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Some informal extensions to mathematical game theory: factoring in elites and religious fanatics.

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Game theory in a sense started with Adam Smith’s "Wealth of Nations" in which he argued, "As every individual . . . endeavors as much as he can to employ his capital in support of domestic industry . . . every individual necessarily labors to render the annual revenue of the society as great as he can."


This "laissez-faire" philosophy seemed to suggest the more individually people are allowed to behave, the more socially they will behave, albeit inadvertently.


More formally, game theory began in 1921 when John von Newmann proved that every conceivable two-person zero sum game of perfect information has what is called an optimal strategy. Lots of assumptions here and here's just a few of them.  One is that the two players are taken to be equally competent.  "Perfect information" means neither player has secret information (which precludes poker) and "optimal strategy" means each player can do no better than follow the optimal strategy which will always fall into one of two categories, depending on whether it guarantees the players a tie game or a predictable win for one of them.


Tick-tack-toe has an optimal strategy that guarantees a tie against any opponent.  This optimal strategy is called fair.  In Nim, an ancient two-person game of perfect information, each player in turn removes any number of sticks from a pile, and the winner is the player who picks up the last stick.  The optimal strategy of this game is “unfair” because the first player will always win.


Then, in 1951 the American mathematician John Nash (yes, the same Nash in "A Beautiful Mind"), wrote a work called “Non-Cooperative Games” in which the outcomes inevitably evolve into two kinds of equilibrium, which he characterized as optimal and suboptimal.  Though Nash's premises are consistent with Adam Smith, his conclusions diverge.  Optimal equilibrium in the game of "stagnation" is one in which all players break away from the group to receive a reward.  Suboptimal equilibrium is when all players chose to stay with the group to avoid a penalty.


Naturally most of the above is simplistic and leaves out major assumptions, but it's enough to suggest some new turns in the road.


Laissez-faire seems to lead (in various ways) to a kind of "pack mentality" in which all the players try to anticipate the moves of the other players who, in turn,  can lead the group to the most desirable state as easily as the most undesirable one.


However, a profoundly unrealistic and implicit assumption in all these game theory models is that of a level playing field, which is addressed with the following three assumptions, classified as “nodes of disequilibrium”.


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A liberal American, PhD mathematician, bipedal Earthling.
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