Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Let $G,H$ be two (combinatorial impartial) games. Consider the following new game $P$: The positions are the pairs of positions of $G$ and $H$. A move in $P$ is a move in $G$, or a move in $H$, or a move in both. If we end in a terminal position of $G$, we go on and play in $H$. Similarly with $H$ and $G$.

What is the name of this "product game"? Has it been studied somewhere? In particular, what are the $\mathcal{P}$-positions of $P$ in terms of the ones for $G$ and $H$?

share|improve this question

1 Answer 1

up vote 2 down vote accepted

In Winning Ways, this is called the "selective compound" of $G$ and $H$.

In general, the selective compound of a finite number of games is the game where you choose some non-empty subset of the component games at each turn and make one move in each of the chosen games.

In the impartial case, the selective compound is P if all the component games are P (because your opponent can respond in whatever subset of games you move in), and otherwise it's N (because you can move from N to P in all the N components).

share|improve this answer
    
Perfect! Thanks a lot. –  Martin Brandenburg Apr 26 '12 at 7:48

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.