In an Investment Game::

• Each agent can either invest $0 or $10.
• If you don't invest, your final payoff is $0.
• If you invest $10: you get back your $10 and make an additional profit of $5 only if more than 90% of the population invested, else you lose the $10 you invested.

1. Is it correct to say that the pure strategy Nash equilibria if agents choose simultaneously are: (a) if no one invests; and (b) if everyone invests?
2. If agents choose simultaneously, can the pure strategy Nash equilibrium also be such that 90% of the population + 1 agent invests?
3. How do I get the Subgame Perfect equilibrium (or equilibria) if agents are choosing sequentially?
4. If agents are choosing sequentially, is the Subgame Perfect equilibrium for everyone to invest? Why would this be the result of the sequential game instead of the other Nash equilibrium in (1)(a) above of no one investing?