Problem #WSP - 000003

Problems Set theory and logic Theory of algotithms Game theory
 10–13  2.0

Problem

A technique that can be used to completely solve certain games is drawing game graphs. Given a game \(G\), we draw an arrow pointing from a position \(g\) to a position \(h\) if there is a move from \(g\) to \(h\).

As a simple example, the game graph of \(\text{Nim}(2)\) is shown below.

image

Draw the game graph of \(\text{Nim}(2,2)\). Is \(\text{Nim}(2,2)\) a winning position or losing position?