The main idea
In an assassination game the players hunt each other and strive to get into a situation where they may apply to each other the playful mock guns dictated by the rules. The game's base format is the so-called murder rings, where players hand over the requested details of their personal lives to the umpires (name, address, portrait, info from the daily routines etc.) and the umpires arrange the players into rings, where Person A's goal is to assassinate Person B, Person B is hunting for Person C, and so on, until Person N hunts for Person A. If the Person A manages to ambush the Person B in manner allowed by the rules and executes a murder with, say, a water pistol, A and B shall contact the umpires and tell their own sides of the story for scoring. After this, the B is dropped from the circle and gives his/her target, the Person C's, information over to the Person A, who starts hunting for the Person C. If the game runs its logical course, the two final survivors are hunting for each other.
The game has been played a lot around the world, often on the campi of universities. One good online source for information about the game is the website of Cambridge's Assassins' Guild: http://www.srcf.ucam.org/assassins/. Steve Jackson Games has collected different rules and game variants into the book "Killer, the Game of Assassination (ISBN 1-55634-351-5)".
Time and location
The game may be restricted to a certain place and time, e.g., one afternoon and a certain park, but in its best and most imaginative form the game is played for several weeks, where the players try to live their normal lives knowing that somebody is stalking them all the time. In the process assassins try to recover free time of their own to gain a time slot and a shot at the murder of their own victim.
For the longer games it is common to agree on off-bounds areas and times, where the targets are safe from murder attempts, i.e, pacified.
There are numerous variants from the game. Several examples include: Duelling Game, where the murders are committed as challenges to duels and with weapons suited to the duel (boffer swords, water pistols etc.). The fallen victims may become polices, who hunt for assassins committing fouls or fails in their desperate attempts. The selection for the weapons may well be rather extensive (alarm clock bombs, hand lotion as a contact poison, tennis ball grenades...).
The role of the umpires
The umpires make the decisions about the rules, maintain the game, resolves the issues risen during the game, work as inter mediator in the fights and scores all the acts. The umpires may choose to end the game, if they see fit. (For example, if the game has become stuck in a situation, where three players are spending their days hiding in their basements in utter terror.) The umpires are the final authority in the game.
Players' safety, privacy and bystanders
The rule number one for the game is common sense. Getting murdered may well be surprising, so it is plainly obvious from the start that people are not shot with water pistols when, say, the are lifting heavy objects or operating heavy machinery. The participation to the tournament means that the palyer is okay with the small violations of their privacy (since the assassination usually requires stalking), but most rule systems (also HGA's) emphasize the physical immunity of the players. Pretty much any serious rule systems also dictate the bystanders to be absolutely pacified from the murder attempts: the purpose of the game is not to cause disturbance to those who are not involved in it.