A supplier and a buyer, who are both risk neutral, play the following game
The buyer orders a good of quality q ≥0 from the supplier and promises to pay s≥0
The supplier decides which quality q'≥0 to deliver
The buyer observes q’ and decides how much to pay s'≥0 for the delivered quality
The buyer’s payoff is q'-s', and the supplier’s payoff is s'-C(q'), where C(q') is a strictly convex cost function with C(0)=C’(0)=0. These payoffs are commonly known.
What is the subgame perfect equilibrium of this game?