In a single-player game with difficulty settings, it seems obvious for players to choose the easy difficulty setting. How can I make incentives for players to choose harder difficulty settings?
You assume it is "obvious," but that's a faulty assumption. For some players, increased difficulty alone is enough of an incentive. Players are driven by a variety of motivating factors, and while story and "experience" is one of those factors (such players may not like challenging gameplay and may thus opt for easier difficulty levels), there are certainly players that revel in overcoming challenging mechanics alone and will always pick the highest available difficulty level.
You can further incentivize players to do this by offering other rewards for completing the game on higher difficulty settings:
- unlocks for cosmetic items
- unlocks for new game modes or abilities
- extra story content (the "true ending")
Note however that being too heavy-headed with putting content behind difficulty gates can result in a negative reaction from players, who may be offended by your giving apparent preferential treatment to the gamers who only want the hardest challenges, and thus considering the ones who prefer simpler experiences "beneath" your game.
It's an open question whether or not it's a benefit to lock the hardest difficulty mode behind a slightly-less-hard difficulty mode, as well. Some players will enjoy the discovery of an even more challenging mode, but some will not find the replay value sufficient.