The Prisoners' Dilemma Model

     Two prisoners, lets call them Joe and Sam, are being held for trial. They are being held in separate cells with no means of communication. The prosecutor offers each of them a deal. He also disclosed to each that the deal was made to the other. The deal he offered is this: 

     a) If you will confess that the two of you committed the crime and the other guy denies it, we will let you go free and send him up for five years. 

     b) If you both deny the crime, we have enough circumstantial evidence to put both of you away for two years. 

     c) If both of you confess to the crime, then you'll both get 4 year sentences. 

     Put yourself in Joe's position. If Sam stays mum and you sing, you get zero years. If he stays mum and you stay mum, you will each get 2 years. On the other hand if both of you confess, you both get 4 years. Finally, if he confesses and you don't, you will get 5 years. For either decision that Sam makes, it is to your advantage to admit your wrong doing. Of course, Sam is also a rational person and he will, therefore, come to the same conclusion. So you both end up confessing -- which nets a total of 8 man-years in the pokey. The paradox is, if you had both denied the crime, a total of only 4 man-years would be spent behind bars. 

     Wait a minute! Can this really be that rationality leads to an inferior result? Let's look at this one more time. We will use a payoff matrix, a common tool of the game theoreticians. Also, to be consistent with the literature on this subject, we will use the standard terms "cooperate" and "defect" where in this case "cooperate" means "not confess" and "defect" means "confess". 

     The payoff matrix is usually presented in the following form: 
              
ACTION	PAYOFF	
Joe	Sam	Joe	Sam	
Cooperate (not confess)	Cooperate (not confess)	-2 (R)    	-2 (R)  	
Cooperate (not confess)	Defect (confess)	-5 (S)	0 (T)	
Defect (confess)	Cooperate (not confess)	0 (T)	-5 (S)	
Defect (confess)	Defect (confess)	-4 (P)	-4 (P)	

   (The codes represent standard terminology for each action: 

     R Reward for mutual cooperation 
     S Sucker's payoff 
     T Temptation to defect 
     P Punishment for mutual defection ) 

     The general form of the Prisoners' Dilemma model is that the preference ranking of the four payoffs be, from best to worst, T, R, P, S and that R be greater than the average of T and S. That is, any situation that meets these conditions will be a "Prisoners' Dilemma". 

     In summary, the Prisoners' Dilemma model postulates a condition in which the rational action of each individual is to not cooperate (that is, to defect), yet, if both parties act rationally, each party's reward is less than it would have been if both acted irrationally and cooperated. 

     The model can be applied to many real world situations, from genetics to business transactions to international politics. 

A Deeper Analysis

Let us examine this Prisoners' Dilemma thing a bit closer. While we might want to dismiss it as some sort of academic nonsense, having little application to real life, there is a basic characteristic here that is common to a much more serious phenomena, the group social dilemmas. Let us go over the logic one more time. 

The exasperating conclusion that the rational prisoner must face here is that there is really no choice but to defect. When you look at what the other person might do, for each case, your best option (less time in jail) is to defect. But the other guy will come to the same conclusion which results in situation that is inferior to the situation you would get if both cooperated. 

It is often stated when this dilemma is described that the prisoners are not allowed to communicate with each other during these deliberations. Actually, that is not necessary and the problem gets even more interesting if they do communicate. Let us assume that they do. 

Joe says, "Sam, you know, we are both rational, logical people. Both of us have looked at this thing very carefully and it's rather obvious what we are going to do. We're both going to defect which means that we will have done a rather stupid thing that we will have four years of time to reflect on." 

"I know. It is really troubling, but how can we come to a better solution? I would like to cooperate if only I could be sure you will." Sam laments. 

Joe responds, "Look Sam, let's be sensible. Let us agree to cooperate, since it is obvious that we will either both defect or both cooperate since we are both intelligent and are both using the same logic." 

Sam agrees. They shake hands and they are escorted back to their own cells. 

That night, both men lay in their cells pondering the agreement they made that day. Their thoughts -- which are the same -- go something like this: 

"How do I know that rascal is still not going to dump on me? Sure, he's talked me into keeping my mouth shut but he can get off scot-free by squealing on me and then I'm in here for five years! Hell, that's worse than the four I would get when we were both going to defect. Well, to protect myself, I have no choice but to defect.
Actually that is not a bad idea -- if he really is sucker enough to go through with our agreement, then I will get off scot-free!" 

So, they are back to where they started. So, what went wrong? Why couldn't they have improved their situation by cooperating? It turns out to be a matter of trust. They can't achieve a better solution because they can't trust each other. 

That conclusion suggests the theme of this essay. As a minimum, this little exercise suggests that maybe mutual trust could provide a far better solution for Prisoners' Dilemma like situations than can be achieved by just using pure logic. Moreover, it may be that this confirms what many wise and kind hearted advisors have been trying to tell us for years -- "Sometimes the heart suggests a better solution than the mind". 

The Prisoners' Dilemma model as presented by Robert Axelrod, Douglas Hofstadter, and others.