A College Paper I Wrote on Rational Decision Making
Posted on February 23 2016
The Quest for Survival
Philosophers from all around the world have been trying to figure out why we as humans cooperate or not. From Thomas Hobbes’s view on the state of nature vs. Montesquieu’s, they both present different reasons. Hobbes believes that humans originally formed societies out of fear of each other. That we thought cooperation was the best bet because of the fear of other men. Montesquieu thought that men cooperated and formed societies because they did not fear each other. They were weak and naturally impotent. They figured their chances of surviving was better together. Two different reasons as to why people cooperate but nothing that really explains why they would choose not to. The Prisoner’s Dilemma gives us an analytical way to determine why individuals would choose not to cooperate and remain in the state of nature.
The two-person, one-shot PD game and its “solutions”
The classical dilemma involves two criminals. Before they were arrested, they jointly committed a crime that carried a high penalty with it. They both agreed to never rat each other out. Now, they have both been arrested for another minor crime. This new crime had nothing to do with the previous major crime. However, the police have a suspicion that these two people committed both crimes. They have absolutely no evidence connecting either one to the previous major crime. They know if they can get a confession then it doesn’t matter. Either way, the criminals will be charged with a crime.
In order for a scenario to be considered a PD game it must follow this equation: T>R>P>S.
T- Temptation (greatest possible outcome)
R- Reward (Mutual Cooperation)
P- Punishment (Mutual defection)
S- Suckers Pill (Worst possible outcome)
T>R>P>S or 0 > 1 > 5 > 10
In the classic PD game described above, defection is the dominant strategy. This means that there is no reason to cooperate since it leads towards the worst possible scenario. If they choose defect (rational choice) then they avoid the worst possible scenario every time.
If both prisoner’s choose to defect (the dominant strategy) then they will both get 5 years. This outcome is much more preferable than the possibility of receiving ten years if one chooses to cooperate and the other doesn’t. There is no reason for one to unilaterally change their position. This is the Nash Equilibrium. But this is not the best outcome for all players.
The best outcome would be to deny all allegations and serve the one year jail sentence for the minor crime. Thus never admitting to the major crime and each getting a better outcome than the punishment; only in this case of the best outcome for ALL players. Each individual’s best outcome is to hope the other player confesses and they deny. Then the individual would walk away as a free man.
Jordan sprinted as fast as he could past the walls of closed doors. He didn’t have enough time to check to see if they were locked with the horde of decaying human bodies right on his heels. He could hear their moans and screams as they trailed behind him. That’s what kept him running. Though he had not eaten in the last three days and barely drank any water, he found the energy to run. His survival depended on it.
At the sometime, David was also on the run. The same amount of zombies were hot on his trail as well. He too was running through the same building, past the walls of closed doors. David had also not eaten in a couple days and had barely enough to drink to keep him alive. Somehow, he too found the energy to keep ahead of his pursuers. David felt the shotgun he had on his back bounce up and down rapidly. He hoped it didn’t smack him in the back of his head with every bound he took.
Sure David had a weapon to fend off the zombies but the problem was scarcity of ammunition. He had five shells and could easily disperse the crowd that chased him. But in doing so, his chance of long term survival would diminish exponentially. Not only would he use up his last resort (suicide or a couple shots to get out of a sticky situation), the loud blasts would draw unwanted attention from zombies in the surrounding areas and other humans.
Why would David be afraid of other humans, wouldn’t they help him? David’s experience taught him that he should be wary of other people. Many of them only care about their survival. They will steal, cheat or even worse, kill you in order to make sure their survival is optimum. David would rather be against a horde of zombies than a strange person. He could at least predict the actions and movements of the dead.
Jordan saw an open door in front of him. He got a burst of adrenaline. Finally, a place to hide and maybe catch his breath. With his eyes on the prize, he completely lost track of his surroundings. He didn’t see the body lying on the floor and tripped right over it. As he fell, the door was quickly forgotten. He landed hard on his hands and then gracefully, his face. He had tripped over a corpse and the horde behind him had almost closed the gap.
