Teams in the National Hockey League historically received 2 points for winning a game and 0 for
Question:
Teams in the National Hockey League historically received 2 points for winning a game and 0 for losing. If the game is tied, an overtime period is played; if nobody wins in overtime. the game is a tie and each team gets 1 point. But league officials felt that teams were playing too conservatively in overtime (to avoid a loss), and it would be more exciting if overtime produced a winner. So in 1999, the officials experimented with mechanism design: the rules were changed, giving a team that loses in overtime 1 point, not 0. It is still 2 points for a win and I for a tie.
a.Was hockey a zero-sum game before the rule change? After?
b.Suppose that at a certain time t. in a game, the home team has probability p of winning in regulation time, probability 0.78 — p of losing, and probability 0.22 of going into overtime, where they have probability q of winning, .9 — q of losing, and .1 of tying.
Give equations for the expected value for the home and visiting teams.
c.Imagine that it was legal and ethical for the two teams to enter into a pact where they agree that they will skate to a tie in regulation time, and then both try in earnest to win in overtime. Under what conditions, in terms of p and q, would it be rational for both teams to agree to this pact?
d.Longley and Sankaran (2005) report that since the rule change, the percentage of games with a winner in overtime went up 18.2%, as desired, but the percentage of overtime games also went up 16%. What does that suggest about possible collusion or conser-vative play after the rule change?
Artificial Intelligence A Modern Approach
ISBN: 978-0137903955
2nd Edition
Authors: Stuart J. Russell and Peter Norvig