In a game system, players' own horse trained by players in a horse racing game of an arcade game machine is allowed to participate in races of a horse racing game Web site managed by a Web server by using a password. The password includes a day of retirement, names of G1 races won, and so on. In the horse racing game Web site, if the day of retirement is within a term of validity, participation for an application related to the password is not allowed. Experience of winning a predetermined number of G1 race is required in order to participate in a specific race held in the horse racing game site, and horses without such experience are not allowed to participate.