Player preferences in \(N\)-player games

In this paper we describe several player preferences in games with \(N \geq 2\) players, in particular the case \(N = 3\), and use them to simplify game trees, using the game of Clobber as our example. We show that, using a fixed starting player and a certain ruleset, any short game can be simplified to a value in a very concise set. Omitting the fixed starting player and generalising the theory to more than 3 players remains a challenge.