Strategic investment decisions in multi-stage contests with heterogeneous players

We study strategic investment decisions in multi-stage contests with heterogeneous players. Our theoretical model of a round-robin rank-order tournament predicts that players conserve resources in a current contest to spend more in the subsequent contest if the degree of heterogeneity in the current (subsequent) contest is sufficiently large (small). We confirm these predictions using data from German professional soccer, where players are subject to a one-match ban if they accumulate five yellow cards. We find that players with four yellow cards facing the risk of being suspended for the next match are (i) less likely to be fielded when the heterogeneity in the current match increases and (ii) more likely to receive a fifth yellow card in the current match when the heterogeneity in the next match increases or when the heterogeneity in the next match but one (for which they return from their ban) decreases.