PRISONER'S DILEMMA

Long time and careful readers of this blog know that Rumpole has a modest expertise in Game Theory, with a keen interest in the Nash Equilibrium and it's application to real life legal decision making. 
In Prisoner's Dilemma, we examine the situation of two individuals arrested and charged with a crime. Each prisoner is in solitary confinement and unable to communicate. The prosecution lacks the evidence to convict both on the main charge.  Each prisoner wants to get a year in jail in a lesser charge. Two prosecutors are dispatched to meet with each prisoner (and their counsel of course, this isn't Miami-Dade) simultaneously. The prosecutors offer each prisoner a deal. Each prisoner must then decide whether to cooperate with the outcomes as follows: 

If P1 and P2 each agree to rat the other out, each will get two years. 

If P1 rats out P2 but P2 remains silent, P1 gets off and P2 gets 3 years in prison. 

If P1 and P2 each remain silent, they each will only  be convicted of a lesser charge  and serve one year. 

Here is the dilemma: If each prisoner acts in their rational self-interest, then each betrays the other and they each get two years. 
If each reject their inclination toward rational self-interest then they each get the desired outcome of one year. 
Acting in rational self-interest and being a rat  leads to a worse result than in remaining silent. However, since by cooperating with the prosecution  the prisoner can possible go free or at worst do two years and eliminate the possibility of the worst outcome- three years,  being a rat is what is called the dominant strategy. And yet, the rational self interested choice to be a rat yields a worse outcome than the non-self interest choice to remain silent. So acting rational is irrational. Oy!

The Nash Equilibrium yields a solution for the dilemma but we will discuss that at another time. 

Let play a little Game Theory. 
Say you are a lawyer. And say you have damaging information on the President of the United States. Say your name is...Cohen. 
What do you do? Remain silent and risk three years (actually more) or cooperate and possibly get two years or walk free? 

Say you are the President of the United States. Being a rational actor do you:
1) Blame Obama; 2) Blame the failing NY Times, Failing CNN, failing MSNBC, and fake news? 
3) Bomb Syria? 4) Make a peace treaty with North Korea and agree to a joint North Korean -US military strike at the Seychelles Islands?  5) Stay in bed all weekend, eat cheeseburgers, watch FOX TV and fire Nicky Halley? 

From Occupied America, even Presidents have dilemmas they cannot reason their way out of. Fight the power and don't be a rat!