Becoming the World's Highest Rated Chess Player
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The Elo rating system measures the approximate skill of each competitor in a game or sport. As a competitor competes, their rating changes based on their wins and losses. Increasing one's rating can be difficult work; one must hone their skills and consistently beat the competition. Alternatively, with enough money you can rig the outcome of games to boost your rating. Say you manage to get together n people (including yourself) and acquire enough money to rig k games. How high can you get your rating? The people you gathered aren't very interested in the game, and will only play if you pay them to. We resolve this question for n=2 and n=Ω(k^1/3) (up to a log factor) for the standard Elo system, and provide close upper and lower bounds for a wider class of rating systems that resemble Elo.
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