Game Theory in Sumo Wrestling
The thousand year old sport of sumo wrestling may seem like an unlikely home of corruption through rigged matches, but sumo wrestlers are still human and their greed for money and power overcome their respect for the sport. Analysis of match data and the sumo community network have shown that players often allow a fellow wrestler to win a match when it is one that determines whether or not he can rise or fall in the ranks.
The sumo wrestling world has a clear cut hierarchy whose changes are determined by the ratio of a wrestler’s wins to loses in a given season. Each wrestler plays 15 matches in a season, and as long as a player wins more than he loses, he will be able to rise in rank; however, if the player loses more times than he wins, his rank will fall greatly. The difference in treatment and prize money between ranks is purposefully set to a large jump as to motivate players to want to win. So a player with a 7-7 record has much more at risk in his last match of the season than a player with an 8-6 record. As a result, when those two players go head to head in their last match, the 8-6 player will often allow the 7-7 play to win, in fact the 7-7 player will win 70% of the time in his last match. So why does the 8-6 player allow the 7-7 player to win?
The sumo community is quite tight knit and wrestlers often have many matches with people of similar rank over the seasons and become more acquainted with each other. The stronger the tie between two wrestlers, the greater the chance there is for them to rig a match. Players who know each other understand how they each struggle in maintaining their status. The same way people empathize in non-sumo related situations, it is harder for one to watch a close friend struggle than it is to watch a stranger go through the same thing. However, the game rigging is not just out of courtesy for each other, the 8-6 player will give up the last match of the season knowing that the 7-7 player will owe him either a monetary payment or a match in later seasons when he is in need of a win. In a way, the 7-7 player is bound to the 8-6 player until he returns the favor. If this were to be expressed in terms of a game theory strategy, the 7-7 player winning his last match is the dominant strategy because the 8-6 player would still have a positive win-to-loss ratio, and the 7-7 player will be able to maintain his rank as well. This strategy is beneficial for both sides. On the other hand, if the 8-6 player wins the match, it would leave the 7-7 with a downgrade in rank and the 8-6 player would advance to the next rank, making this the aggressive strategy. Since the 8-6 player will have the same result in both cases, the best response strategy is for the 7-7 player to be able to win.
How has this kind of cheating been allowed to go on for so long without getting caught? Sumo has such a deep history and a strong connection to religion that few ever dared to question the legitimacy of any of its matches. The sumo players themselves are also aware of the watchful eyes that follow them. When the final match of the season is one that is in the spotlight with the press and fans, the probability of game rigging drops significantly. On the rare occasions that someone exposes the sumo community for game rigging, the big companies that sponsor sumo will use their power to quiet the press and prevent uproar. This kind of corporate power is a whole other topic on economy and corruption. A millennium old sport that is seemingly simple and even barbaric has a much more complex web tied to the economy and corruption than the face value suggests.
Sources:
http://www.nber.org/papers/w7798
http://www.nber.org/papers/w7798.pdf