We empirically model performance in the final round of a multiple-round tournament as a spatially autoregressive process, allowing us to sign and quantify the endogenous interactions between competitors. Doing so speaks to significant regularities in the data that suggest that a player's own performance generally tends to improve with the improving performance of competitors. However, we also find significant asymmetries in the interdependency of player performance that suggest that social interactions, even those found in a fairly straightforward game, can be rather complex. For example, while the positive complementarity in performance is particularly strong between tied players, own performance suffers in response to improving performance of lagging, lower-ability competitors.