Dynamics of competitive games

Dynamics of competitive games
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During competitive games, we typically see one team (or player) make more progress than another, allowing us to predict that this team is likely to win.

Progress often changes the shape of the game, with progress creating a bias, and making the game easier to win from that point on. There are three distinct ways that a game can change shape:

(1) Positive Feedback - Imagine a ball balanced on a hilltop. The ball has a tendency to roll downhill. Any bias to one side and the ball will have a tendency to roll further in that direction, and amplify the bias. With this type of dynamics, advantage has a positive feedback effect. Advantage amplifies.

Most strategy games are like this. On one hand, it makes competition sensitive to error, encouraging perfect play. But it has also been criticized for making games boring as once a team has gained an advantage, the challenge is gone, and it is time consuming having to "clear up" in the latter phase of the game.


(2) Negative Feedback - Imagine a ball sitting in a bowl. The ball has a tendency to roll back to the middle if disturbed either way, opposing bias and restoring equality.  With this type of dynamics, advantage has a negative feedback effect, which can both mitigate luck, and provide an opportunity for a lagging team to recover.

ie, The recovery rate of the lagging team is accelerated above the winning team, allowing them to quickly catch up.

Football is rather like this: If the ball moves close to your goal, then your defenders provide an additional challenge to the opposing team, and successfully keep the ball near the middle of the field for much of the game.


(3) No Feedback - Finally, imagine a ball sitting on a flat plate. The ball has no tendency to move if it is disturbed. With this type of dynamics, advantage has no feedback effect. Progress doesn't make the game harder or easier. The game retains the same shape throughout.

This is rather like a tug of war. The difficulty of pulling the rope doesn't change, no matter which team is closest to winning.