HOW TO MAKE YOUR FAVOURITE PLAYER WIN A TOURNAMENT Veronica Chiarelli*, Anil Maheshwari, Saeed Mehrabi. School of Computer Science, Carleton University, Ottawa, Ontario, Canada. K1S 5B6. Suppose you are running a tournament where a single winner will be determined, but you wish to have your favourite player win. What strategies can be used when organizing the tournament to guarantee that your favourite player is the winner? How many different ways are there to set up the tournament to ensure this result? If it is impossible to organize the tournament so that your favourite player wins, how can bribery of some of the opponents be used to achieve the goal? Knockout tournaments are commonly used for sports competitions. Manipulating their outcome is a problem that has been a topic of interest in recent computational social choice research [1,2,3]. In this project, we study the structure of knockout tournaments. In particular, we are interested in organizing a tournament to make a specific player the winner. To this end, we formulate the problem as a graph-theoretic problem. Properties of the graph correspond to how the tournament proceeds. Exploiting structures of the graph allows us to compute the initial set of the tournament. Then we can organize the tournament, using the graph’s structure, to make our favourite player win. If no such structure can be found, we then bribe some of the opponents: we “fix” the graph so as to ensure the existence of the desired structures. We also explore an algorithm by Aziz et al. [1], which counts the number of ways in which our favourite player can win the tournament, and we provide an implementation of that algorithm. References [1] Haris Aziz, Serge Gaspers, Simon Mackenzie, Nicholas Mattei, Paul Stursberg, Toby Walsh: “Fixing balanced knockout and double elimination tournaments”. Artif. Intell. 262: 1-14 (2018) [2] Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi: “Winning a Tournament by Any Means Necessary”. IJCAI 2018: 282-288 [3] Sushmita Gupta, Sanjukta Roy, Saket Saurabh, Meirav Zehavi: “When Rigging a Tournament, Let Greediness Blind You”. IJCAI 2018: 275-281