15.07.2022 - 21:48

# 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 p

Question:

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.

a. The extensive form game is shown in the diagram below:  Project Creator / $1,000$1,500 / Contributor 2 Contributor 1 / / $250$750 $250$750 | | | | F F F F  where F represents the outcome of the project not being funded, and the numbers represent the amount of money pledged. b. The strategy set for the project creator is {choose $1,000, choose$1,500}. The strategy set for each contributor is {pledge $250, pledge$750}. c. The strategic form game is shown in the table below:  | $250,$250 | $250,$750 | $750,$250 | $750,$750 | ------------------------------------------------------------------- $1,000 chosen | 0, 0 | 750, 250 | 0, 750 | 1500, 500 |$1,500 chosen | 0, 0 | 1000, 500 | 500, 0 | 1500, 500 |  In this game, the first number in each element of the table represents the project creator's payoff, and the second number represents the total payoff for both contributors. For example, if the project creator chooses a funding target of $1,000 and both contributors pledge$250, the project is funded and the payoffs are 0 for the project creator and 0 for each contributor. If one contributor pledges $250 and the other pledges$750, and the project creator chooses a funding target of \$1,500, the project is funded and the payoffs are 1000 for the project creator and 500 for each contributor.