theory - definition is quite straightforward in its meaning. It is a practical math concept on how a certain game is played using effective strategies. From every point of view, the player’s information such as timing, type of move, the direction of motion, the order of playing, etc. are some of the Game theory’s important determinants.
The Game theory is based purely on strategic playing. Balancing the diplomatic behaviour along with awareness about the rules of the event and each candidate participating is vital to winning the play.
The essence of a given game lies in its interdependence of the next move of each player.
The game theory falls under the Probability Distribution majors.
This interdependence is classified into 2 forms - Sequential and Simultaneous.
Being cautious about the other player, the person will move and arrange entities in a game within a specifically ordered fashion. This is called sequential game theory.
On the other hand, the simultaneous game theory involves playing all in 1 go, not accounting the moves or actions of the other player (s).
Game theory is referred to as the ‘science of strategies’.
The only best possible outcome is expressed only when the game theory is balanced between logic and mathematics.
This mathematical tactic deals with both conflict and cooperation among each player. Hence, rational decision-making can affect a player’s interest in their part.
What is the Theory of Zero-Sum Game?
Zero-sum game or the ‘constant-sum game’ deals with increasing or reducing the resources available during certain games. As the name says, the addition of every strategic combination will sum up to zero (0) only. Hence, the benefits gained by each player adds to zero. So, if 1 opponent wins, the other exact will lose the game.
Unlike the definition of game theory, here in a zero-sum game, there is an opposition between the interest of 2 players.
If a player wins the match but it is not probable to state if the other wins or not is termed to be the ‘non-zero-sum game’.
The Applications of Game Theory
The idea of studying sociological, psychological, and political framework or something or someone, makes the application of game theory important in the field of social sciences like the population census, psychiatry, sociology, social work, etc.
From understanding the behaviour of firms and agencies to consumers and the market, this theory is preferred in the fields of economics and certain business sectors as well.
Even a few analysis-related subject-matters are discussed inside the fields of biology and zoology.
Game theory is useful in the learning of animal and human behaviour.
Not only is the application of game theory defined in the understanding of general behaviour in elements. Even developmental, normative, legal and ethical behaviours and motives are also assessed and judged with better precision using the game theory.
Let us finally close our learning with a simple example of game theory in the context of the most classic example of history deemed the ‘Prisoner’s Dilemma.’
The Classic Instance of Game Theory
The imaginary case of the Prisoner’s Dilemma involves 2 individuals stealing a vehicle and is held up. Upon further enquiry, it is also found that both the men were involved in a bank robbery issue as well. 2-years imprisonment is going to the judgement here.
Both the persons were put in different jails. Till now, both the men are suspected for the bank robbery case. Since the prisoners are jailed in 2 separate chambers, the line of communication between the 2 is already cut.
Now, with the investigation procedures forwarded, the following 2 response situations are about to be given for the 2 prisoners:
3-years of imprisonment, if both accused of bank robbery and vehicle theft.
1-year imprisonment for the one confessing the truth behind bank robbery. The other unanswered is given the order for 10-years imprisonment.
The table below includes the possible solutions/outcomes to be expected from both.
2-CONFESS
2-DENY
1-CONFESS
Both punished 3 years
Prisoner 1 punished 1 year
Prisoner 2 punished 10 years
1-DENY
Prisoner 1 punished 10 year
Prisoner 2 punished 1 year
Both punished 2 year
The table displayed above is drawn based on Game theory. And now, the likely choice is to not accept the theft. In that scenario, both the prisoners would serve 2-years imprisonment. However, it is nearly impossible to say whether the other person will confess or not. Hence, the chances are high for both the men to get confessed and serve the 3-years jail sentence.
Conclusion
Game theory is a practical concept and is regarded as the science of strategies. Game theory involves logic and mathematics. There are 2 forms of playing a game - sequential and simultaneous. Sequential gameplay takes account of the other player’s move and simultaneously is randomly ordered. Fields such as psychology, biology, statistics, social sciences and more use game theory. The ‘Prisoner’s Dilemma’ is the famous case of interpreting the outcomes using game theory.
