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Contrary to the popular belief, chess is not a finite game without at least one of the fifty move rule or threefold repetition rule. Strictly speaking, chess is an infinite game therefore backward induction does not provide the minmax theorem in this game. [6] Backward induction is a process of reasoning backward in time.
A variant first described by Claude Shannon provides an argument about the game-theoretic value of chess: he proposes allowing the move of “pass”. In this variant, it is provable with a strategy stealing argument that the first player has at least a draw thus: if the first player has a winning move in the initial position, let him play it, else pass.
Ernst Friedrich Ferdinand Zermelo (/ z ɜːr ˈ m ɛ l oʊ /, German: [tsɛɐ̯ˈmeːlo]; 27 July 1871 – 21 May 1953) was a German logician and mathematician, whose work has major implications for the foundations of mathematics.
The phrase “Zermelo-Fraenkel set theory” was first used in print by von Neumann in 1928. [8] Zermelo and Fraenkel had corresponded heavily in 1921; the axiom of replacement was a major topic of this exchange. [7] Fraenkel initiated correspondence with Zermelo sometime in March 1921. However, his letters before the one dated 6 May 1921 are lost.
[1] [2] Ernst Zermelo introduced the axiom of choice as an "unobjectionable logical principle" to prove the well-ordering theorem. [3] One can conclude from the well-ordering theorem that every set is susceptible to transfinite induction, which is considered by mathematicians to be a powerful technique. [3]
There are several different degrees of incentive-compatibility: [4] The stronger degree is dominant-strategy incentive-compatibility (DSIC). [1]: 415 It means that truth-telling is a weakly-dominant strategy, i.e. you fare best or at least not worse by being truthful, regardless of what the others do.
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There is a class of chess positions called Zugzwang in which the player obligated to move would prefer to "pass" if this were allowed. Because of this, the strategy-stealing argument cannot be applied to chess. [5] It is not currently known whether White or Black can force a win with optimal play, or if both players can force a draw.