Three rms use water from a lake. Each rm has two possible actions: treat sewage (T) or dump sewage (D). If no or only one (1) rm dumps sewage, the…

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Three firms use water from a lake. Each firm has two possible actions: treat sewage (T) or dump sewage (D). If no or only one (1) firm dumps sewage, the lake remains clean. If two or more firms dump sewage, the lake becomes polluted. Each firm gets a revenue of 4 if the lake is clean, and a revenue of 1 if the lake is polluted. The cost of treating sewage is 1. There is no cost to dumping sewage. Each firm’s payoff is given by its revenue minus sewage treatment cost, if any.

(a) Describe this situation as a normal form game using payoff matrices.

(b) Is there a (strongly or weakly) dominated action for each player? If yes, which one? If no, explain why.

(c) Find all pure strategy Nash equilibria of this game. (d) Is there any equilibrium in which the lake is polluted? If yes, which one(s)?