[qfwfq_]

The efficiency gap is just one measure of partisan bias that can be used to assess the utility/efficacy of any redistricting plan. The game the authors propose is (basically) an algorithm to draw good districts between two players. So, there's no real or expected relationship between the two... partisan control (the objective the authors cite) isn't necessarily related to the efficiency of that control measured by the efficiency gap. The problem is that so many different measures of fairness exist, have validity, and can be used in different legal or jurisprudential contexts, we're always talking past each other on the meaning of these measures.