Question for Game Theory

Five friends have an opportunity to invest their $10 into very attractive prospect with return of 50%! The catch is that to get 50% return, all ve of them must invest $10. If less than ve people invest, all those who have invested loose their $10. A person who decided not to invest does not loose any money. Everyone prefers more money to less. Each player's strategy set is {invest, don't}. (a) Constructed the payoff function for a representative player, where M is the number of people other than the representative player who choose to invest. Underline the best responses. (b) Do players have a dominant strategy in this game? Explain. (c) Identify all Nash equilibria in this game. Explain in detail. (d) Consider strategy combination (don't, don't, invest, invest, don't). Is it or is it not a Nash equilibrium? Explain in detail. (e) For each of Nash equilibria from the previous part indicate whether it is or it is not (i) strict, (is) the payoff for each friend and (iii) whether it is or not the Pareto-optimal. Explain in detail. (f) Is any of the Nash equilibria from part c) more likely to happen