Tuesday, July 10, 2007

Zero-Sum and Non-Zero-Sum Games

I was very fascinated by these definitions coming from the game theory. The name zero-sum games was given to games where for one player to win the other player needs to loose just as much, making then the total for the game 0 (1 -1 = 0). In opposition a non-zero-sum game is a game where the resources are not limited and players can develop cooperation or synergy in order to get to win-win situations.

It looks like most of us were raised to learn and enjoy zero-sum games. There are games as soccer that have actually a little bit of the two depending on which level you look at the game as if you think one team versus the other there is the zero-sum game but then if you look inside any one team you can see a non-zero-sum game going on, even if it's only in a tribal sense (my tribe I help, the opposite tribe I destroy).

Once you look at it at the light of the game theory it seems almost trivial to decide that non-zero-sum games are so much positive and desirable. How could a 0 outcome be good for anybody in the end? I read that in fact they seem to be the games that exist in nature (such as economics and life itself) where the resources are not constant as opposed to human artificial games being the zero-sum ones. I'm not too sure about this, I tend to think that zero-sum games are played all the time in nature, are part of evolution such as the strongest animal getting the food or mate competing fiercely for it and leaving a winner and looser in its way. One argument in this direction is that per wikipedia: "In 1944 John von Neumann and Oskar Morgenstern proved that any zero-sum game involving n players is in fact a generalized form of a zero-sum game for two players, and that any non-zero-sum game for n players can be reduced to a zero-sum game for n + 1 players; the (n + 1) player representing the global profit or loss. This suggests that the zero-sum game for two players forms the essential core of mathematical game theory."

It's noticeable how today's education is trying and tending to get kids involved in non-zero-sum games much more that it did in my school days, which is a good thing.

In my way of reading more about this theory I came across HipBone games, increasing interest of economics and its relation to everything (such as Nash equilibrium principle) and the novel by Herman Hesse "The glass bead game" that is one more addition to my list of pendent books ...

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