Extra Credit Assignment Susie Q
February 23, 2005
Hansel and Gretel: A Lesson about Gaming Theory
Once upon a time there lived a woodcutter and his family in the forest. The woodcutter and his wife had two children named Hansel and Gretel. Unfortunately, hard times had fallen upon the family and they had no food or money to survive.
One evening the woodcutter tossed and turned anxiously in his bed and finally asked his wife, “How will our family survive? I have no way to feed us or our children!”
“We must survive ourselves husband,” the wife cruelly replied. “Tomorrow we will leave Hansel and Gretel alone in the forest with two pieces of bread and a burning fire. We will all be better off to survive on our own.”
Although the woodcutter felt that this idea was cruel, he did not see any other option.
The next morning, the family headed off into the forest.
“Children” the mother said, “your father and I will light a fire and we will return with food to prepare. Stay put here and nibble on these two pieces of bread until your father and I return.”
Hansel and Gretel patiently waited for their parents to come back. Hours and hours passed by. The sun began to set and the moon appeared in the sky.
“Hansel?” Gretel asked “Do you think mom and dad are coming back?”
“No” replied Hansel. “I believe that we will have to survive on our own. We are too young to work. The only way for us to survive is to steal. Do you remember hearing about the witch that lives in the Gingerbread house? We do not want to fall for her antics. She would simply fatten us up until she could eat us.”
The next day, Hansel and Gretel began their quest for food and survival. They stole pies from window sills, apples from trees, and farmer’s cattle for milk and meat. Anything the children could get their hands on they stole. The two became quite skilled at their robbery until one day their luck changed.
“Look at that chicken” Hansel exclaimed to Gretel. “It is so plump and juicy. We could eat it for weeks.”
The two crept into the fenced property where the chicken rested. Just as Hansel put his hands around the chicken’s neck they heard a noise.
“Put your hands in the air!” exclaimed the farmer. “You two kids have been stealing things all over this forest and you are not going to get away with it anymore. I’m calling the Sheriff.”
The local police immediately arrived on the scene and separated Hansel from Gretel. Hansel and Gretel both knew that they faced a dilemma…a prisoner’s dilemma!
Although Hansel had always loved his sister, he always had his own best interest in mind. Gretel cared deeply for her brother but was well aware of his selfishness. Therefore, both knew they must think strategically when deciding whether or not to make a confession.
The sheriff questioned Gretel first. “Are you guilty of the attempted robbery of a chicken?” he inquired.
Gretel thought carefully. If she confessed and Hansel did not she would be freed and he would go to prison for twenty years. If Gretel chose not to confess and Hansel did she would go to prison for twenty years. Neither of these appeared to be good options for her. She cared too deeply for her brother to make him suffer for twenty years. Gretel also knew that if both she and Hansel confessed, they would each receive eight years in prison and if they both remained silent, they would go to jail for only one year each.
The dominant strategy would be for both Hansel and Gretel to confess. Unfortunately, Gretel knew Hansel well and thought strategically. Gretel Pondered “I know that Hansel will not confess. He will think that I am going to confess and therefore he will remain silent in order to avoid jail time. Therefore I must confess.”
Gretel confesses and Hansel remains silent. Therefore, Hansel receives twenty years in prison. The moral of the story is that if Hansel had thought more strategically and applied the game theory, he would have known that by confessing, he would subscribe to the dominant strategy and would have reduced his jail time.
Unfortunately for this fairytale, only Gretel lived happily ever after.