Kingmaker Scenario - Gladiator Example

Gladiator Example

Consider this simple game: Three gladiators play, with strengths 3, 4, 5. In turn, each gladiator must engage another, and they begin combat. The result of combat is that the weaker player is eliminated, and the stronger player loses strength equal to that of the weaker player. (For example, if "5" attacks "3", "3" will die and "5" will have strength 2.) The winning gladiator is the last one standing.

Each round of combat eliminates one gladiator, so there will be two rounds of combat. The first round of combat will eliminate one participant and weaken the other to a strength no greater than 2. The nonparticipant's strength is at least 3, so he is guaranteed to win the second round of combat, and the entire contest. Therefore, the game collapses: The winning gladiator is the one not involved in the first battle.

Hence, the gladiator whose turn comes first is the kingmaker. He must be involved in the first battle, hence cannot win, but with the liberty of choosing his opponent in that battle, can elect either of the other two players to be the winner of the contest.