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 in 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 1 for a tie.
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Was hockey a zero-sum game before the rule change? After?
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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.
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Imagine that it were 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?
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@Longley+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 3.6%. What does that suggest about possible collusion or conservative play after the rule change?