where k1i is the installation cost, k2i is the relative weight between the maintenance cost and the installation cost, Pj is the ratio of the number of writes over the number of reads and writes, Update Size j is the size of an update, Object Size j is the size of the object, and T is the update period. We see tradeoffs between different parameters in this equation. For example, placing replicas becomes more expensive as Update Size j increases, Pj increases, or T decreases. However, note that by varying αij itself we can capture the full range of behaviors in the game. For our analysis, we use only αij.