Instead of designing a multiplayer game with perfectly balanced abilities across both players (such as chess or checkers), some element of imbalance, if done correctly, will create an evolving meta-game which is far more interesting to players. This is because all players at all levels must continue to evolve there strategies to combat this current meta-game and more importantly it allows players to develop skills naturally. A Novice player might originally think a strategy is unbeatable but when he gets to a certain rank or skill level immediately realize it is hard countered by something else and consider how to beat that.
Example 1: League of Legends Edit
League of Legends has 132 somewhat unique heroes that almost perfectly counter each other in a cyclical way much like rock paper, scissors. For example hero #1 might be strong but if too many people plan them, many players will quickly flock to champion #2 and so forth until it is discovered that no hero is perfectly 'the best'. This is only intensified when the free rotation of heroes is introduced; you might need to work out how one of the heroes in the rotation can counter the most popular week or desperately wait until the one that does is unlocked.
Example 2: Overwatch Edit
Overwatch essentially took the fundamental formula of MOBAs (An array of characters with unique abilities and ultimates) and put it into a FPS setting. It's also important to mention that utilizing unbalanced design in these sorts of games creates a shifting meta because of the ever changing balance changes that are made to the game to create a more fair gaming experience for the player. Taking what would ordinarily be considered a negative (perpetual balancing) and making it into a positive is brilliant design. Any additional characters the developers add also shifts the meta making the game continually feel fresh and exciting.
Example 3: Cosmic Encounters Edit
In the board game Cosmic Encounter, you are randomly given a race to play, from a pool of 50. Each race has a unique ability that you can then use in the game. Your strategy for each race changes, this combined with everyone else's different race, making it so that each time you play it is a different and unique experience. But another twist to the game is that each race is not equal to the other, many races are far stronger then others. This also can change your strategy and may require people to team up in order to battle the over powered abilities of one race.