We extend the study of procedural fairness in three new directions. Firstly, we focus on lotteries determining the initial roles in a two-person game. One of the roles carries a potential advantage over the other. All the experimental literature has thus far focused on lotteries determining the final payoffs of a game.
Secondly, we modify procedural fairness in a dynamic—i.e. over several repetitions of a game—as well as in a static—i.e. within a single game-sense. Thirdly, we analyse whether assigning individuals a minimal chance of achieving an advantaged position is enough to make them willing to accept substantially more inequality. We find that procedural fairness matters under all of these accounts. Individuals clearly respond to the degree of fairness in assigning initial roles, appraise contexts that are dynamically fair more positively than contexts that are not, and are generally more willing to accept unequal outcomes when they are granted a minimal opportunity to acquire the advantaged position. Unexpectedly, granting full equality of opportunity does not lead to the highest efficiency.