Conceptualizing the Game Structure through Theory

In creating my outline for the theory behind the game, I have thought more and more about the meaning that the game conveys through its game mechanics. I have thought more in detail about the structure and how the rules create the meaning of the game.
 
I have found that poor designs and structures will allow certain players seeking more power to far transgress others, which eventually leads to taking away from their peers in order to be the most successful and keep their competitive status. This is why I have created the karma system in the game. When people play games in which their progress will never affect those around them, this is a major point that they miss.

Thinking about individuals and groups is a huge issue in the topics of power and influence. I cannot expect to have 100 players play my game but that would certainly bring more interesting results. I do expect a group to play and if there are enough players and the game requires a certain amount of time to get through, I'm sure groups or partnerships will form. I realize that favoritism plays a role in distribution of wealth, and players can certainly just share among a select few, in which case inequality is still an issue.

This helped me come up with my equation for determining karma, which is dependent on the total  number of players and the number of keys a person has. I will leave room for flexibility, but each player will have to share keys in some resemblance of an equal model in order to keep a decent karma score in the game. The model between x (total number of players), y (player's number of keys) and z(player's karma score) will be described tentatively as x/y=z. I have yet to decide if z is the total karma score of a player or if it is an amount added or subtracted to the karma score, each time keys are gained or shared. In that case it would be more like x/y = K(- or +) z.

What happens exactly when the karma score reaches 0 or a low range is also yet to be determined. This equation can be worked out with paper prototypes, including cards and chips that represent karma.