First-mover advantage in best-of series: an experimental comparison of role-assignment rules

Kingston (J Comb Theory (A) 20:357–363, 1976) and Anderson (J Comb Theory (A) 23:363, 1977) show that the probability that a given contestant wins a best-of-2 k+ 1 series of asymmetric, zero-sum, binary-outcome games is, for a large class of assignment rules, independent of which contestant is assigned the advantageous role in each component game. We design a laboratory experiment to test this hypothesis for four simple role-assignment rules. Despite significant differences in the frequency of equilibrium play across the four assignment rules, our results show that the four rules are observationally equivalent at the series level: the fraction of series won by a given contestant and all other series outcomes do not differ across rules.