Tit for Tat – Game Theory Reflection
Some people think Game Theory is just about games, but it's not. It is the mathematical study of decision making and was created by John Von Neumann in the 1920s. A “game” is any situation between players that results in gains or losses for each player. It allows to assign a numerical value to each benefit or deficitt from the result of the game (situation) This might sound too theoretical but all you really need to know is peoples' relative
The picture of the two people on my first page shows a game The picture is of a 2x2 matrix. Each square in the matrix has two numbers. One for you and one for your opponent. These numbers represent a numerical payout for each player. A negative number represents a loss. The particular picture on the page is called “Prisoner's Dilemma. It is a situation in which two people are suspected of a crime. Both people have a choice to make. They can confess or they can remain silent. The picture on the page helps you understand the consequences of each combination of choices ie. One player could confess and the other could remain silent, on both players could confess. The numbers on the picture represent the number of years in jail each person will have to serve. For example, if one player confesses and the other doesn't the confessing player will have no years in jail and the other player will receive 20 years in jail. However, If you look at the numbers carefully you will actually notice that no matter what you r opponent does it always best to confess. This makes things not very interesting. The interesting part comes when you start having multiple players each playing multiple one-ones. Is cooperation now a useful thing?
This game of “Prisoner's Dilemma was so famous that a man named Robert Axlerod held a tournament. He invited about a dozen players including other game theorists, mathematicians, economists, and people from all fields. They players themselves did not consciously play in the tournament, however, their strategies did. They had to submit an algorithm that would tell you what move to make based on all the previous games. Axelrod decided that each game would have 200 iterations (choices) and that the tournament would be round robin . The player with the most cumulative points wins.
Many players submit detailed complicated strategies to the tournament. Strategies that take many lines of computer code to write. However a strategy named “Tit for Tat” won the tournament . And had less than five lines of code. Everybody was astounded. How could this strategies have won?
After this the tournament got more popular and this time the tournament had 200 players. A Cinderalla story, Tit for Tat wins again. No only did it win but everyone knew exactly what strategy it was before the tournament.. This made such a commotions that they started analyzing what was going on.
You can see from my infrograph that they determined that Tit for Tat had three important qualities. Being nice, being punishing, and being forgiving.. but what exactly do I mean..
- Being nice is cooperating on the first move
- Punishing is punishing your opponent after they hurt you
- Forgiving is when you stop punishing an opponent when they
start cooperating again.
This data led to more research. What if we looked at things from an evolutionary view point? One game theorist did. He used a super computer and ran 9000 sequential tournaments. Meaning there were 9000 birth and deaths cycles to allow for evolution. Amazingly, the data they found showed strategies that were very similar to Tit for Tat. This is beautiful and gives a mathematical reason that our evolution is towards altruism.
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