So I’ve said that there’s 2 types of multiplayer game fundamentally: Efficiency Race and Rock Paper Scissors. This video (re)introduced me to the mathematical concept of Transitive and Non-Transitive relations. This is an amazing lens for describing the difference between these two fundamental games.
In an Efficiency Race, there is always one option, or set of options that is always better than the others, per some metric of efficiency (time or victory points). This means that options (or combinations thereof) can be ranked against each other in a transitive fashion. If A > B > C, then A > C. Trackmania is the most pure example of this out there, since you cannot interact with the opponent in any way and a given route will always be faster or slower than another route (assuming you follow it exactly).

This is the payoff matrix for an efficiency race version of rock paper scissors, notice that rock always wins, and scissors always loses, unless they tie