He then remembered that he still had the pistol with five rounds on his hip. He could easily dispel all his troubles with a couple headshots (if he was still accurate). But then Jordan would be in the same predicament that David would have been. Alert other zombies in the area and possibly other human beings. Plus his last resort would be diminished. Was killing the zombies worth the trade off? Was there another way?
That’s when Jordan decided to look up. He saw the open door and judged that it was possible to get into before the horde fell upon him. That’s when he sprung up with lightning fast speed and bounded towards the door, as if it was do or die (which it was). He could feel the dead’s breath of the back of his neck as his body gave every last bit of energy. He entered the door way and with a quickness turned and slammed in it shut with such force, one of the dead’s arms was caught between the door and frame. The door slammed closed effortlessly, severing the arm. Jordan turned around and slid down the door with a sense of relief. Then he noticed the man staring at him in exactly the same position on the opposite side of the room.
David stared at the individual who was panting on the opposite end of the room. He was now faced with an even more dangerous opponent. He looked around for another escape but found that he was trapped with him. The room had no windows because it was in the center of the building. It had a couple desks and chairs but nothing really of importance. David was trying to catch his own breath. He could hear the scratching and moans of the dead just inches away from his head. Only an inch of cheaply made wood separated him from the horde but nothing separated him from the other stranger.
Analysis of the prisoner’s dilemma
Players: Jordan, David
Strategies: C (Cooperate), D (Defect)
Payoff: S=Survival; 2(S), ½(S), ¾(S), 0 (loss of life)
Outcomes= (C,C), (D,C), (D,C) and (D,D)
The payoff for any player to defect is in the (D,C) or (C,D) outcome = Temptation (T)
The payoff for cooperation is in the (C,C) outcome = Reward (R)
The payoff for the defectors in the (D,D) outcome = Punishment (P)
The payoff for the cooperator is in the (C,D) or (D,C) outcome = Suckers Pill (SP)
In order for this to be a prisoners dilemma game; T>R>P>SP
Therefore the above scenario is a PD game.
Defect is the dominant strategy for each player. If Jordan chooses to defect and so does David, then they both receive Punishment. This would be ½ their ability to survive the event. This however is not a bad as receiving the SP which happens to be loss of life. A rational being would choose to defect since in all cases, it would not lead to the worse outcome (SP). Let’s take a look at what would happen if both players chose to defect.
Jordan doesn’t trust the being he saw before him. He doesn’t even wish to utter a word towards him. They both reach for their weapons at the same time and drew them while standing up. Both David and Jordan now have their fingers on the trigger. “What to do? What to do?” Jordan asks himself.
But David already had a plan. He swiftly opened the door behind him and sandwiched himself behind the wall and the door. All of the zombies came rushing in at once towards the only thing they could see, Jordan. Now Jordan had no choice but to open fire onto the horde with hopes he could thin their numbers before they entrapped him. David ran out into the hall while the zombies were distracted and continued on his way through the building.
In this instance both players defected. But just because they defected, didn’t mean they lost their life. Their chance for surviving was cut in half. A bullet could have easily hit David as he escaped. More zombies could have collected out the door and David would have ran right into them. Jordan still has a chance to escape and survive. However, by them both choosing to defect their ability to survive was cut in half due to chance and circumstance.
So what happens if only David chooses to defect and Jordan cooperates? Well, this would almost be the same if Jordan cooperates and David chooses to defect. In these scenarios, the person who chooses to cooperative will lose their life. This is (SP) or the suckers pill. It is the worst possible outcome for both players. Whoever, chooses to defect then they would get the reward of temptation. The reward being a double chance of survival. The defector would then acquire everything the cooperator had. Another weapon, more ammunition, possible food/water, and other objects that maybe pertinent to survival. This also removes any future possibility of this man becoming a threat. The reward would be the best possible outcome for an individual. Let’s see how this would play out in the story.
Both parties stood and drew their weapons but David wasn’t even going to chance losing his life. He saw Jordan as a pure threat. A diminishment in his survivability that had to be eliminated. Kill or be killed. Before David had he even stood up fully, he squeezed the trigger.
