### Does either firm have a dominant strategy

##### Reference no: EM131391983

Two firms, A and B, are situated next to a lake, and it costs each firm €1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake's water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake depends on how many firms are polluting the lake. The cost to each firm is €1,000 multiplied by the number of polluting firms. Assume that the firms do not communicate with each other. Each firm is facing a choice of either buying a filter or not

a. Write out this situation in normal form (i.e. matrix form).

b. Does either firm have a dominant strategy? Explain your answer carefully.

c. What is the Nash equilibrium of this game if it is played once?

d. Is this game an example of a Prisoner’s Dilemma game? Explain your answer carefully.

e. Suppose this game was played repeatedly. Discuss whether the equilibrium outcome of the game would be the same as when it is played once, referring to both finite and infinite games in your answer.

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