Game Theory

By Anisha Mata

Game Theory is a concept that we hear about a lot in the 21^stcentury. Its applications range far and wide, across disciplines and fields. A working knowledge of game theory can help you figure out the best strategy, whether that’s for a game like rock, paper, scissors or negotiating a deal with your competitor. So, let’s try to understand this concept.

Interesting Fact: 11 game theorists have won the Nobel prize for Economics for their contribution to Game theory.

Game Theory is essentially a model for decision making and strategy that involves weighing the benefits of each choice as well as the interaction between the participants. The main objective of game theory is to predict the optimal decision the participants will make in a particular situation, assuming that the players are rational and will strive to maximize their gains. 

Game Theory Definitions:

Let’s begin by defining a few words that are commonly used in Game theory.

• Game: Situations or circumstances, the results of which are dependent on the actions of two or more participants/decision-makers.
• Players:The participants that take decisions in the context of a particular game.
• Strategy: A concrete plan of actions that a player will take considering all circumstances of a game.
• Payoff/Gains: The payout that the player receives from arriving at a particular point after taking a particular decision or set of decisions.
• Equilibrium: The point in the game where all players have taken their decisions and an outcome is reached. 

Interesting Fact: According to game theory, the actions and decisions of each player affects the outcome of every other player.

Game Theory in action:

A very popular example of Game Theory is the Volunteer’s Dilemma.

The Volunteer’s Dilemma involves a situation in which one volunteer can make a small sacrifice that benefits everybody, or instead wait to receive the benefits from someone else’s sacrifice. The worst possible outcome is if no one volunteers.

Let’s take a situation where the water supply for an entire neighborhood has stopped. All the inhabitants are aware that the supplier will fix the issue if at least one person calls to notify them. If no one volunteers, the worst possible outcome is the fate of all participants and the water supply doesn’t resume until the supplier themselves realize the issue. However, if only one-person volunteers to call for public wellbeing, all the inhabitants benefit from it.

Social phenomena of the Bystander Effect and the Diffusion of Responsibility heavily relate to the Volunteer’s dilemma.

Another, more advanced application, of Game Theory is the Ultimatum Game.

In the Ultimatum game there are two players, namely, the proposer and the responder.  The game takes place as follows:

The players are given a certain sum of money, let’s say Rs. 100. The Proposer must propose how the Rs. 100 will be split. He/she can take Rs. 5 or Rs. 50 or any such division. However, the responder must decide whether he/she accepts the proposal. If the responder rejects the proposal, then neither of the two receive any money. 

In every situation, it benefits the responder to accept the proposal. The worst possible outcome in this situation is that neither of the players receive anything. Hence, the optimal decision will be to accept. 

Another famous example of Game Theory is the Prisoner’s dilemma.

Let’s assume that two criminals have been arrested for a crime. However, there is no solid evidence against them. So, in order to get confessions, the prosecutors decide to question them separately. This way, neither of them has any idea what the other has said. So, there are actually two decisions available to each prisoner, which means there can be 4 different outcomes:

1. Both prisoners confess and get a 5-year prison sentence each.
2. Prisoner 1 confesses but prisoner 2 doesn’t. Prisoner 1 gets a 3-year prison sentence and prisoner 2 gets a 10-year prison sentence. 
3. Prisoner 2 confesses but prisoner 1 doesn’t. Prisoner 1 gets a 10-year prison sentence and prisoner 2 gets a 3-year prison sentence. 
4. Neither of them Confess and they get a 2-year prison sentence each.

The best possible outcome would be that neither of them confess. However, since they cannot know for sure whether or not the other will confess, they will likely both end up confessing and getting a 5-year prison sentence each.

The prisoners take the decision best for them individually but worse for them collectively. 

In this way, game theory can be applied to a multitude of situations. 

Interesting Fact: During the Cold War between the United States and Soviet Union, strategic decisions taken by each nation was viewed as an example of game theory in real life.

Limitations of Game Theory:

Even though game theory has various applications and can help in making optimal decisions, it is not perfect. The biggest limitation of game theory is that it assumes that humans are rational players that always act in self-interest and for the purpose of maximizing utility. However, this is not always the case. Human Beings are social animals that at times cooperate and care about the welfare of others, especially those in our community. Game theory, at times, fails to take into account the social context in situations and the nature of the relationship between the players.

Interesting Fact:The phrase “tit for tat” is often used in game theory to describe a situation when a player responds with the same action used by the opponent in the previous turn. 

Game theory has applications in fields such as economics, psychology, evolutionary biology, warfare, politics as well as business. And despite its impressive advances in the last century, it is still a young and developing science, which will require individuals with multidisciplinary knowledge and skills to take it forward and expand the limits of human understanding.  And that’s why we’ll continue to explore game theory in a series of article coming up soon!