The shotgun went off sending fragments of hot, shredded metal towards Jordan’s shocked face. The fragments pierced through his head and a release of red liquid painted the door behind him. You could hear the wail of zombies on the other side of the door as the fragments tore through their rotting flesh. A couple of them collapsed to the ground with a loud thud. David quickly ran over and frisked David’s body. He regrets having to take a human’s life but the decision paid off immensely. Not only did he acquire a new weapon and ammunition, he also collected a bottle of aspirin, some water and a large military grade looking knife.
He peeped through one of the holes the shotgun tore through the door and only saw two zombies still standing. David could easily outrun them. He was getting out of that room alive. He made the rational choice. He couldn’t trust the lifeless body he was crouched next to. It was just too risky. Jordan had to survive.
The Nash Equilibrium in this problem would be both players defecting. But it is not pareto optimal. What would be best for both players, would be choosing to cooperate. This option gave both players a ¾ chance of survival. Why just ¾ chance? Though they may choose to cooperate to exit the room, there is still chance and the consequence of future actions by the other player. What if one is accidentally bitten during the escape? What is after they escape, one player decides to turn on the other? Sure, cooperation improves their overall chance of the current problem but it also effects the future of their survivability. Let’s explore this with the scenario.
David and Jordan both drew their weapons on each other while rising to a stand. The zombies clawing on the doors deadened as they stared into to each other’s eyes. There was a brief moment of complete silence as they continued to stare. Then David broke the silence. “How many did you have following you?” ”Around four or five” replied Jordan. “I have about that many as well” David said while lowering his weapon. Jordan followed suit.
“Here is how I see it. We can work together and escape without having to use all of our resources and then split up afterwards. There is no reason why we can’t work together to escape. It improves both our chances of getting out of here alive.” Jordan looked at David as he spoke. He nodded his head in agreement. “We can go out one door and leave the other zombies alone. We split the risks between each other. Do you have anything other than that pistol?” asked David. “Yes I have a knife that is relatively effective. I could take them on one by one if you opened the door enough to let them fall in single file.” “Brilliant plan” bellowed David.
As David slowly opened the door, a handful of zombies began to walk through the door in a single file. Jordan quickly and effortlessly drove the blade through each one of their heads. The zombie threat was eliminated without any real loss of supplies or energy. As Jordan pulled the blade out of the last zombie’s head, they both exited the room. “Thanks for the help, maybe we will run into each other again” said David as he turned to walk away. Jordan replied, “No we will not” as he raised the pistol and squeezed the trigger putting a bullet through David’s skull.
Both parties escaped the room through cooperation but one party decided to dish out the suckers pill after they had exited. The original prisoner’s dilemma was solved with cooperation but the next one was not.
The PD game has really opened my eyes to understanding certain rational behavior. I understand why, in an analytical means, people hardly choose to cooperate and seem selfish. In the above scenario I portrayed, the reason to cooperate knowing that you would have a less chance at surviving is irrational. I have never been able to make a case for an irrational action or thought until now. I always that cooperation was rational and everyone else being selfish was irrational. I was wrong. I have always been the person to choose the greater good over my own good. I honestly thought that was the rational choice. Long term stability for the whole vs short term stability for the individual. In both PD games, it’s fair to say people may not always choose right choice but they choose the best choice when it comes to them. Can we blame them when the worst possible scenario comes from cooperation?
- “Thomas Hobbes." com. A&E Networks Television. Web. 22 Feb. 2016. <http://www.biography.com/people/thomas-hobbes-9340461#leviathan>.
- "CONSTITUTIONAL RIGHTS FOUNDATION Bill of Rights in Action." BRIA 20 2 C Hobbes, Locke, Montesquieu, and Rousseau on Government. Web. 22 Feb. 2016.
- Kuhn, Steven. "Prisoner's Dilemma." Stanford University. Stanford University, 1997. Web. 22 Feb. 2016.
 "Thomas Hobbes." Bio.com. A&E Networks Television. Web. 22 Feb. 2016. <http://www.biography.com/people/thomas-hobbes-9340461#leviathan>.
 "CONSTITUTIONAL RIGHTS FOUNDATION Bill of Rights in Action." BRIA 20 2 C Hobbes, Locke, Montesquieu, and Rousseau on Government. Web. 22 Feb. 2016.
 Kuhn, Steven. "Prisoner's Dilemma." Stanford University. Stanford University, 1997. Web. 22 Feb. 2016.