4. [This problem is an example of the \"Free-rider problem\"] Suppose there are 7; members in a team collaborating to win a prize worth R. Each member puts in effort, and the probability of the team winning the prize is given by pm where e,- is the effort put in by member i. In other words, as each member puts in more effort, the chances of the team winning the prize goes up. If the team wins the prize, they will share it equally among themselves, irrespective of how much or how little effort each has put in. The cost to member i of putting in effort e,- is given by 06,-. The members simultaneously (and non-cooperatively) each decide how much effort to put in. Each member is interested in maximizing her expected utility i.e. ex- pected value of her share of the prize minus the cost of effort. (1') Find the Nash equilibrium of this game i.e. how much effort does each member put in? (ii) Suppose instead the CEO of the company dictates how much effort each member should put in so as to maximize total surplus of the firm i.e. total expected value minus total cost. How much effort would she choose for each member? How does this compare (i.e. is it bigger or smaller) with what you found in the non-cooperative equilibrium in part (i)