Competitive peer rating system (Game Theory?)

[kohler1000]

Hi there,

I'm developing a game where a small group of players will rate each other's performance and the best rated player will win.

The problem is: players will have a twisted incentive to give out low ratings, because this increases the chances that they're the best player.

To clarify the problem, here's a simple example with 3 people and a 0 to 10 rating range:

player A (fair) - gives a 9 to B and a 6 to C
player B (fair) - gives a 10 to A and a 6 to C
player C (cheater) - gives a 0 to A and a 0 to B

If we simply do the average, we'll notice that

A ends up with a final score of 5
B ends up with a final score of 4,5
C ends up with a final score of 6

So C will win the round because he cheated and didn't give fair ratings to his peers, and A will be second place, while he should be first.

So the final rank would be:
C
A
B

While the correct rank should be
A
B
C

Is there a theoretically optimal and preferably simple solution for the final score calculation for such a game, instead of just the simple average? I must be able to rank the players in the end.

Does this kind of rating system have an official name?

Thank you.