4. Consider the following game played by four individuals, players 1, 2, 3, and 4. Each individual has $10,000. Each pla

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4. Consider the following game played by four individuals,
players 1, 2, 3, and 4. Each individual has $10,000. Each player
can donate between $0 and $10,000 to build a public park that costs
$20,000. If they collect enough money, they construct the park,
which is worth $9,000 to each of them. However, if they collect
less than $20,000, they cannot build a park. Furthermore,
regardless of whether the park is built or not, individuals lose
any donations that they make. a) Describe the Nash equilibria for a
simultaneous game. What makes them equilibria? Hint: There are many
equilibria, so you may want to use a mathematical expression! b)
Suppose that players 1, 2, and 3, each donate $4,000 for the park.
How much will player 4 donate and why. What are the resulting
payoffs for the players? c) Suppose instead that player 1 donated
first, player 2 second, player 3 third, and player 4 last.
Furthermore, players could only donate in intervals of 1,000 (0,
$1,000, $2,000, etc.). How much will each player donate in Subgame
Perfect Nash Equilibrium? Show how you use backward induction to
solve this. Hint: Part c is challenging. Try using a game tree to
solve it.