Sannolikhets- och statistikseminarium: The "No justice in the universe" phenomenon: Why honesty of effort may not be rewarded in matchplay tournaments
- Plats: Ångströmlaboratoriet 64119
- Föreläsare: Peter Hegarty, Chalmers
- Kontaktperson: Fiona Skerman
Abstract: Consider two facts. First fact: In real-life sports tournaments, situations often arise where it is in the interest of a competitor to deliberately underperform, even to the extent of deliberately losing a game. That this doesn't actually happen too often is probably because of the resulting high-profile "scandal", though a famous instance in Swedish sport occurred at the 2006 Olympic Ice Hockey tournament, where the team were, and still are, credibly accused of throwing their final group game in order to lower their seeding for the knockout phase. Second fact: A truel is like a duel, but with three shooters. It is known that for certain values of the shooters' "competences" (represented as probabilities in a 3x3 matrix), the worst shooter has the highest probability of surviving. Now in a truel, it is clear that the rules are the same for everyone and it can never be in someone's interest to underperform (assuming competences are public knowledge). By contrast, in real-life tournaments, "unfairness" is often built into the rules in that one or other of these two conditions is lacking. This motivated us to ask whether it is possible for the rules of a matchplay tournament to ensure "symmetry", meaning equal treatment of all competitors, and "honesty", meaning that a situation can never arise where it is in a competitor's interest to lose a game, but that the tournament is nevertheless "unfair" in the sense that for certain values of the competitors' competences, a worse player has a higher probability of winning than a better one. Having rigorously defined terms, we will show that this is indeed possible. The question of "how unfair" a symmetric and honest n-player matchplay tournament can be then turns out to be mathematically non-trivial and we will formulate a conjecture and some partial results. (Joint work with Anders Martinsson and Edvin Wedin. Preprint with same title available on arxiv).