A Glance at Game Theory

‘Game Theory is the science of strategy’

Game Theory is all around us, from the strategies economists use to predict the behavior of oligopolies to the moves you make in your game of chess. Our subconscious is constantly making decisions you might not even realize using the fundamental laws of game theory as a guide to optimizing the outcome in your favor. But what is game theory anyway? How does it work?

John Von Neumann was an American/Hungarian mathematician widely recognized at the time for his works on computers at Princeton and was one of the founding fathers of game theory. Along with Oskar Morgenstern, an Austrian economist, the duo in some sense ‘created’ what we now know as game theory and worked specifically on its applications in the field of economics.

Let’s take a look at the basics of game theory. Don’t worry; it's simple and just requires a bit of rational thinking.

First, let’s define what a game is. Simply put, a game is a set of circumstances with rigid rules that cannot be changed as the game progresses. An example of this could be chess, where the rules direct the movements of different pieces. The result of the game itself is based on the actions of two or more strategic, rationally thinking players. Each player, as game theory states, always strives towards the best outcome for themselves, however, this may vary based on the manner of game being played. More on that later.

Note that the ‘game’ can range from chess to war games, and the players can also be animals, hence the usage of game theory in fields such as biology to predict how different organisms interact with their environment and other animals.

Next, it might be useful to define outcomes and their repercussions or payoffs. Each ‘move’ or action a player takes has a certain outcome, which may be useful or detrimental based on the actions of other players. After each outcome, a player receives a payoff based on their action which can range from things such as monetary gain to utility. A bit confused? Well, an example of this could be seen in a game of monopoly. Let’s say you have just landed on a property near the middle of the board. Your choice to buy it or not is based on various factors which can be modeled with game theory, such as the likelihood of others landing on it. After you have bought the property, the payoff may be that of another person landing on the property and paying you rent. Keep in mind that the payoff can also be negative, such as losing utility or money. After a series of moves by everyone, the result of the game is affected by each action made by a player, and the player who has made the best moves throughout the course of the game wins.

Now that you have gained a basic understanding of game theory, let us examine different kinds of games based on 2 parameters, the first one being whether the game is cooperative or not.

If a game is cooperative, it means that two or more players can form coalitions and proceed with the game playing with the best interests of each other, dividing payoffs and supporting each other for the best possible result for both. The behavior in cooperative games can be extensively seen in oligopolies. Non-cooperative games exist when all players' moves are solely based on the principle to receive the highest payoff possible for themselves.

The second parameter to classify a game is whether it is a Zero-Sum Game. In a zero-sum game, the sum of all payoffs at any given time is 0, meaning that any utility or money a player receives is directly proportional to the loss of utility or money of another player. In a non-Zero-Sum game, many players can benefit at the same time, and the sum of all payoffs can vary. An example of a Zero-Sum game would be Rock-Paper-Scissors, in which when a player wins, the other always loses.

A diagram of game theory modeled with the popular game monopoly, showing the probability of players landing on certain properties.

Real life Applications

Game Theorists are present everywhere, be it in large corporations to analyze the behavior of rival companies or even advising the managers of football teams during a match by assessing the movements of players in opposition teams. However, did you know game theory was used in World War 2, aiding in the analytics and strategic deployment of troops to ensure the least casualties as well maximizing the effectiveness of attacks?

Even in everyday life, players in games such as chess will be actively using game theory to predict their opponent's response, and how to thwart it and even possibly make counterattacks.

Good game-theorists can even make extremely precise predictions on things such as the value of stocks and shares in companies based on data collected from past and current trends.

Cool Trick:

First, write the number 7 on a piece of paper, and put it in your pocket. Ask a friend to keep multiplying 1 by 2, 10-times (they should say something along the lines of ‘1, 2, 4, 8, 16, …’) until they reach 512. Next, ask them to choose a number between 1 and 15 and to keep it in their head. Now, pull the paper out of your pocket, and Voila! According to game theory and its psychology, their number is more likely than not to be 7.

The diagram above, created by Oliver Brenan, shows the probability of each piece on a chessboard surviving.

Nash Equilibrium

John Forbes Nash Jr. was a Nobel Laureate who was awarded the 1994 Nobel Prize for his works in the field of Economics, particularly Game Theory. The Nash Equilibrium is the state of a game where all players will follow a particular course of action and have no incentive to deviate, regardless of what other players do. It is often reached when the outcome of the action for all situations will be the best possible. The Nash Equilibrium can only be observed in non-cooperative/competitive games, which may contain none or many Nash Equilibriums.

Game Theory and its usage in Covid

Game theory is not only used in economics or warfare — in fact, game theory has been extensively used during the current global pandemic. The optimized distribution of limited supplies of PPE (Personal Protective Equipment) during the pandemic was entirely decided using basic principles of game theory, with researchers from Kingston University London modeling how to efficiently distribute as well as secure sufficient levels of PPE for the UK and mitigate shortages in key areas.

Undoubtedly, Game theory is an essential part of every-day life, be it in the distribution of life-saving equipment for front-line medical workers, or even in the chess game you played last Saturday.

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Aritro

Aritro

My name is Aritro. Fascinated from a young age at the wonders of math, I like to think of myself as a charismatic, approachable, and curious student…