Concept explainers
Golf In a simplified variation of the Ryder Cup golf competition between the United States and Europe, each team captain must choose between a very good golfer (V) for the first game of a one-to-one match and a good golfer (G) for the second, or vice versa. Suppose that pvv represents the probability that a very good golfer from one team will beat a very good golfer from another, with analogous meanings for pGG, pVG and pGV. Assume that for either side to win the tournament, they must win both games, so the payoff for choosing a strategy is the probability of winning both games. Assume that these probabilities are independent. Source: Interfaces.
(a) Explain why the payoff matrix (from the point of view of the United States) is given by
(b) We will assume that pVVpGG ≠ pVGpGV. (Why would the problem be trivial if this assumption were not true?) Explain why this implies dial there is not a saddle point.
(c) Under the assumption of part (b), find the optimal strategy for each team. What is the value of the game?
(d) Explain why, because of symmetry, the optimal strategy found in part (c) is obvious, without doing any calculations.
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