Dynamic Adjustment in Zero-Sum Games to Prevent Positive Feedback

Positive feedback in games occurs when winners are rewarded and losers are penalized. Being in the lead

makes it easy to stay in the lead and it will become more and more difficult for players who are fall behind

to catch up. Based on the MDA framework (Mechanics, Dynamics, and Aesthetics), there exists a feedback

system in Monopoly. And according to this system, mechanics will be adjusted in order to fine-tune its

overall dynamics and to prevent positive feedback. For instance, in Monopoly, as the wealth gap between

leaders and poorer players widens, feedback system makes some particular changes in mechanics to keep

poorer players within a reasonable distance of wealthier ones, including changing the probability of die rolls.

But is this dynamic adjustment fair enough? Or would it bring negative impacts to the balance of game?

Monopoly is an economic game well known for its zero-sum mechanics, which means one’s loss is others’

gain. It is true that some dynamic changes that help lagging players and punish rich players could be able to

keep poorer ones more competitive and interested for longer periods of time. However, one player’s pleasure

results from another player’s pain, these measures are taken at the cost of the impact of fairness and the

decrease of playability. Sometimes these adjustments are so obvious that everyone could realize that it

should not happened in normal rules based on game mechanics.

I made several experiments to certify the existence of probability adjustment. At the beginning of one game

in Monopoly, there are two players and each of us was allocated 150,000 dollars as initial capital. As the

game went on, my rival came to a block where there were four spaces for building and I have three of them.

At that time, he could be free from heavy taxes if he rolls three, five or six. Otherwise he has to pay me a lot

of money. Then I repeated 100 times saving and loading to let him play and it supposed to be an event of

equal probability. Surprisingly, my rival was free from taxes 79 times in a 100-time experiment, which

means he rolled three, five or six with 79% of the probability and it was much higher than 50%.

After that I did the same experiment 100 times respectively at different wealth gaps from 50,000 dollars to

300,000 dollars with an interval of 50,000 dollars. The result showed that as the wealth gap widens, the

probability my rival could be free from taxes increases. That is, the probability for me to get richer reduces.

And when wealth gap reached 200,000 dollars or more, the probability was extremely high and I could

clearly feel the abnormality and injustice of mechanics.

As I evolved my understanding I consider this difficulty adjustment for hardcore players indispensable

because as your mastery of the game rises, so does the challenge. And according to the theory in Flow In

Games, the difficulty of a game should change dynamically based on its player’s skill and performance, and

this dynamic difficulty adjustment is part of the core elements which could bring flow experience to players.

But we have to admit that zero-sum mechanics is a double-edged sword. It could easily evoke one’s primal

emotions but at the same time, adjustments against basic principles in zero-sum games just like changing

probability of die rolls can only be made very carefully under specific circumstances. Because once we

clearly feel their existence and find negatives they bring to us, mechanics and gameplay will be seperated so

that dynamic difficulty adjustments are no longer embedded very well in the gameplay. As a result we get

out of immersion stage, ignore the pleasure and challenges the gameplay brings to us, and start to pay

attention to the injustice of mechanics. It would be fetal if it is not controlled well.

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WEALTH GAP - PROBABILITY