Each firm has the choice to use either their own private ranking or the common algorithmic ranking to order the
candidates. In a random order, each firm hires the highest-ranked available candidate according to the ranking they chose. For example, if firm 1 uses their private ranking and firm 2 uses the algorithmic ranking, then firm 1 hires candidate
, and firm 2 hires candidate
. If both firms use the algorithmic ranking, then the firm randomly selected to hire first hires candidate
, and the firm randomly selected to hire second hires candidate
.