The Blackmailer's Paradox

[XLFD]

Not long ago, Nobel Prize winner Robert Aumann presented an interesting scenario dealing with the mathematical concept of Gaming Theory and how it sometimes applies to real-life negotiations.  Here it is:

 

Reuben and Simon are placed into a small room with a suitcase containing $100,000 of cash. The owner of the suitcase offers them the following: "I'll give you all the money in the suitcase, but only on the condition that you negotiate and reach an amicable agreement on its division. That's the only way I will give you the money. "

Reuben, who is a rational person, appreciates the golden opportunity presented to him and turns to Simon with the obvious suggestion: "Come, you take half the amount, I'll take the other half, and each of us will go away with $50,000." To his surprise, Simon, with a serious look on his face and a determined voice says: "Listen, I do not know what your intentions are with the money, but I'm not leaving this room with less than $90,000. Take it or leave it. I'm fully prepared to go home with nothing."

Reuben can not believe his ears. What happened to Simon? he thinks to himself. Why should he get 90%, and I only 10%? He decides to try to talk to Simon. "Come, be reasonable," he pleads. "We're both in this together, and we both want the money. Come let's share the amount equally and we'll both come out ahead."

But the reasoned explanation of his friend does not seem to register on Simon. He listens attentively to Reuben's words, but then declares even more emphatically, "There is nothing to discuss. 90-10 or nothing, that's my final offer!" Reuben's face turns red with anger. He wants to smack Simon across his face, but soon reconsiders. He realizes that Simon is determined to leave with the majority of the money, and that the only way for him to leave the room with any money is to surrender to Simon's blackmail. He straightens his clothes, pulls out a wad of bills from the suitcase in the amount of $10,000, shakes hands with Simon and leaves the room looking forlorn.

 

This case in Game Theory is called the "Blackmailer Paradox." The paradox emerging from this case is that the rational Reuben is eventually forced to act clearly irrationally, in order to gain the maximum available to him. The logic behind this bizarre result is that Simon broadcast total faith and confidence in his excessive demands, and he is able to convince Reuben to yield to his blackmail in order for him to receive the minimum benefit. 

 

Can you think of a way to rationally thwart this paradox, so that sanity can prevail?  Can you think of anywhere this paradox may be on display on the international or domestic scene? 

[AQUAMAN]

Reminds me of the old story of the King that lost his Sanity, after all the King's people drank from the tainted well. The only way the King could regain his people's faith and allegiance, was to also drink from that tainted well to also lose his sanity. Does that dovetail?

[XLFD]

That's close to what we have here, though this one here deals more with bargaining than the dilemma of having to choose between losing your sanity for allegiance or retaining it and being an outcast king.

Closer to this is the Prisoner's Dilemma, another one that makes you think: Two suspects, A and B, are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal: if one testifies for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both stay silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a two-year sentence. Each prisoner must make the choice of whether to betray the other or to remain silent. However, neither prisoner knows for sure what choice the other prisoner will make. So this dilemma poses the question: How should the prisoners act? The dilemma can be summarized thus:


1.If I screw you, but you don’t screw me, I win very big and you lose very big.
2.If you screw me and I don’t screw you, I lose very big and you win very big.
3.If neither screws each other, we both suffer mild punishment.
4.If we both screw each other, we both suffer medium punishment.


In deciding what to do in strategic situations, it is normally important to predict what others will do. This is not the case here. If you knew the other prisoner would stay silent, your best move is to betray as you then walk free instead of receiving the minor sentence. If you knew the other prisoner would betray, your best move is still to betray, as you receive a lesser sentence than by silence. Betraying is a dominant strategy. The other prisoner reasons similarly, and therefore also chooses to betray. Yet by both betraying they get a lower payoff than they would get by staying silent. So rational, self-interested play results in each prisoner being worse off than if they had stayed silent.

Is there a winning strategy here, to get you minimal time?

[Guidothesemipsuedocaptitalistpig]

It does sound similar to the two major party political environment right now. As far as thwarting it..I think depend more on the personalities of those involved I think. There is a difference in personalities between leadership types, and congressmen which in essence are simply supposed to vote their constituents bidding are they not? The major problem in Washington right now is the Democratic leadership chose to ignore the will of even their own constituents I think.

[XLFD]

It does occur in party politics, whenever one side decides to go almost-all-or-nothing on an issue and refuses to budge on a certain item or two, forcing the other side to give in. Democrats have used it successfully lately, but one could say Ronald Reagan controlled some issues through this means.

But... it is even more pronounced elsewhere.

[charlemagnetism]

labor union negotiations?

rje and his ex wife?

soupers and torchies?

[XLFD]

Darn fine observation, RJE, about it being more of a dilemma than a paradox, and not truly blackmail-- but I didn't name it. But then you wander into the paradox of defining who is the greedy (or the rational) party in this case.

[Sweater Cows!]

"I'll give you all the money in the suitcase, but only on the condition that you negotiate and reach an amicable agreement on its division. That's the only way I will give you the money. "

Well, if they each get ALL the money in the suitcase, the way my mind works it doesn't matter how it is split because as long as they agree on it they each get 100K.

[Willy]

:Lando
At some point there must be a division of the money in order to make this scenerio realized. I don't think the money would be allowed to leave the room until it is divided.