Not actually equivalent to the median.
If all the scores are 1s and 5s, then the median will be a 1 or a 5, but the average will be somewhere in between.
The problem is slightly easier to understand if we consider the grading scale from 0 to 100. Then every agent, trying to manipulate the score as much as they can toward their "ideal grade", will submit a grade of 0 or 100.
The average will converge to the unique number, X, where X percent of the graders want the final grade to be above (or equal to) X.
