Question

Suppose fishermen of two neighboring towns, Town A and Town B, use a shared port. Building a lighthouse near the port would cost $20,000, but it would benefit both towns by improving fisherman safety, and therefore each town is considering the decision to sign off on lighthouse construction. A town's payoff from a new lighthouse is given as ui = W; +ri - Ci, where w; is a town's monetary endowment, ri is a town's reservation price for the lighthouse, and c; is the provision cost incurred by the town. If the lighthouse is not provided, neither town gains utility from it (i = 0). However, if at least one town agrees to begin construction, the lighthouse will be built.
Town A has a monetary endowment wa = $40,000 and a reservation price ra = $15,000. Town B has a monetary endowment wp = $30,000 and a reservation price rb = $17,000.

(a) Suppose the towns attempt to coordinate and equally share the $20,000 dollar cost of the lighthouse construction if they both choose to invest. However, there is no legal system in place that will hold them accountable to each other if they chose to not to follow through on their promises. Build a 2x2 game table based on the decision that each town makes, including all three components of a normal form game.

(b) Identify the Nash Equilibrium Equilibria in this game. What is each town's dominant strategy in this game?


(c) What problem does this highlight?

Answer 1

Answer and Explanation:

As per the data given in the question,

a)

W R C U

A 40,000 15,000 20,000 35,000

B 30,000 17,000 0 47,000

A 40,000 15,000 0 55,000

B 30,000 17,000 20,000 27,000

A 40,000 15,000 10,000 45,000

B 30,000 17,000 10,000 37,000

A 40,000 15,000 0 0

B 30,000 17,000 10,000 -10,000

A 40,000 15,000 10,000 -10,000

B 30,000 17,000 0 0

Since if one of the parties stops cooperating, the project will be shut down in the middle by the other town Which will concede negative returns.

                                          Town B

                                   Pay           Doesn't Pay

            Pay     45,000 37,000    -100000 0

Town A Doesn't Pay 0                -10,000 0 0

By completing the project(even without cooperation) the town will earn positive returns.

Hence, started project will be completed.

                                        Town B

                                 Pay                      Doesn't Pay

              Pay 45,000 37,000              35,000 47,000

Town A Doesn't Pay 55,000 20,000   0 0

b)

                                              Town B

                                Pay                     Doesn't Pay

               Pay 45,000 37,000            35,000 47,000

Town A Doesn't Pay 55,000 20,000 0 0

Here

If Town A pays, Town B will not pay.

If Town B pays, Town A will not pay.

That means it shows an inverse relation

Therefore, the Nash Equilibrium in this game = (Pay A, Doesn't pay B) and (Doesn't pay A, Pay B)

In this game, there are no dominant strategy for any town.

c) Since, there is no dominant strategy for any town so it would be difficult for each town to cooperate.

Thus, this game indicates the problem how each town corporate on a Nash equilibrium which gives inequitable payoffs of towns.