Although theory on corruption is well developed, it has proven difficult to isolate corrupt behavior empirically. In this paper, we provide overwhelming statistical evidence documenting match rigging in Japanese sumo wrestling. A non-linearity in the incentive structure of promotion leads to gains from trade between wrestlers on the margin for achieving a winning record and their opponents. We show that wrestlers win a disproportionate share of the matches when they are on the margin. Collusion, rather than increased effort, appears to explain the results. Wrestlers who are victorious when needing a victory lose more often than would be expected the next time they meet that same opponent, suggesting that part of the payment for throwing a match is future payment in kind. Cheating disappears in times of high media scrutiny. In addition to collusion by individual wrestlers, there is also evidence of reciprocity agreements across stables of wrestlers, suggesting a centralized element to the match rigging.