The Weekly N&C for December 1st, 2008

Does the Predictor exist?

In a more than slightly amusing moment of converging interests, this author has recently needed to revisit the study of elements of Game Theory as it applies to negotiations and the expected conduct of the participants in and after a negotiated agreement. While Game Theory is a vast and widely applicable concept, having been applied to Economics, Political Science, Biology and Military Science (specifically Strategic Deterrence), in this particular need the application is more philosophical. When asked to evaluate the post-negotiation conduct of a participant in an ongoing negotiation, are there some lessons that can be taken from the problems and paradoxes of Game Theory exercises that shed some illumination?

That, as is wryly said, depends on what kind of illumination one is in need of.

Most all the basic exercises in Game Theory as applied to economic choices and group behavior call upon the three elements of: Rational Actors; Minimized Losses; Maximized Gains. Casting academic posturing aside for a moment, those are actually very straightforward concepts and they all work and play together very well. “Rational Actors” simply means that the participants in the event *that may make choices that effect the result* will act in a manner that is rationally consistent with reaching goals. “Minimized Losses” states that losses in the course of the activity are to be avoided, and if possible reduced to nil. “Maximized Gains” states that where gain can be had, the greater gain is the more desirable outcome. Put these three things together and one has pretty much what any student of human nature could identify: People will make reasoned choices to lose as little and gain as much from any arranged exchange as possible.

At least, that is the simple model. But even by the time von Neumann and Morgenstern published their classic work “Theory of Games and Economic Behavior” (1944), many other and more complex factors were under consideration. If one is a fan of American biographies or movies, the portrayal of mathematician John Forbes Nash Jr. in “A Beautiful Mind” includes his pioneering work in identifying key elements of Game Theory, in particular the situation where each participant in the situation identifies the best possible choice based on the best possible choices the other participants are making, and none of the participants changes their choice from that point on even if greater rewards are possible if the other participants were to change their choices.

Continued theoretical work in a host of fields added vastly to the complexity beyond equilibrium choices, considering all sort of variations in rationality and in common knowledge held by the participants. Perhaps the most challenging exercises came to be focused upon conduct in a two-actor exercise where a Predictor has some very high probability of (if not perfection in) knowing what the choice the Chooser will make *before it is made*, and the Chooser is aware of that capability before being asked to choose. Arguably, such an exercise seems at first to be of no use other than of philosophical weight-lifting, but let us be certain of understanding the elements of that sort of problem before seeking to find applicability.

The text-book example of the Predictor-Chooser exercise in Decision Theory is Newcomb’s Problem (also called Newcomb’s Paradox). It was first analyzed and shortly thereafter popularized in the philosophical community in 1969 in Robert Nozick’s essay “Newcomb’s Problem and Two Principles of Choice”, and here is a common example of the situation (the “player” is the Chooser):

The player of the game is presented with two opaque boxes, labeled A and B. The player is permitted to take the contents of both boxes, or just of box B. (The option of taking only box A is ignored, for reasons soon to be obvious.) Box A contains $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.

By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.

What makes this such an engaging exercise is that by the two schemes of optimal decision-making, (Expected Utility and Dominance, respectively) opposite choices are called for with equally valid rationality, and yet when addressed philosophically this problem devolves into a challenge to the possibility that such a (near-?) perfect Predictor could exist, and if it did, is there then no such thing as Free Choice…

What should be immediately noted is that in this exercise, one of the basic elements is missing. There is no loss to be mitigated or avoided, other than the “opportunity cost” of not gaining the minimum guarantee-able result (in this example $1,000, the least result of a "take A and B" choice).

Furthermore, if one *believes* in the infallibility of the Predictor, the B-only choice is perfectly rational and *should* reward one with $1,000,000.

Let us now look into an alternative problem, one with a similar basis in Chooser-Predictor structure and that includes some element of loss as a part of the choice. Again, looking to the text-book examples, one finds The Toxin Puzzle (1983), by Gregory S. Kavka. In this example “the Billionaire” is the Predictor and the “You” is the Chooser:

An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is. . . intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

Note very carefully the wording “All you have to do is… intend…”, and then consider the philosopher’s immediate challenge to the exercise that one can not intend to do something that when the moment arrives one will not do.

The money is in the bank, if one did at midnight so intend.

Once the money is in the bank, can any rational Chooser then keep to that intention knowing that there is no practical obligation to actually drink the toxin at the appointed time?

Would not that imply then that any Predictor who actually put the money in the bank would be in fact predicting an irrational Chooser?

Presuming the goal of the Predictor in initiating this exercise is to actually get the Chooser to drink the toxin, has the Predictor made himself a prisoner of his own infallibility in discerning intention as well as required for his own success the irrationality of the Chooser?

With all that in hand, this is a time for an application to reality.

From the U.S. Department of State Briefing on North Korea, October 11th, 2008:

QUESTION: Yeah. If the North does not fulfill its verification promises, then what happens? Would they be put once again on the state sponsors of terrorism list? And do you have a package of punitive measures prepared in case they don’t comply with what they’ve said they’re going to do?

AMBASSADOR KIM: I mean, I don’t want to – speculation on North Korean noncompliance. I think we need to focus on the next step, which is to make this into a Six-Party protocol. And you know, they’re obligated to cooperate with verification activities. In fact, they stated in their declaration that they would cooperate fully with the verification activities. And in numerous discussions, they have reaffirmed that they’re prepared to cooperate fully with verification activities, so we will hold them up to their word.

“…they’re obligated to cooperate…”

Says who? The entire effort to negotiate the de-nuclearization of North Korea is, and has been from the earliest promises of reward for negotiated intentions, nothing more than a real-life Toxin Puzzle. The gain to the Chooser (North Korea) continues to be one they receive in return for the confidence of the Predictor (the U.S. and other negotiators) in the Predictor’s ability to *both* accurately detect intention *and* to believe that the Chooser will “irrationally” suffer the toxin having already received the gain desired.

So long as the methodology of the negotiation is more akin to The Toxin Puzzle and less like a conventional negotiation-to-mutual-and-contemporaneous-obligation, then the only hope for success is that the Predictor is really perfect and that Intention can not exist without (“irrational”) Commitment to fulfillment.

Is anyone really willing to play that game?

***
End Notes:

In addition to the DeptState document embedded as a link, the following general information may be of use to readers. The usual caveat regarding Wiki-p entries applies: Check the sources cited there.

General Information on Game Theory

General Information on the Nash Equilibrium

General Information on Newcomb’s Problem

General Information on The Toxin Puzzle