Talk:Backward induction

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paradox of backward induction[edit]

The so-called paradox of backward induction is really about backward deduction. --Arno Matthias 14:33, 1 August 2006 (UTC)

Why not include both game theory and optimization meanings in this page?[edit]

The meaning of "backward induction" in game theory is closely related to its meaning in dynamic programming. I see no reason this page couldn't include sections on both topics. Moving that discussion to the Bellman equation page, section "solution methods" would likely make the Bellman equation page far too long (at least once the Bellman equation page progresses past stub class). I'll be happy to provide a short section here on backwards induction in dynamic programming. Rinconsoleao 17:17, 13 November 2007 (UTC)

They didn't strike me as being that closely related. If you can incorporate the dynamic programming stuff into this article such that it forms a coherent whole, then power to you!
I figured eventually there would grow to be pages Backward induction (game theory) and Backward induction (dynamic programming), so it's a question of whether that growth should come from this article or Bellman equation getting split. Vagary 19:10, 13 November 2007 (UTC)
I'll give it a try. If the page becomes too complicated, we can separate it into two. Rinconsoleao 11:39, 14 November 2007 (UTC)
By the way, I removed a discussion of American options from the subgame perfect equilibrium page, because as far as i can tell it is an example of an optimization problem, not an example of a game. If someone can spell that example out in greater detail on this page, it could be useful here. Rinconsoleao 13:46, 14 November 2007 (UTC)

Unexpected Hanging paradox[edit]

The prisoner assumes her jailers are telling the truth in a completely precise way.

The actual meaning of their words are, "you will have no information about which day you will be executed on, until you find that you are alive at the end of a day."

The only way for the wording to be precisely correct is if there is a chance she will not be executed at all, or that the execution will be delayed. —Preceding unsigned comment added by (talk) 22:00, 11 May 2008 (UTC)

oops, autosigned by SineBot :p forgot.

Not convinced by a source[edit]

In the "prologue" of the page it is written:

In game theory, backward induction was first employed by John von Neumann and Oskar Morgenstern in their Theory of Games and Economic Behavior (1944). [1]

The reference quoted mentions vN and M, here:

Others claim he used a method of proof, known as 'backwards induction' that was not employed until 1953, by von Neumann and Morgenstern.

I am quite suspicious about this reference: 1953 is just the date of the 3rd edition of the book by vN and M, while it is the year in which it appeared the proof of the Kuhn's theorem which guarantees that finite games with perfect information have a Nash equilibrium in pure strategies. And the proof is based on backward induction.

I would like to see some more reliable attribution of backward induction to vN and M (quoting page or chapter of some edition of the book). --Fioravante Patrone en (talk) 06:38, 8 March 2009 (UTC)

checked. The reference is OK. Not only von Neumann and Morgenstern use induction for perfect information games (even if restricted to the zero-sum case) in pages 111 and ff. They even say: "can be used to work backwards" in page 116. I refer to the original 1944 edition of the book. -- (talk) 02:44, 13 June 2009 (UTC) Sorry, I was not logged in. --Fioravante Patrone en (talk) 02:46, 13 June 2009 (UTC)

May be a typo?[edit]

I guess the "time 9" in below line should be "time 8"

Since we have already concluded that offers at time 9 should be accepted, the expected value of waiting for a job offer at time 9 is 0.5*($200+$88) = $144.