Talk:Extensive-form game

Merge
Game tree seems to be about extensive form games, except it primarily deals with computer science problems. I think it would be best to merge that content here. Barring that, I think that Game tree should be moved to a different name, and cross links should be included here. What do folks think? --best, kevin [kzollman][talk] 00:00, 20 March 2006 (UTC)


 * Agree. Pete.Hurd 00:50, 20 March 2006 (UTC)


 * Now leaning towards not merging, but making game tree more explicitly CompSsi rather than Game theory. The backwards induction solution section in game tree seems to indicate that empty threats and information sets just aren't an issue in solving game trees.  If that's the case then I don't think merging is in order. Pete.Hurd 14:42, 27 April 2006 (UTC)


 * Uhh, how long has this merge request been pending? I ask because this article has been sitting on hold on the GA nom page for a long, long time.... Homestarmy 19:36, 11 June 2006 (UTC)

Sorry, I think there is no consensus for merging the two articles. I have removed the tag. --best, kevin [kzollman][talk] 19:40, 11 June 2006 (UTC)

In case it isn't blindingly obvious, game tree describes the trees of extensive-form games with perfect and complete information. The only stuff that differs is the terminology. It's probably good to have that simpler article around because linking to extensive-form game from most CGT articles (via redirect) will result in confusion unless we provide dual terminology in this article, which would make it even harder to read. Tijfo098 (talk) 10:17, 26 March 2011 (UTC)

failed GA - reasons
The article itself is interesting, my reasons for failing this article are purely formating and referencing. Gnangarra 00:45, 12 June 2006 (UTC)
 * The lead needs to edited to WP:Lead format with the list moved into the article suggest an introduction section to cover the basic theory.
 * References need to follow WP:Cite, include ISBN numbers for books
 * The formula had originating Author(s) this need to be Cited

Sources for the infintie action space section?
According to Kuhn's 2003 book (ISBN 0691027722), which I had hoped to use to fix that section: The games which have been discussed up to now have been restricted by two conditions [...]: (1) every move has a finite number of alternatives and (2) every play contains a finite number of moves. It is clear that these restrictions can be relaxed in a wide variety of combinations. Actually, only three general types of infinite games have been studied to any extent: the matrix games with a denumerable number or a continuum of pure strategies and infinite game trees in which condition (1) above is satisfied.

And he only treats matrix games over [0, 1], but even there you need to be careful and consider Borel sets etc. So, can someone let me know what a good RS for games of type "(2) and not (1)", which that troubled section describes? Tijfo098 (talk) 07:49, 27 March 2011 (UTC)

Ah, I see that Kuhn's book is a blast from the past: "The reader is deserved an explanation as to why these lectures are published nearly 50 years after they were taught as a course in the mathematics department at Princeton University". So, there have probably been some developments since, thus there's hope for that section yet. :-) Tijfo098 (talk) 07:57, 27 March 2011 (UTC)

Responding to help request
The following was posted on talk:axiom of determinacy:
 * By the way, can someone (meaning Trovatore almost surely) look at the infinite action spaces section of Extensive-form game (the game described here is of that kind). Herrlich says that omega-long games and games where the action sets have omega cardinality are "complementary", but I'm not sure what that entails for the determinatness of perfect games of finite length but with infinite action spaces of various cardinalities. Tijfo098 (talk) 06:23, 27 March 2011 (UTC)

The framework here is too general for me to be able to immediately evaluate the most general answer to what I believe was being requested. However, if you limit yourself to two players, then the determinacy of perfect-information games of finite length (possibly unbounded length, but where every run must eventually reach a terminal node) is equivalent to the axiom of choice. Given AC, you just wellorder all possible nodes, and then a player who is not in a lost position can win simply by always playing the least node (in the wellorder) that does not put him in a lost position.

The other direction requires only the determinacy of a two-move game, and goes as follows: Suppose A is a collection of nonempty sets. The first player plays an element X of A; the second player wins if he can play an element of X. Clearly the first player has no winning strategy. But a winning strategy for the second player is a choice function for A.

Given these facts, I'm not sure the main link to axiom of determinacy is entirely appropriate here (given that AD is inconsistent with AC). -Trovatore (talk) 09:29, 27 March 2011 (UTC)

Org note
This article should probably be organized along the lines of Formal grammar: some introductory examples, the formal definition, and then details on the equilibria etc for each sub-type. Tijfo098 (talk) 13:35, 19 April 2011 (UTC)

Verification of incomplete information sample problem solution
It is stated that "if both types play U, player 2 again forms the belief that he is at either node with probability 1/2. In this case player 2 plays D', but then type 1 prefers to play D". While it makes sense why type 2 would always play U (as is stated elsewhere in the article), it needs to be clarified why "type 1 prefers to play D" because: (1) if player 2 always plays D' (as is stated) when type 1 plays U then player 1 gets +2; (2) if, as suggested is "preferred", type 1 plays D then player 1 gets +1 (because player 2 will play U' to get +2 with the supposed belief that player 1 only plays D with type 1). Note that the "non-optimal" action of type 1 playing U produced a greater reward than the stated "preferred" action of playing D. It seems that the answer would be correct if e.g. t1/D/U' and t1/D/D' first player rewards were swapped, yet note that "if nature selects t1 as player 1's type, the game played will be like the very first game described".

Also it is stated that "player 2 ... randomising if he observes U" (under the assumption that U is always and exclusively played in type 2), presumably because either actions produce the same reward (specifically +1). Here "randomizing" is probably meant as with equal probability. However, given that both actions produce the same outcome, any probability assignment is "optimal", and not just the equal probability one (as is implied in the article). — Preceding unsigned comment added by 184.175.29.158 (talk) 03:36, 23 July 2012 (UTC)

"Gioco in forma estesa" listed at Redirects for discussion
An editor has identified a potential problem with the redirect Gioco in forma estesa and has thus listed it for discussion. This discussion will occur at Redirects for discussion/Log/2022 February 12 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. User:1234qwer1234qwer4 (talk) 02:11, 12 February 2022 (UTC)