CS36A: Algorithmic Game Theory Lecture #1: Introduction and Examples

We begin with a cautionary tale. In 2012, the Olympics were held in London. One of the biggest scandals of the event concerned, of all sports, women’s badminton. The scandal did not involve any failed drug tests, but rather a failed tournament design that did not consider carefully incentives. The tournament design used is familiar from the World Cup. There are four groups (A,B,C,D) of four teams each. The tournament has two phases. In the first ”round-robin” phase, each team plays the other three teams in its group, and does not play teams in other groups. The top two teams from each group advance to the second phase, the bottom two teams from each group are eliminated. In the second phase, the remaining eight teams play a standard ”knockout” tournament (as in tennis, for example): there are four quarterfinals (with the losers eliminated), then two semifinals (with the losers playing an extra match to decide the bronze model), and then the final (the winner gets the gold, the loser the silver). The incentives of participants and of the Olympics committee (and fans) are not necessarily aligned in such a tournament. What does a team want? To get as good a medal as possible, of course. What does the Olympics committee want? They didn’t seem to think carefully about this question, but in hindsight it’s clear that they want every team to try their best to win every match. Why, you ask, would a team ever want to lose a match?