A unifying additive theory for standard conventions in combinatorial game theory

Absolute Combinatorial Game Theory

We propose a unifying additive theory for standard conventions in combinatorial game theory, including normal-, mis\``ere-and scoring-play, studied by berlekamp, conway, dorbec, ettinger, guy, larsson, neto, nowakowski,milley, renault, santos, siegel, sopena, stewart (1976-2019), and others.Here, we reveal when the fundamental game comparison problem simplifies to a constructive `local' solution, which generalizes conway s foundational result in onag (1976) for normal-play games.This happens in a broad and general fashion whenever a given game universe is absolute.