Looter Shooter

A sub genre of shooter video game with the core mechanic of progression being drops, container loot, rewards, and shops in conjunction with a leveling system and likely crafting systems using components from drops, container loot, rewards, shops. A looter shooter can be first and/or third person, cooperative, mmo, single player, or competitive or a culmination of some or all with the inclusion of a story. Battle Royale can be considered pseudo-looter shooter but as they lack meaningful progression systems they do not fall into the genre except in lax semantics.

Obtaining loot at a progressive rate with the primary game mechanic being first/third person shooter I guess would be the best way to describe it