A transitive relationship defines a one-way relationship between two or more entities. (Rollings and Adams 2003) For example, A can beat B, B can beat C and C cant beat anyone. (in other words, A can also beat C).
Transitive relationships can be seen in many FPS games such as Quake (id_Software 1996) where each time a new weapon is found it does more damage than all the ones found previously. In general terms, games in which the players capabilities are improved, augmented or upgraded within the game makes use of transitive relationships. (Rollings and Adams 2003)
Rollings, A. and E. Adams (2003). Andrew Rollings and Ernest Adams on Game Design. Indianapolis, IN, New Riders Publishing.