Chaos theory and Game theory

As Hollywood would portray it, John Forbes Nash, the subject of A BEAUTIFUL MIND, created game theory in a bar. His drinking buddies as well as fellow math students were in a local student night spot. In walks a number of young ladies looking for mates or someone to pass the night. For whatever reason, all the males wanted the same young lady. He surmised that this could not happen and that became the genesis of game theory. If we can step aside for a moment, the women were doing the same thing. Further, they may have wanted only one male also but would have to play their strategies slightly varied from the males.

Game theory thus had it’s beginnings.

The strategies vary from the most altruistic to the most selfish. It can be reduced to algebraic form (Thomson, 2001) The theory has spread it’s wings and infiltrated into math, science, philosophy, and advocacy (Shubik, 1998.) One of the authors commented that the decline of small group research from primary group to game theory and it’s cousin “Prisoners Dilemma) were due to the ease of research into the latter rather than the former(Snell, 1988 .)

In the March 18,2001 issue of BUSINESS WEEK, Peter Coy describes and condenses work from Goeree and Holt in AMERICAN ECONOMIC REVIEW.

Basically, they found that individuals often act irrationally which would sully the game theory premises.

We want to quote Coy. He states:

"Holt says the purpose of the paper was to shock theorists into seeing situations where game theory doesn't work. Without insights from behavioral economiics and other fields, pure game theory can be a beautiful minefield."

Chaos theory can compliment Game theory. On balance, it would suggest that regardless of the motives of the actors (rational, irrational, non-rational, or other) complications about actions are assumed. Game theory will work up to a point and when that tipping point is reached chaos begins.

For the purpose of this discussion, let’s go back to the bar of the famed night when Nash began his theory. Hollywood has it that the most attractive female

(in the eyes of the males) gravitated to Nash. Within a few minutes, she was so repulsed by him that she sought out other males. Hollywood stops there, but let us continue. She probably returned to the other unattached females and through glances and gestures established a territory and proceeded to indirectly pursue another male. Thousands of outcomes may have occurred after that meeting. It is likely that none of the females married any of the math males from the night spot. Each actor, regardless of sex may probably marry some one on numerous criteria. Chaos theory suggests that strategies may still be identifiable, but probably non-rational. In other words, the bigger picture is that through a chaos of beginnings and endings, most will marry, reproduce, perhaps divorce, and die. The big picture or micro-level is that mating occurs, along with reproduction, and then the actors pass on into the ages. Thus, through the chaos, order still perserves.

In the mean time, game theory may catch strategic actions in certain settings and still make the theory viable, but flawed. However, the flaws are not enough to put it on the ash heap of history. This also applies to the meaning model, conflict model, and equilibrium models used in the social methodologies or social sciences.

Thus chaos can compliment game theory.

Coy, Peter (3/18,2002) “Game theory’s hidden holes: people often act irrationally, BUSINESS WEEK, page 28.

Shubik, Martine (4/15/98)”Game theory, Complexity, and Simplicity” publications@santafe.edu

Snell, Joel and Donald W. Green( 1988) “Whatever happened to primary group?”

Community Social Science Convention, spring.

___________________, (12/23/2001) GUARDIAN UNLIMITED OBSERVER, ”Game theory for a laugh: Nash’s theory explained”