Kickstarter provides a platform for raising venture capital through crowd sourcing. A project creator sets a funding target and posts the project at Kickstarter. People then decide how much money to pledge. If the total pledges are at least as great as the funding target, then the pledges are converted into contributions and the project is funded. Though the contributors do not own a share of the project, they can receive rewards from the project creator. If the pledges fall short, then the project is not funded. Assume there are three players: one project creator and two potential contributors. The project creator chooses between a funding target of $1,000 and $1,500. With the funding target posted at Kickstarter, the two contributors simultaneously decide whether to pledge $250 or $750. Assume the project creator’s payoff equals three times the amount of funding (which is zero if contributions are less than the funding target). A contributor’s payoff is zero when the project is not funded (irrespective of the pledge made), and is two times the total amount of pledges minus three times the contributor’s own pledge when it is funded.
a. Write down the extensive form game.
b. Write down each player’s strategy set.
c. Write down the strategic form game.