Chapter

Effective Playability in Arithmetical Games

Kumaraswamy Velupillai

in Computable Economics

Published in print January 2000 | ISBN: 9780198295273
Published online November 2003 | e-ISBN: 9780191596988 | DOI: http://dx.doi.org/10.1093/0198295278.003.0007
 Effective Playability in Arithmetical Games

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Class games, called Arithmetical Games, are defined and recursion theoretic questions such as effective playability, diophantine complexity, etc. are posed and formally answered. In the process, classic computable issues are also introduced: the Halting problem for Turing machines, the Busy Beaver, and the Unsolvability of Hilbert's 10th Problem. A complete exposition of Rabin's classic results on arithmetical games is also given in this chapter.

Keywords: Arithmetical Games; Busy Beaver game; computational complexity; decision problems; effectively playable games; Gale‐Stewart Games; Halting problem; Hilbert's 10th Problem; Rabin, M.O; Turing machines

Chapter.  10158 words.  Illustrated.

Subjects: Macroeconomics and Monetary Economics

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