Question

Consider the following public goods game. There are more than 2 players. Each player is given...

Consider the following public goods game. There are more than 2 players. Each player is given $20 at the start. Players individually decide how much of the $20 to invest in the public good. Each $1 invested in the public good generates a benefit of $2. A player’s payoff is the $20 minus the amount they invested plus an equal share of the total benefit.
a. What is the Nash equilibrium?
b. If players could decide on investment collectively, how much would be invested?

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Answer #1

Nash equilibrium will be at 12$ investment as as one maximize it's profit on such scenario . ( Take two situation in which A decides to invest some amount and B decides to not invest any .2- B decides to invest while A decides not to both will loosing in such scenario but in case of 12$ ~ 8$ +24/2 =20$ no one will suffer loss and in any case if other invest any amount ,it will be profitable for both.

If players coluld decide collectively they will invest total 40$ to maximize their profit.

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