A public good is one for which those who do not pay for the good enjoy the

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Question:

A public good is one for which those who do not pay for the good enjoy the same benefits as those who do pay for it. Think of publicly supported television or radio; paid members cannot exclude nonmember “free-riders” from watching or listening. With this in mind, consider the following three-person game involving contributions to a public good. Call the three players: Arzu, Irmak, and Lale. Each player has two action choices: contribute or not contribute d unit to the public good, where d denotes the last digit of your student number. Each player who chooses to contribute pays a cost of 1.5×d units. If a player contributes, his payoff is the total number of units contributed by himself and all other players (a maximum of 3 × d units), less the cost of making his own contribution, 1.5 × d units. If a player does not contribute, his payoff is the total number of units contributed by all other players.

a. Draw the game tree for this three-player game.

b. How many strategies does each player have?

c. Find the rollback equilibrium of this game. Is this equilibrium the most efficient outcome? Explain why or why not.