FAQs on Game Theory: Concepts, Strategies & Math Applications
1. What is Game Theory in mathematics?
Game theory is a branch of applied mathematics that provides a framework for analysing situations of strategic interaction, known as 'games'. It studies how rational decision-makers interact and make choices when the outcome of their decision depends not only on their own action but also on the actions of others. Key concepts include players, strategies, and payoffs.
2. What are the fundamental elements that define a 'game' in game theory?
Every situation modelled by game theory consists of three fundamental elements:
- Players: The rational decision-makers involved in the game.
- Strategies: The complete set of possible actions or moves each player can take.
- Payoffs: The outcome or consequence (like a win, loss, or numerical value) that each player receives for a given combination of strategies chosen by all players. This is often represented in a payoff matrix.
3. How is mathematics, especially probability and matrices, applied in game theory?
Mathematics is central to game theory for modelling and solving strategic problems. Matrices are commonly used to represent the payoffs for all players based on their chosen strategies (a 'payoff matrix'). Probability theory is crucial for analysing mixed strategies, where players choose their actions randomly based on certain probabilities. Calculus may also be used to find optimal strategies and equilibrium points in more complex games.
4. What are the main types of games studied in game theory?
Games in game theory can be classified in several ways, including:
- Cooperative vs. Non-Cooperative: Based on whether players can form binding agreements.
- Zero-Sum vs. Non-Zero-Sum: A zero-sum game is one where one player's gain is exactly another's loss. In non-zero-sum games, players' interests are not always in direct conflict, allowing for mutually beneficial outcomes.
- Simultaneous vs. Sequential: Based on whether players make their moves at the same time or one after another.
- Symmetric vs. Asymmetric: Depends on whether the identity of the player matters in determining the outcome.
5. What is the difference between a pure strategy and a mixed strategy in game theory?
A pure strategy is a complete plan that specifies a single, deterministic action for a player in any situation they might face. The player decides on a move and sticks to it. In contrast, a mixed strategy involves the player randomly choosing from their available pure strategies according to a set of probabilities. This is often used when there is no single best pure strategy, allowing players to be unpredictable.
6. Can you explain the concept of Nash Equilibrium with a simple example?
A Nash Equilibrium is a state in a game where no player has an incentive to unilaterally change their strategy, given the strategies of the other players. For example, in the "Prisoner's Dilemma," two suspects are questioned separately. The Nash Equilibrium occurs when both confess, as neither can improve their own outcome by changing their decision alone, even though they would collectively be better off if they had both stayed silent.
7. What are some real-world applications of game theory?
Game theory has numerous applications beyond simple board games. It is widely used in:
- Economics: To analyse market competition, auctions, and bargaining.
- Political Science: To study voting strategies, international relations, and conflict resolution.
- Biology: To understand evolutionary strategies, such as animal cooperation and competition.
- Business: For strategic decision-making in pricing, product launches, and negotiations.
8. How does game theory help in making business and economic decisions?
In business and economics, game theory provides a mathematical model to anticipate the reactions of competitors to strategic decisions. For example, it helps a company decide on a pricing strategy by modelling how rival firms might respond (e.g., matching a price cut). It is also used to design effective auction mechanisms and to formulate strategies for negotiations, ensuring a business can make the most rational choice in a competitive environment.
9. What are the major limitations or criticisms of game theory?
While powerful, game theory has several key limitations. A major criticism is its assumption that all players are perfectly rational and always act to maximise their own payoff, which isn't always true in reality. Additionally, it becomes incredibly complex to model games with a large number of players or strategies. The theory often relies on having complete information about the payoffs and strategies of all players, which is rare in real-world scenarios.
10. Why is assuming 'rationality' of players a potential weakness in game theory?
The assumption of perfect rationality is a significant weakness because human behaviour is often influenced by emotions, psychological biases, social norms, and altruism, not just logical self-interest. Players might make 'irrational' choices, cooperate when the model predicts they shouldn't, or fail to calculate the optimal strategy. This gap between theoretical rationality and actual human behaviour can make game theory predictions inaccurate in certain real-life situations.
