# Game Theory in Economics

As an introduction to Game Theory, an important concept in Economics, let’s take an example.

Put yourself in the shoes of Walter White from Breaking Bad (a professor-turned-drug-lord) and you have an accomplice (Jesse!) in your sweet little crime.

You are under investigation by the DEA (Drug Enforcement Administration) after they managed to trace the whole gamut of illegal activities you were involved in over the period of last two years. But they have insufficient proof and hence they require a testimony from either of you to go ahead with the prosecution.

Both of you are interrogated separately and do not come in any kind of contact whatsoever. You don’t want to end up rotting in jail, obviously. Now here are the rules of the game decided behind your back:

1. If you plead not guilty and Jesse confesses (defects), Jesse will be released and you might have to stay in the jail for twenty years.
2. Similarly, if Jesse pleads not guilty and you confess, you will be released and Jesse might have to stay in the jail for twenty years.
3. If nobody makes any implications and hold their ground (i.e. both co-operate), both might receive the maximum sentence of six months (good!)
4. If both of you decide to plead guilty and implicate the other (i.e. both defect), both will receive a sentence of eight years (not so good).

The complicated situation cited above is an example of a game analyzed in game theory, called the prisoner’s dilemma.

## What is Game Theory?

Game theory attempts to take into consideration the interactions between the participants and their behavior to study the strategic decision-making between rational individuals. It tries to find out the actions that a “player” should perform which would maximize his chances of success mathematically and logically.

Actions by everyone involved directly alter dynamics of the game, and hence the players are all interdependent. The games can be broadly classified into two categories: zero-sum and non-zero-sum. In zero-sum games, the loss of one is gain of another. It is not the case in non-zero-sum games, there can be a net gain or net loss.

‘Game’ is defined in a way that ensures feedback from the surroundings — if you are preparing for a stellar MBA interview, the response from the AdComs should be factored into your preparations. There might be chances of both cooperation and conflict! Another important feature is — you will learn from the experience and modify your strategy accordingly for the next one.

John von Neumann is the pioneer of the field of game theory. It is distantly related to the rational-agent model in traditional Economics and gave an impetus to Bernoulli’s theory of utility. There are two main branches of game theory: cooperative and non-cooperative.

As the name suggests, in the cooperative branch a coalition is present between players and the competition is between coalitions of players. Non-cooperative branch of game theory deals with purely rational (and selfish) behavior, in an effort to achieve one’s goals.

## The ‘Nash Equilibrium’

The famous mathematician John Nash showed the following: in non-cooperative games there exists an equilibrium at which no side has any rational incentive to change the chosen strategy even after running through all the choices available to the opponent(s).

The movie ‘A Beautiful Mind’ is based on his life and if the movie is to believed — the insight for game theory struck him when he observed that all his friends hit on the most pretty girl around, and he decided that he should hit on the second or the third prettiest to improve his chances (also to the benefit of everyone involved). A less pretty girl is indeed better than no girl at all!

[Please note how all the boys will automatically gravitate towards girls according to their own ‘social order’, and also the side-fact that they have no incentive to change their strategy after knowing what their ‘competitors’ planned to do. An efficient and elegant solution indeed!]

By mathematically proving that an equilibrium point exists, John Nash showed that important economic, political or social interactions can be hinged on desirable outcomes without the need for any contracts.

## Examples of Game Theory

There are multiple real-life examples for understanding the basic concept of game theory. Let us take up a simple one: Apple and Samsung involved in a ‘game of advertising’. As both firms have a stable market reputation, the advertising costs are a direct drain on the net corporate profits.

If both do not advertise, their profits will remain the same (with many simplistic assumptions, including that there are no other competitors).

But advertising budgets are assigned in both the firms so that they do not lose market share to the competitor (spending on advertising is a good strategy for both irrespective of the decision taken by the competitor).

The same analogy can be comfortably replicated for the US-USSR cold war, in which both the nations seemed to be hell bent on adding more nukes in their arsenal.

Another common example that we see in everyday life is related to public goods: if all the residents of a society decide to become good citizens and decide not to throw trash in the open— the society benefits as a whole (even the property rates might go up!).

But an individual might behave in a rogue way (selfish?) by throwing trash in the open— the cost of cleaning is borne by the whole society. This also extends to the free-rider problem and tragedy of commons.

Game theory has a variety of applications in diverse fields — economics, business, political science, biology, computer science and even philosophy. It has helped and is currently helping strategists of every kind all over the world to better design their environments, to suit their overall needs.

We are constantly ‘in the game’ — our life is impacted by the actions and decisions made by others. And here is a thought that might as well be the ultimate philosophical rhetoric originating from game theory: “We can create a better world by becoming better human beings ourselves”.

## Other important topics in Economics

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1. Bharat says:

Keep up the good work.

2. Priy anshu says:

The article presents a nice illustration of the prisoner’s dilemma but one important omission has been made. The payoffs from the choices are not decided behind their backs but it is known to them. And both of them know that the payoffs are common knowledge. Refer to Hal R Varian, Intermediate Microeconomics, Game Theory.

3. nishanth reddy says:

Why property rates go up if we behave good

4. Tyion says:

This is wonderful illustrations….. Keep it burning.