Intro to Game Theory – The Prisoner’s Dilemma
As mentioned, this idea seems to be as old as warfare itself, becoming codified by Sun Tzu’s Art of War and later quantified by von Neumann’s mathematical models. The most famous model example of game theory is called The Prisoner’s Dilemma. The scenario generally goes like this:
*** Two criminal partners have been caught robbing a bank. When they are arrested, they are immediately separated so that they cannot communicate with each other. They only know that both they and their partner are both in custody. ***
Each is offered the same plea bargain. Remain silent and go to trial or testify against the other and go free. If they both stay silent and go to trail, they will get 6 months of jail. However, if one is willing to be a witness against the other, that person will have their sentence reduced to no jail time, while the other person will get ten years of jail time. If both testify against the other, they both get five years in jail. Both of the accused are offered this deal at the same time, with no idea what the other person was offered.
This scenario creates what is known as a zero-sum game. With each “player” knowing the entire stakes of each choice they ask themselves, “what is the best course to maximize their own positive outcomes and minimize their own negative outcomes?” This is of course greatly complicated by the fact that another, thinking human is making the same decisions with the same thought process.
Consider in the prisoner’s dilemma the two accused are, or were, partners. They worked together for their mutual benefit (forget for a moment that they were caught robbing a bank), but they don’t have any real loyalty to one another. In addition, each knows they will not be able to influence the other’s choice with threats or promises. So there is risk involved for any decision they may make. In fact, we have Conflict, Risk, Choices, and Consequences all hanging in the balance. And it is extremely well balanced.
So what do we expect game theory to tell us about this dilemma?
Since both of the accused are individual agents operating in their own self-interest, the more predicable choice is for each to betray the other. Of course, we can change the parameters of the dilemma to experiment with different outcome predictions. What if we changed the jail times for more slanted results? Would the choice be easier or harder to decide if the jail time reduction for betrayal was a mere month? What if both of the accused have been in this situation before with each other and remember the negative consequences of a selfish choice? What if they keep playing the game ten times? Do they learn from their mistakes and make new choices at some point?
People Generally Choose in Their Own Self Interest Unless Specifically Working with Others
The Prisoner’s Dilemma has many different facets and configurations that we, as game designers, can utilize to further understand game theory and how it is related to making balanced video games. It basically comes down to applying various mathematical configurations and models that are based on the choices that people have actually made in other situations. Once you apply these models and see the results you can make informed decisions and have a more likely outcome of players responding well to and understanding your game.