What a game gives Cauldron2D.World to run: a pure value and the callbacks that change it.

defmodule MyGame do
  @behaviour Cauldron2D.Game

  def init(opts), do: ...
  def join(state, player_id, props), do: {:ok, state}
  def leave(state, player_id), do: state
  def handle_input(state, player_id, %{held: held, aim: aim}), do: state
  def step(state, dt), do: state
  def view(state, player_id), do: ...
  def drain_events(state), do: {events, state}
end

Every callback is pure. step/2 is called once per fixed tick with dt in seconds; handle_input/3 before the tick for each player whose input changed; view/2 after it for each player, and what it returns is sent to that player; drain_events/1 after it, once, and the events go to every player. Nothing here reads a clock, and a game built with the same options and given the same calls in the same order runs identically.

join/3's props are the game's to define. The clients in the cauldron_2d_* packages pass :username (the player's name as a string) and whatever the game's own join_props callback adds; a game that wants teams, spectators or anything else names those props itself and reads them here.