Suppose that a certain society consists of only two people and that each of thes

Question

Suppose that a certain society consists of only two people and that each of these people drives a car. Suppose that each person could voluntarily choose to put a pollution control device on his or her car. Installing such a device on one car costs $100 and provides a benefit (in the form of cleaner air) that is worth $70 to each of the two people (so total benefit if both install is worth $140). Each person in this society has two possible actions, Install or Not install.

(a) Assuming this game is a simultaneous, one-time game, draw a payoff matrix showing the net (dollar) benefit (or cost) to each of the two people for all four possible outcomes of the game.

(b) Find the Nash Equilibrium.

(c) How would you describe this game? (Prisoners Dilemma or Battle of Sexes)

Explanation / Answer

A) The payoff matrix for this game is shown below. Note that when both A and B install the device, they both get a total utility of worth $140 and hence, their cost of $100 each is recovered. But when one of them installs and the other does not, the payoff turns negative for the installer.

Individual B

Individual A

Install

Not install

Install

(40, 40)

(-30, 0)

Not install

(0, -30)

(0, 0)

B) There are two Nash equilibriua for this game, either they both install or they both do not install.

C) The game resembles the situation of Battle of Sexes since there is no dominant strategy of any individual unlike the Prisoners Dilemma where both convicts have dominant strategy to confess. Here, Both would prefer to choose the same strategy rather then different ones.

Individual B

Individual A

Install

Not install

Install

(40, 40)

(-30, 0)

Not install

(0, -30)

(0, 0)

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