PRISONER'S DILEMMA

To join the limited registry or not?  Game Theory can assist our solution tree. 
Game Theory- a  strategic decision making model based on mathematics; developed by Jon Von Neumann and Oskar Morgenstern.  See, Theory Of Games and Economic Behavior, Von Neumann and Morgenstern (1944). 
Terms you will need: Zero Sum Game: one winner all others are losers.  For example, Poker (hi-lo games excluded).  Non-zero sum game: a gain by one player does not necessarily mean a loss for another and players can act in concert to achieve greater results. Example: 


Prisoner's Dilemma is the classic example of game theory analysis. The analysis shows why two individuals might not cooperate even if it can be shown mathematically that it is in their best interests to do so. 
The Dilemma: Two people are arrested. The police do not have enough complete information to convict either on the most serious charge. They are separated. The deal is made to both: If one confesses and betrays the other (betrayal strategy) he goes free if  the other one  remains silent (loyalty strategy). The silent prisoner  goes to prison for five years. If each choose to confess they each get one year. if each chooses to remain silent and loyal,  they both go free. 


It is assumed for this game that each player's interest is only in maximizing their own benefit. i.e, they have no emotional loyalty to the other player.  Thus the simple/first glance answer is that the player is better off remaining silent. But that is not what the math and game theory shows. 


                   PRISONER B BETRAYS  /    PRISONER B SILENT 


PRISONER
A SILENT             (each goes free)              /       (A gets 5 years, B goes free)

PRISONER A
BETRAYS          (B gets five years,            /    ( each gets one year)
                              A goes free )


The choice for A or B individually is always to betray. By doing so they minimize their exposure (by betraying they will never get five years) and maximize their chance for going free or getting one year (known as a Mini-Max strategy). The individual strategy choice of betrayal is said to dominate the known best strategy of staying loyal which yields the best result for both participants.  Since the rational strategy for each is too betray the other, they get more time acting rationally ( 1 year)  then not ( going free). 


Lets apply this to the limited registry. 


If you apply to the limited registry (the betrayal option in prisoners dilemma)  you will have first crack at all cases since by law the clerk must appoint a LR attorney if available. However choosing LR yields less money. 
If you choose not to go on the LR wheel (the loyalty option in prisoners dilemma) you maximize your chances for income because as a general registry attorney you can exceed the cap if needed but you also expose yourself to not getting any cases if your colleagues join the LR wheel. 


The solution to Prisoner's Dilemma that allows players to choose the best strategy is to allow exchange of information which allows both prisoners to then choose the best strategy (remain loyal and silent)  and go free.  


Game theory analysis conclusively shows that if all attorneys chose not to join the LR then every attorney achieves the optimal solution of getting more money per appointment. 


We can mathematically (email us for the solution if you need it) demonstrate that as long as everyone communicates,  their best personal solution is to remain loyal and not join the LR. The  optimal and rational answer to the question of whether to join the LR is to not join LR and force the clerk in every case to appoint a general registry attorney. The only time the non-optimal solution dominates the  optimal solution is when the parties cannot communicate. Since all attorneys can communicate in regard to this issue, THERE IS NEVER ANY BENEFIT TO ANY ATTORNEY TO JOIN THE LIMITED REGISTRY WHEEL. *


Please pass this information on to your colleagues and if they don't understand this solution have them email us and we can explain it better in further detail. 


The choice is yours. Act  rationally. 
H.R.


* One might posit that an attorney could say that by joining the LR  they will get more cases and thus more money. But observe that is the non-optimal solution. Once the LR is in existence and working with attorneys who have signed up, then the non-optimal choice will dominate  the rational choice- as in prisoners dilemma. And recall that the non-optimal choice  in prisoners dilemma  resulted in each player receiving a year in prison ( a non-optimal result). When an attorney chooses the non-optimal solution and joins the LR -they make the LR a success which means they lose the result of getting more money per case.  They also lose the result of just getting more money, since once LR succeeds  more attorneys will join LR and dilute their appointment opportunities. The attorney who makes the non-optimal  choice and joins LR achieves only the worst result: working longer and harder for less money. There can be no rational incentive- and no mathematical solution that yields an optimal result by joining the LR.