5. [10 Points] Three cities use water from a lake for production and consumption. Each city...

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5. [10 Points] Three cities use water from a lake for production and consumption. Each city has two pure strategies: purify sewage (P), or dump raw sewage (D). If zero or one cities choose D, the water remains pure, but if two or three cities choose D, the water becomes polluted and each city suffers a loss of 3. A city's cost of choosing P is 1. What numbers of cities choosing P are part of a pure strategy Nash equilibrium of this game? Your answer should be some or all the integers {0, 1, 2, 3), unless the game has no pure strategy Nash equilibria or more information is needed (if either of these is the case, you must state which to receive credit). 5. [10 Points] Three cities use water from a lake for production and consumption. Each city has two pure strategies: purify sewage (P), or dump raw sewage (D). If zero or one cities choose D, the water remains pure, but if two or three cities choose D, the water becomes polluted and each city suffers a loss of 3. A city's cost of choosing P is 1. What numbers of cities choosing P are part of a pure strategy Nash equilibrium of this game? Your answer should be some or all the integers {0, 1, 2, 3), unless the game has no pure strategy Nash equilibria or more information is needed (if either of these is the case, you must state which to receive credit).