The effort-maximizing contest with heterogeneous prizes

•We study effort-maximizing contest design with heterogeneous prizes.•Contestants' effort efficiencies are their private information.•An all pay auction maximizes expected total effort under regularity condition.•Any division of a grand contest leads to lower expected total effort.•An increasing return to scale effect prevails in all pay auctions.

We establish the effort-maximizing rule of allocating heterogeneous prizes when contestants privately observe their effort efficiencies. With ex ante symmetric players and increasing virtual effort efficiency, an all pay auction maximizes the total expected effort.