Three workers work in a team to produce a car. Worker 1 is in charge of the car body, worker 2 is in charge of the interior of the car, and worker 3 is in charge of engine. The game begins with worker 1 who decides whether to "work hard" to develop a good car body or to "slack off" to make a defective car body. Worker 2 then observes whether or not the car body is in good condition and decides similarly whether to "work hard" or "slack off". By working hard, he is able to design a good car interior, while slacking off results in a bad interior. Finally, worker 3 observes the quality of both the car body and the quality of the interior, and decides whether to "work hard" or "slack off." Again, working hard ensures that the engine is of high quality, while slacking off results in a defective engine.

The resulting car is good (and can be sold) if and only if all three worked hard and otherwise results in a bad car (which cannot be sold). Working hard is costly for each player and results in a disutility of 1 util, while slacking off results in 0 utils of disutility. A good car results in a net benefit to each player of 10 utils of utility, while producing a bad car results in a net benefit of 0 utils to each player. Thus, if a good car is produced, then all players received 9 utils. If instead a bad car is produced, any worker that expended effort receives 1 utils while all workers who slacked off obtain

0 utils.

Part a: Draw the extensive form representation of the above dynamic game.

Part b: Explain why the game is of perfect information. Solve the game by backward induction. What are the resulting payoffs of all the players?

Part c: We now modify the above game. Suppose that the game begins with worker 1 deciding whether to work hard or not. Then workers

2 and 3 simultaneously decide to "work hard" or "slack off" having observed worker 1's decision to work hard or not. Suppose that the payoffs of

the players remain unchanged. Draw the new extensive form representation of the game