Question

Two firms, A and B, are situated next to a lake, and It costs each lakeside firm $4000 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 is $3000 times the number of polluting firms. Assuming there are only two firms (and listing all payoffs in thousands of $).
Does either firm have a dominant strategy? Explain your answer carefully.

Answer 1

Answer:

we can prepare a matrix to determine the best strategy:

                                                   firm A

                                      buy filter            not buy filter

                                     -$4,000 /             -$3,000 /

            buy filter                     -$4,000                -$7,000

firm B

           not buy filter     -$7,000 /             -$6,000 /

                                                -$3,000                -$6,000

Firm A's expected value for buying the filters = -$4,000 - $7,000 = -$11,000

Firm A's expected value for not buying the filters = -$3,000 - $6,000 = -$9,000 ⇒ LOWER EXPECTED COST = DOMINANT STRATEGY

Firm B has he same expected values as Firm A.

So both firms' dominant strategy is not to buy the filters, then both firms will probably not buy them. But that action will also result in the highest total cost = -$6,000 - $6,000 = - $12,000

In this situation the Nash equilibrium would be that both firms purchase the filters, but since the dominant strategies for both firms tell them not to, it will not happen.