What is Game Theory?

by Elijah Whitehouse on 09/05/13 06:05:00 pm

The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company.

A definition of what Game Theory is according to Investopedia, "*A model of optimality taking into consideration not only benefits less costs, but also the interaction between participants."* Additionally also from that same segment on Investopedia, "*Game theory attempts to look at the relationships between participants in a particular model and predict their optimal decisions."* What this means is that not only does it look at the outcomes of a certain "game" so to speak, but it also looks at how the participants interact with one another. It's a table and formula of how people may interact with one another and a system of possible predicting what the outcome might be. The most famous example used in conjuction of Game Theory is the Prisoner's Dilemma.

The Prisoner's Dilemma works as follows: two people are accused of a crime and are being interrogated separately and have no idea what the other is saying. Obviously both parties want to minimize the amount of time spent in jail and herein lies the dilemma. The sentences vary as follows:

1) If Person A pleads not guilty and Person B confesses, Person B will receive the minimum sentence of one year, and Person A will have to stay in jail for the maximum sentence of five years.

2) If nobody makes any implications they will both receive a sentence of two years.

3) If both decide to plead guilty and implicate their partner, they will both receive a sentence of three years.

4) If Person B pleads not guilty and Person A confesses, Person A will receive the minimum sentence of one year, and Person B will have to stay in jail for the maximum five years.

Pleading guilty obviously is the most attractive offer, but only if the other party pleads not guilty since the sentence is the least amount compared to the other sentences possible. If both parties plead guilty, they will both end up serving three years. Another outcome if they both plead not guilty they'll each serve two years in jail whereas the risk of pleading not guilty is a five year sentence should the other member decide to confess to the crime.

The Prisoner's Dilemma is the most popular example as it can highlight the true nature of people and can be applied to a multitude of scenarios and not just one where two people might be facing jail time. Now according to GameTheory.net, "*Game theory is the study of how people interact and make decisions. This broad definition applies to most of the social sciences, but game theory applies mathematical models to this interaction under the assumption that each person's behavior impacts the well-being of all other participants in the game. These models are often quite simplified abstractions of real-world interactions but offer a tractable way of predicting likely outcomes." *

Basically what this means is that it is entirely possible to use a formula to determine possible outcomes of a certain scenario. For a real world scenario, look at what President Truman had to struggle with - whether or not to drop the atomic bomb on the Japanese people to put an end to one of the fronts of the war his country was fighting. If he didn't, then not only would Japan continue to fight back, but countless American lives would have been lost. If he did greenlight the operation, then thousands if not millions of innocent human life would be annihilated as a result of his decision. So you can see the struggle that President Truman had and the weight of the decision he had to make, but the Game Theory can apply to that just as well as two people facing jail time.

Basically what this means is that it is entirely possible to use a formula to determine possible outcomes of a certain scenario. For a real world scenario, look at what President Truman had to struggle with - whether or not to drop the atomic bomb on the Japanese people to put an end to one of the fronts of the war his country was fighting. If he didn't, then not only would Japan continue to fight back, but countless American lives would have been lost. If he did greenlight the operation, then thousands if not millions of innocent human life would be annihilated as a result of his decision. So you can see the struggle that President Truman had and the weight of the decision he had to make, but the Game Theory can apply to that just as well as two people facing jail time.