Politics

Politics is where things in the game revolve around the players' relationships to each other.

Politics can easily push aside other forms of strategy, as a player's fate is decided arbitrarily by who the other players choose to attack. "I'll use my dragon to destroy… umm…YOU!" It can also lead to unpleasantness, and accusations of unfairness. 

All politics, or none

A game should be about politics, or have no politics at all. Do not throw small political elements into a game that's largely not political. However, if players are bashing away at each other all game, and the game is about their relationships to one another, that's fine.

The classic game Diplomacy has about the simplest rules possible. Each player has three pieces on the map, and if you move into the same territory as an opponent, you both stay where you are. If you use another piece to support your piece, you'll move in, instead of the opponent. However, all players negotiate for a while, then write their moves in secret. The moves are then revealed, and you see who does what they said they'd do. This game does politics so well, because everything else has been removed.

Take that

Games about politics tend to be the most basic and inane of all designs. Designers who know nothing about design constantly make "take that" games, where the players just play good cards on themselves, and arbitrarily play bad cards on other players. This is an extremely weak and overused format. Don't do it.

It's fine that players can choose who to attack. However, there should be a reason for their choice. If the decision is completely arbitrary, other players can't plan around it, and it's just random and feelbad.

Make the game two-player-only

For very adversarial games, I like this answer best. It enables you to make the game for the player count it's best for, without forcing it to be something else.

Remove the choice of who to attack

In my gangster game, attacks hit all other players.

In my pirate game, you can only attack someone on the same space as you. You could technically travel to any player, but you'd need a logical reason to do so. It's far less arbitrary.

Provide a benefit for attacking

Make attacking about theft, not just beating down the opponent.

In my pirate game, you attack someone, in order to steal their cargo. Attacking just to hurt them would be far less satisfying.

Tack on a bonus to attacking, so a player will do it for their own benefit. That benefit might be greater than the loss incurred by the attacked player.