Strategies to find Lisa and obtain justice for her
With the news that no searches have been done the last couple of days I felt inclined to post about a strategy I am thinking about.
This post is to discuss the case from a LE perspective, of how to get a conviction.
To get a conviction, a body is vital IMO to achieve this.
It is apparent that possibly a new lead is needed to know where to search next.
IMO, a confession is the best scenario, and so wanted to speculate about that and get input from other posters, including other thoughts on strategies.
I feel that it is quite possible that LE has quite a bit more evidence than we know about, including who may have been walking down the street at midnight. There have been no sketches, descriptions, or anything of that nature released. The Amber Alert was cancelled after ten hours. Clues like that tell me that it is possible they know more than we do.
I feel that some kind of application of Nash Equilibrium may be helpful to this situation. This is in reference to who committed the crime and any accomplice.
In my theory, Debbie is responsible for Lisa's death and had an accomplice in staging this kidnapping. This is only opinion.
Therefore, in application of the Nash Equilibrium to that theory, we have the law stated as follows:
A Nash equilibrium, named after John Nash, is a set of strategies, one for each player, such that no player has incentive to unilaterally change her action. Players are in equilibrium if a change in strategies by any one of them would lead that player to earn less than if she remained with her current strategy. For games in which players randomize (mixed strategies), the expected or average payoff must be at least as large as that obtainable by any other strategy.
http://www.gametheory.net/dictionary/NashEquilibrium.html
Stated simply, Amy and Phil are in Nash equilibrium if Amy is making the best decision she can, taking into account Phil's decision, and Phil is making the best decision he can, taking into account Amy's decision.
The Prisoner's Dilemma has the same payoff matrix as depicted for the Coordination Game, but now C > A > D > B. Because C > A and D > B, each player improves his situation by switching from strategy #1 to strategy #2, no matter what the other player decides. The Prisoner's Dilemma thus has a single Nash Equilibrium: both players choosing strategy #2 ("defect"). What has long made this an interesting case to study is the fact that D < A (i.e., "both defect" is globally inferior to "both remain loyal"). The globally optimal strategy is unstable; it is not an equilibrium.
[ame="http://en.wikipedia.org/wiki/Nash_equilibrium"]Nash equilibrium - Wikipedia, the free encyclopedia[/ame]
Prisoner's dilemma
The Prisoners Dilemma, is an aspect of game theory that shows why two individuals might not agree, even if it appears that it is best to do so. A classic example of the prisoner's dilemma (PD) is presented as follows: It was originally framed by Merrill Flood and Melvin Dresher working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence payoffs and gave it the "prisoner's dilemma" name (Poundstone, 1992).
Two men are arrested, but the police do not possess enough information for a conviction. Following the separation of the two men, the police offer both a similar deal- if one testifies against his partner (defects / betrays), and the other remains silent (cooperates / assists), the betrayer goes free and the cooperator receives the full one-year sentence. If both remain silent, both are sentenced to only one month in jail for a minor charge. If each 'rats out' the other, each receives a three-month sentence. Each prisoner must choose to either betray or remain silent; the decision of each is kept quiet. What should they do?
If it is supposed here that each player is only concerned with lessening his time in jail, the game becomes a non-zero sum game where the two players may either assist or betray the other. In the game, the sole worry of the prisoners seems to be increasing his own reward. The interesting symmetry of this problem is that the logical decision leads both to betray the other, even though their individual prize would be greater if they cooperated.
In the regular version of this game, collaboration is dominated by betraying, and as a result, the only possible medium in the game is for both prisoners to betray the other. Regardless of what the other prisoner chooses, one will always gain a greater payoff by betraying the other. Because in almost all solutions, betraying is more beneficial than cooperating, all objective prisoners would seemingly betray the other.
[ame="http://en.wikipedia.org/wiki/Prisoner%27s_dilemma"]Prisoner's dilemma - Wikipedia, the free encyclopedia[/ame]
It seems to me that the GJ could be used to establish that there is enough evidence to make the two arrests. Once that has been approved, arresting both and then applying this principle of Nash Equilibrium could result in the two betraying each other. I am certain that Debbie will claim complete innocence, and the curtains will come down by the accomplice as to the real story. He will betray her as well, in other words. There is no equilibrium for loyalty to be maintained.
This then could allow for Lisa to be located, and more evidence for trial.
Hope this made sense.
MOO. :seeya:
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