The player, an alien creature named Vetvel, must compete with six other acolytes (each a different alien species) for the Shepherdship. Each of these characters has a distinct personality. Each morning, the acolytes wake up knowing one of each of the three "auras" the others possess. They must trade knowledge with each other in order to try to gain enough knowledge for the "mind combat" that takes place every night, which is basically a fancy Rock, Paper, Scissors game that depends on the aura counts for the players involved. The game is won when a player gets eight auras in all three categories. However, in giving away somebody's aura count, the player betrays that person, which angers them and may make them less likely to trade aura counts with the player. Therefore, a player has to know whom to trust and whom to betray, hence the title: Trust & Betrayal.
Source: Wikipedia, "Trust & Betrayal: The Legacy of Siboot", available under the CC-BY-SA License.