29
Apr
2013

## Ariel Rubinstein Has Amazed Me

At NYU my “field” was Game Theory, because I figured, if we’re going to formally model economic actions, then let’s get nuts. I have elsewhere criticized the big guns of game theory when they try to talk to the layperson.

So, when Tyler Cowen linked Ariel Rubinstein’s article titled, “How Game Theory will solve the problems of the Euro bloc and stop Iranian nukes,” I was getting ready to knock it out of the park. (Here’s an ungated copy of it.)

If you understand where I was coming from, then just click that link and be amazed. Read the whole thing, the end is the best part.

These 3 paragraphs are simply brilliant:

Nice.

And, by the way, much how I describe to my students how to think of all the models I teach them.

How about describing to me how to think about your sentence, because I have no idea what you said?

There was an implicit “The above post is” before “much how I describe…”

Everything about this blog post (including the links) was outstanding.

Echoing (favorably) Callahan’s post about Achilles and the Tortoise, I think game theory, while useful for logic training purposes, can only ever be an incomplete explanation (and hence flawed if the gaps are filled in with arbitrary, false assumptions) of human activity. Game theory cannot validate itself. I like to think that this means game theory excludes the concept of learning and adaptation.

Even if one tried to set up a game theory scenario *with* learning, for example the model Murphy critiqued in his Mises.org article, where the same game is repeated 1000 times, which seems to allow for learning and tit for tat adaptation, game theorists nevertheless “solve” such a scenario by turning it right back into a static, equilibrium form, with no learning once again. Backwards induction is in fact a technique to erase any learning and adaptation. One by one, step by step, game by game, from game number 1000 on down to game number 1, learning and adaptation is gradually eliminated, and we’re again left with “In equilibrium, the rational strategy is to defect all 1000 times”.

What backwards induction does wrong is manifold. Murphy touched on one aspect, but there is another. Backwards induction is at its root a positive belief to be able to scientifically predict people’s future learning and future actions. Yes, it is constrained to the assumption that people are rational, i.e. that people think the way game theorists think, but that assumption is for now, in the present. It is grounded on present knowledge, not future knowledge. The present knowledge is baselessly extrapolated into the future, which is the same thing as saying there is no learning at all over time during the 1000 games.

Personally, I think there exists a logic that does validate itself. I think it can be found using the philosophical tradition of German Idealism (Kant, Fichte, Mises, Hoppe, etc). In a word, it is

activityitself. The same activity that is being taken for granted when a personusesgame theory models, and every other model. The using of modelsisthe “model” itself. Activity, pure activity, has no grounding, and needs no grounding. It is not deduced, nor is it induced. Passive models presuppose active modelling, and vice versa. Strange loops.Here’s an interesting aside:

The paradox expects Achilles to use his quickness to overtake the tortoise, with the constraint that he must reach every half-way point.

But since the concept of quickness pertains to distance over time, rather than reaching milestones, Achilles and the Tortoise is internally inconsistent.

There’s nothing wrong with logic.

I read Rubinstein’s book a couple of months ago. It was pretty good. This article is basically a distillation of the book’s themes.

Hey, wait a second–isn’t the Regression Theorem a form of backward induction?

Ariel is just brilliant!! The end …….