In order to learn how people actually play in game situations, economists and other social scientists frequently conduct experiments in which subjects play games for money. One such game is known as the voluntary public goods game. This game is chosen to represent situations in which individuals can take actions that are costly to themselves but that are beneficial to an entire community.
In this problem we will deal with a two-player version of the voluntary public goods game. Two players are put in separate rooms. Each player is given $10. The player can use this money in either of two ways. He can keep it or he can contribute it to a “public fund.” Money that goes into the public fund gets multiplied by 1.6 and then divided equally between the two players. If both contribute their $10, then each gets back $20 × 1.6/2 = $16. If one contributes and the other does not, each gets back $10 × 1.6/2 = $8 from the public fund so that the contributor has $8 at the end of the game and the non-contributor has $18–his original $10 plus $8 back from the public fund. If neither contributes, both have their original $10. The payoff matrix for this game is:
(a) If the other player keeps, what is your payoff if you keep? $10.
If the other player keeps, what is your payoff if you contribute? $8.
(b) If the other player contributes, what is your payoff if you keep? $18. If the other player contributes, what is your payoff if you contribute? $16.
(c) Does this game have a dominant strategy equilibrium? Yes. If so, what is it? Both keep.