A system of linked gaming machines is disclosed herein. Upon a certain triggering event occurring, eligible gaming machines simultaneously receive a signal for initiating a free game bonus round. The players that have been playing the gaming machines will then play a certain number of free games in a competition with other players involved in the same bonus round. The player awarded the most credits or points from the play of the free games is awarded a special jackpot. Other jackpot games (e.g., split jackpot) are also envisioned. In another embodiment, a jackpot award or any award to the players may be granted based on the outcomes of the free games. In one embodiment, the base awards to the player(s) for the bonus round are multiplied by a multiplier that may be based on the number of players, based on the players' rankings, based on other outcomes of the bonus round, or a fixed or random multiplier. The possibility of the free game bonus round occurring at any time provides incentive for players to keep playing the linked gaming machines. The free game bonus round may also be played on a single non-linked machine where bonuses may be granted for credits exceeding certain levels.