Three game theorists work on a team project. Assume they work independently, andit is not possible for them to monitor each other. No one likes working, and the costof e§orts is measured in dollars. Each player can work up to 5 hours, and the costper working hour is $6: The quality and hence the proÖt of the project is determinedby the joint efforts (total number of working hours) of the three players. For eachadditional hour that the team invests in the project, up to 10 hours, the total proÖtwill increase by $15: After 10 hours, efforts will not increase profits. Assume playersdivide the profit equally among them. Hence, each playerís payoff is his share of theprofit minus his cost. There is common knowledge of rationality. (a) What is the strategy space (the set of strategies) for each player?
(b) What is the payoff for each player as a function of the strategy profles?
(c) Compute the set of rationalizable effort levels for each player.
(d) Suppose one player is kicked out of the team, and the remaining two players stillshare the profit equally. Compute the set of rationalizable effort levels.