# Game Theory (Prisoner’s Dilemma): Nash Equilibrium and Criticism

Game theory is based on human psychology and how humans make decisions. The theory was first introduced by a famous mathematician named John von Neumann and a famous economist Oskar Morgenstern in the year 1940. The layout of the theory is very similar to a game. It portrays an interactive situation between rational players or decision-makers. In this article, we shall see game theory in detail.

## Game Theory (Prisoner’s Dilemma): Nash Equilibrium and Criticism

The game theory presents a framework for theoretically determining social situations and strategies between players in a competitive setting. The game theory tries to explain the behaviour of rivals and their strategic decisions. The theory can be used in real-life situations to predict the outcome. The decision of one player influences the decision made by the opposition player.

The game also takes into consideration the identity of the players, their personal preferences and all the possible strategies they can adopt. The assumptions and requirements change depending on the situation. Game theory has evolved a lot over the years, and it is now used in many different professions and fields of life such as economics, business, biology, war, politics, and psychology. The theory is still under work, and it is developing with the progress of information available.

According to this theory, every action of a participant involved in the game has an impact on the decisions and outcomes of all the other participants. It is usually assumed in the theory that all the players are rational decision-makers, and they strive to maximize their payoffs.  There are some common and often-used terms used in game theory, which are as follows.

a) Game

It is the set of situations and given circumstances that influence the decisions of the players involved and ultimately their outcomes as well.

b) Players

The rational decision-makers and participants of the game are called players.

c) Strategy

The actions taken by the players of the game to maximize their payoffs are called strategy. It is a set of step-by-step actions that the players' design keeping in mind the circumstance and conditions of the game.

d) Payoff

The result or benefit the player receives after completing the game and receiving the outcome of the game is called a payoff. The payoff can be in quantifiable form, or it can be nonquantifiable as well.

e) Information set

The information that is available to each player regarding the circumstances and conditions of the game and most importantly about their competitors at any given point of the game.

f) Equilibrium

When both the players have made their decisions after rationally thinking and the outcome of the game has been reached, that stage is called equilibrium.

## What is Nash Equilibrium

Nash equilibrium is a state when the players of the game have made their decisions and they cannot further change their strategy or can do anything to change the outcome. The players have no regrets regarding their decisions regardless of the consequences. All the cases and games ultimately reach the stage of Nash equilibrium.

Usually, there can be more than one equilibrium stage in a game and the Nash equilibrium usually occurs in more complex games when the players have multiple options to choose from. The games tend to be repeated several times before it reaches equilibrium after experiencing errors and trials.

An example is when two firms are dealing with highly interchangeable products, and they want to set a profitable but competing price like soft drinks. Game theory can be used in various fields of life and many different professions such as:-

a) Economics

Game theory has proven to be revolutionary in the field of economics and has addressed many difficult questions and gaps that were present in economic models. Such as the neoclassical model, which failed to explain the situation of imperfect competition. This theory shifted the focus from a steady state equilibrium condition of the market to a much more diverse market process. Many economists also use this theory to understand the situations of oligopoly and try to predict the strategy and outcomes of the game.

In business, game theory has the most value and benefits. Business managers and analysts can use this theory to analyze the behaviour of market participants. Game theory is also useful for determining competing prices for products. Some other important uses of this theory for business gains include determining whether the business requires new products and inventions and retiring old products or only a new marketing strategy can help the business progress.

Businesses can also determine their competitors some businesses choose internal competition and compare their progress with their previous statistics, while other businesses choose external competition and compare their progress with other companies in the market.

c) Project management

Over time the game theory has evolved enough to prove useful in fields such as project management. Project managers must analyze the right strategy and plan for completing a project and by using this theory the project manager can also predict the behaviour of other players such as construction workers, investors, and rival construction companies.

## The Prisoner’s Dilemma

The prisoner’s dilemma is the most common example of game theory. The example is of two prisoners convicted of the crime. The prosecutors have little evidence against them. Hence, the officials decide that to make them confess and acquire more evidence against them they shall be removed from the solitary confinements and must be questioned separately. Both the prisoners can no longer contact each other. The officials offer them four options:-

• If both are to confess to their crimes, they will each receive a prison sentence of five years.
• If prisoner 1 confesses he will receive three years in prison and player two will receive 9 years (in case player 2 does not confess).
• If player 2 confesses and player 1 does not, in this case, prisoner 1 is to spend 10 years in prison and player 2 only gets two years.
• If no one confesses then both players get 2 years in prison.

The best choice for both of them is option 4 but both of them are unaware of what the other person is going to choose. There is uncertainty about whether the other person is confessing or not. In such a case it is more likely that both will confess and will receive five-year imprisonment. The Nash equilibrium suggests that under situations of uncertainty each player will make a choice that is good for them individually but harmful for them collectively.

## Criticism

Even though game theory represents realistic scenarios and is very practical in various fields, it still has shortcomings. In game theory, each action of the player is rationalized if it is in their self-interest. There is a big problem with this theory that there are a lot of factors that impact the behaviour of the players, and each element cannot be defined, limited, or accounted for in the overall outcome.

## Conclusion

To conclude, Game theory is a theory that predicts the strategy and behaviours of the players involved in the game. There are many different types of games which are used for predicting the outcomes of different situations. These games explain how the decision of one player can influence the behaviour of the other player in the game. There are also some major drawbacks in the theory like the assumption that all players are rational decision-makers.