Optimal Real-Time Bidding Frameworks Discussion

This note is a complementary material for the solution of optimal real-time bidding function in paper [1], where the estimated cost is taken as the bid price, i.e., the upper bound of the true cost. Here we discuss a more general bid optimisation framework with various utility and cost functions. 1 Preliminaries Define the bidding function as b(r) which returns the bid price given the estimated clickthrough rate (CTR) r of an ad impression. Winning probability. Given the market price distribution pz(z) and the bid price b, the probability of winning the auction is