Introduction
Game Theory is the science related to strategic thinking and decision-making, developed and categorized by mathematical models, to determine the best possible outcome. Officially developed by John von Neumann and Oskar Morgenstern in the 1940s, these various “games” or strategies had been an integral part of human history since eternity. Game theory outcomes are determined based on the Nash equilibrium, which is a situation in which none of the players can improve their condition through strategic thinking. Here, in this blog post, we are going to discuss four such intriguing games that influence our everyday life directly or indirectly.
Game 1: Prisoner’s Dilemma
Suppose there is a robbery in a building. The local police arrested two individuals on suspicion. They are kept in two separate cells with no possible way of interaction between them. Now, the investigating officer went to the individual suspects and gave the following offer. If both confess, they get 3 years of imprisonment. If neither confesses, they get 1 year for a minor crime they committed earlier. But if one confesses and the other doesn’t, the one confessing is immediately released, while the other gets 10 years of imprisonment. So, the following situation arises:
From the matrix, let us assess the choices available. As they cannot contact each other, they should make choices based on assumptions about the other. So, if we consider that B has confessed, the best decision for A is to confess, as he will serve 3 years of prison instead of 10. Similarly, if B doesn’t confess, A still should confess, as he will be immediately set free instead of serving one year. The situation is the same from B’s side. So, the Nash equilibrium for this game is both confessing and serving 3 years.
Game 2: Game of Chicken
In this game, there is not one but two Nash equilibria. Let us consider a situation in which two drivers, A and B, are driving towards each other. They made the agreement that the one who swerves will be labelled a chicken. Now, if none of them swerves, they will crash, leading to serious injury and even death. Let us rate the choices based on the positive outcome. Let injury or death be 0, being called a chicken be 1, while the opponent gets 3, and if nothing happens, each gets 2. We get the following matrix:
Now, even though the safest outcome is both swerving, their individual situation can be improved. Also, neither of them swerving could be fatal. Thus, the Nash best outcomes arise when one swerves and the other doesn’t, thus leading to two different Nash equilibria.
Game 3: Stag Hunt
This game was devised by the French philosopher, Jean Jacques Rousseau. As per the game, hunters A and B can hunt a stag together, which is a large animal, or can hunt rabbits individually. But group hunting needs trust, as there is a chance of betrayal. So, let us give points to their decision based on the amount of success. If both successfully hunt the stag, we give 10 to each. If they individually hunt rabbits, each gets 2. But if one goes after the stag and the other goes after the rabbit, the one hunting the stag is almost destined to fail and will get 0, while the rabbit hunter gets 4, as he is the only successful hunter. Thus, the following situation arises:
From the matrix, we see that going to hunt stag alone is a very poor outcome, so the hunters have two choices: either to hunt rabbits individually or to hunt stag together, thus giving rise to two different Nash equilibria.
Game 4: Battle of the Sexes
Let us consider a couple where the man wants to watch an action movie together, while the woman wants to watch a romantic movie together. In both cases, they prefer watching together over alone. Now we rate their satisfaction levels. If they watch different movies, they both get 0 as they feel lonely. But if both watch the same movie, the person whose preferred movie is chosen is more satisfied and gets 2, while the partner gets 1, as shown in the following matrix:
Thus, here too, there are two equilibria where they watch the same movie.
Conclusion
Thus, we see how Game Theory plays an important role in understanding human interactions. Many such games describe many more complex decision-making. Studying these models can help us better understand the strategic thinking of individuals.
You can also read my original, more detailed article, published in theindicscholar.com, here.