Friday, February 08, 2008

Games Of Life - Part 2: Equilibrium

Equilibrium is the state where all players have equal benefits and losses. There are several ways to achieve equilibrium. Assuming perfect play, a game reaches equilibrium if the game is balanced. A "balanced game" is the game which when played perfectly reaches equilibrium. Almost all popular games are balanced games. Poker is a balanced game. Card games like Hearts, Bridge, and Tricks are all balanced games. Chess is believed (although not proven) to be a balanced game!

In the case of card games, this does not mean that every round or game will end in a draw!! This means that if the game was repeated a large number of time, the scores will be drawish. The idea is, since cards are shuffled and given to players randomly, then making large number of games will be drawish. The concept is same as rules of chances in experiments like throwing dice. Everyone knows that for a "fair dice" each outcome from 1-6 will appear almost equally given a large number of trials. Thats why to reach balance we need repetitions to form statistically valid results.

Is life a balanced game? Assuming each player is unique from his parents, and considering the way things work, I would think that life cannot be considered a balanced game. Different amounts of effort are required by different players to reach equivalent statuses. This may not be true. It might be that if all the players played "perfectly" all the humans would reach a state of equality (even though they might not start with equal statuses). If we think of life as a balanced game and assume all players are playing perfectly, it should be that the rich get poorer and the poor get richer, until all players reach a state of equality. This may or may not be true. It is observed that the rich gets richer, and the poor gets poorer. But this outcome is not based on perfect play, and so it is not indicative of what would happen in the case of perfect play!

The concept of a "fair" game is different from a "balanced" game. A balanced game is defined as the behavior of the game on the long run. But not all balanced games are necessarily fair games. A fair game is a balanced game that requires equal effort to reach the state of equilibrium. If we assume that life is a balanced game, it probably is not a fair game. Maybe everyone can reach an equal state as other players, but this does not constitute equal effort.

Concepts of evolution suggest that life is not a fair game. A term like "survival of the fittest", suggests that certain individuals are more fit for the game of life than others. Thats why biologists model life as a game with bias towards certain traits that are more adaptive to the environment.

In this series:
Games Of Life - Part 1: The Broad Lines
Games Of Life - Part 2: Equilibrium
Next: Games Of Life - Part 3: Games Of Non-Zero-Sum
Next: Games Of Life - Part 4: Advanced Insight Into Games Of Perfect Information
Next: Games Of Life - Part 5: Gaming Theory And Decision-Making Theory


The Observer said...

Interesting read. So how exciting can be a non-fair game? Would it be more challenging to those with less chances to win?

Devil's Mind said...

The answer is yes if we assume perfect play. But if we take the possibility of mistakes, things might change.

In life there are numerous example of people who have clear advantages over other people, yet they do several mistakes that transforms them from taking the lead to falling behind!

Here I can refer to the chess position I talked about recently. In that game the black player had a definite winning situation (he had a "forced mate" if you are familiar with chess terminology). With one wrongful move the black turned from a definite win to a definite loss!!

So a disadvantaged player can possibly win easily if the opposing player did a mistake or two. But if the player is playing against strong opponents, a disadvantage would make things a little too hard!!

In real life, we find that many poor people have become powerful people. Also, some powerful people have become poor people!! If this would mean anything, it would mean that humans make too many mistakes, and we are far away from being tough competitors.

The Observer said...

"it would mean that humans make too many mistakes, and we are far away from being tough competitors."

Which makes it a fair game in a different way?

Devil's Mind said...

Not really. At least not from an academic point of view.

Gaming Theory classifies games according to its characteristics in perfect play or at least strong competition where the error margin is small enough so as not to dramatically affect the result of the experiment.

Think about this for a minute: Does using favors ("Wasta" in Arabic) make employment fairer because people with inferior skills have better chance to get employed?!

(I would say No for the above question) So my point is: Giving the less advantaged people a better chance for success doesn't make a game fairer!! Maybe the example of using favors ("wasta") that I gave isn't a perfect analogy, but the point stands still...

The Observer said...

I understand what are you trying to say, but even based on darwin model, the survival of the fittest, and the competitive nature of us, when someone has less chance in this game, he gets challenged to give more and thus to grow and gain an advantage.

Like in wasta for instance, if someone else less competent won a job because of a wasta, it would push the loser to challenge himself and develop his own skills in order to win. As a result the real user would be the one who got the wasta because he got too comfortable depending on it and didnt develop his other skills.

Does that make sense?

Devil's Mind said...

Yes, sure. Unfairness can teach us somethings. For example, if you wish to develop skills in a certain game, a good way is to give an (unfair) advantage to your opponent and play against a medium strength opponent...

For example, if you play chess you may give your opponent the advantage of taking back bad moves. Or maybe play Trix and give your opponent a chance that a certain round is canceled and not taken in calculations if he loses too many points. Or whatever game by giving your opponent a chance that you don't have.

Sure, you can learn from such "generous" advantages you give to your opponent... But those advantages are by definition not fair part of the game.

The Observer said...

Got it :)

The Observer said...

DM, we need you at no_angel blog. He is trying to explain quantum mechanices, and I would like to read your input there :)