Reductions of partizan games

The reduced canonical form of a game G, denoted by G, is the simplest game infinitesimally close to G. Reduced canonical forms were intro- duced by Calistrate (2), who gave a simple construction for computing G. We provide a new correctness proof of Calistrate's algorithm, and show that his techniques generalize to produce a family of reduction operators. In addition, we introduce a completely new construction of G, motivated by Conway's original canonical-form construction.