On tame, pet, miserable, and strongly miserable impartial games
نویسنده
چکیده
We consider tame impartial games and develop the Sprague-Grundy theory for misère playing the sum of such games that looks simpler than the classical theory suggested by Conway in 1976, which is based on the concept of genus. An impartial game is called pet if the sets of P-positions of its normal and misère versions are disjoint. We provide several equivalent characterizations and show that the pet games form a proper subfamily of the tame games. For example, NIM, Wythoff’s NIM, and game Euclid are tame but not pet, while all subtraction games, the Fraenkel extension NIM(a) of Wythoff’s NIM(1), as well as its further extension NIM(a, b) recently suggested by the author are pet games whenever a > 1. Thus, very many important impartial games are tame or pet.
منابع مشابه
Miserable and strongly miserable impartial games
An impartial game is called (strongly) miserable if its normal and misère versions differ just slightly; more precisely, if some (all) zeros and ones of the Sprague-Grundy (SG) functions swap, while all larger values remain the same. We obtain necessary and sufficient conditions for (strong) miserability and show that NIM, Wythoff’s NIM, and game Euclid are miserable but not strongly miserable,...
متن کاملMiserable Migrants? Natural Experiment Evidence on International Migration and Objective and Subjective Well-Being
Miserable Migrants? Natural Experiment Evidence on International Migration and Objective and Subjective Well-Being Over 200 million people worldwide live outside their country of birth and typically experience large gains in material well-being by moving to where incomes are higher. But effects of migration on subjective well-being are less clear, with some studies suggesting that migrants are ...
متن کاملTowards NEXP versus BPP?
We outline two plausible approaches to improving the miserable state of affairs regarding lower bounds against probabilistic polynomial time (namely, the class BPP).
متن کاملPolicy Analysis No
National prohibition of alcohol (1920-33)--the "noble experiment"--was undertaken to reduce crime and corruption, solve social problems, reduce the tax burden created by prisons and poorhouses, and improve health and hygiene in America. The results of that experiment clearly indicate that it was a miserable failure on all counts. The evidence affirms sound economic theory, which predicts that p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012