Skip navigation

rewarding survival leads to cooperation

It would be nice to encourage spontaneous cooperative play in competitive games, like death match. By scoring on survival, you get a system that encourages ad-hoc teamwork without any fancy ‘teaming’ algorithms.

Consider a system that scores a player based on two parameters — the amount of time they’ve played, and the number of times they’ve died. The player with the lowest death rate is the best; their rating is how much higher their mean survival time is than that of the other players:

// mean of player i
mi = ti / di
// average of others
oi = (mi – ∑ m) / (1 – n)
// rating of player i
ri = mi / oi

The rating reduces to 1 for the average player. There is thus no reward for a bunch of people logging in to a level and hanging out, as that will just cause their scores to converge. This formula can be applied in a game, across games and across game servers to rate players in a uniform manner, re-normalizing at each hop.

How does this formula reward cooperation? While beating down other players is a sure way to reduce oi, surviving longer is a more powerful way to grow your score. A small number of players, working together, can reduce the survival rate of other players while enhancing their own. If too many players work together, however, then oi gets big, reducing the payoff for all concerned. Basically, you want the smallest group of players who can effectively defend one another or launch an assault — and that depends on the situation. If two players come across a jeep with a gun in the back, they can kill each or they can ride around in the jeep, jinking and weaving and blasting rocket dudes to survive. On the other hand, if it’s a tank, you might need four people to get good mileage out of that, so it’s better for one of the players to kill the other.

It’s worth examining how reweighting the time — multiplying by the number of players in the arena, for example — can encourage players to take on the risk of deadlier arenas. How can we make the score for survival depend on the skill of the other players? This has a non-linear flavor and I will leave it to another time.


Post a Comment

You must be logged in to post a comment.
%d bloggers like this: