From MHWiki

There are several Minigames within the Sandtail Desert locations. Participation in these quests is optional, but they unlock various mice that can't be caught otherwise, and allow hunters to collect Garden Essences at a faster rate. Each game appears as part of the Heads-up Display of the particular area, and involves the use of Charms that can only be purchased in that location. Each game also causes entries to be logged in the Hunter's Journal. It is possible to leave the location and hunt elsewhere, and have the same game state on return to the area.

The set of games are:

Game Location Charms Mouse
Dewdrop Minigame Living Garden Sponge Thirsty
Lost Curse Minigame Lost City Searcher Essence Collector
Grubling Stampede Minigame Sand Dunes Grubling Chow Grubling
Red and Yellow Dewdrop Minigame Twisted Garden Red Sponge
Yellow Sponge
Fear, Darkness and Mist Curses Minigame Cursed City Bravery
Essence Guardian
King Grub Minigame Sand Crypts Grub Salt
Grub Scent
King Grub

With the Living Garden Expansion on 14 January 2013, the twisted reality minigames also unlocked the ability to catch the Shattered Carmine, Dark Magi, and King Scarab boss mice, when hunting with a Shattering Charm.