A bicycle manufacturer (the "buyer," abbreviated B) wishes to procure a new robotic system for the production of mountain-bike frames. The firm contracts with a supplier (S), who will design and construct the robot. The contractual relationship is modeled by the following game:
The parties first negotiate a contract specifying an externally enforced price that the buyer must pay. The price is contingent on whether the buyer later accepts delivery of the robot (A) or rejects delivery (R), which is the only event that is verifiable to the court. Specifically, if the buyer accepts delivery, then he must pay p1; if he rejects delivery, then he pays p0 . After the contract is made, the seller decides whether to invest at a high level (H) or at a low level (L). High investment indicates that the seller has worked diligently to create a high-quality robot-one that meets the buyer's specifications. High investment costs the seller 10. The buyer observes the seller's investment and then decides whether to accept delivery. If the seller selected H and the buyer accepts delivery, then the robot is worth 20 units of revenue to the buyer. If the seller selected L and the buyer accepts delivery, then the robot is only worth 5 to the buyer. If the buyer rejects delivery, then the robot gives him no value.
(a) What is the efficient outcome of this game?
(b) Suppose the parties wish to write a "specific-performance" contract, which mandates that the buyer accept delivery at price p1. How can p0 be set so that the buyer has the incentive to accept delivery regardless of the seller's investment? Would the seller choose H in this case?
(c) Under what conditions of p0 and p1 would the buyer have the incentive to accept delivery if and only if the seller selects H? Show that the efficient outcome can be obtained through the use of such an "option contract."
(d) Fully describe the negotiation equilibrium of the game, under the assumption that the parties have equal bargaining weights.