(Answered) Question prior to 1999 teams in the national hockey league

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Question: Prior to 1999, teams in the National Hockey League received 2 points for a win, 1 for a tie, and 0 for a loss. Is this a constant-sum game? In 1999, the rules were amended so that a team receives 1 point for a loss in overtime. The winning team still gets 2 points. How does this modification change the answers to the questions above? If it were legal to do so, when would it be rational for the two teams to secretly agree to end regulation play in a tie and then battle it out in overtime? Assume that the utility to each team is the number of points it receives, and that there is a mutually known prior probability p that the first team will win in overtime. For what values of p would both teams agree to this arrangement?

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