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)?