Social Equations, Marriage, Game Theory, And Zero-Sum Games

I wrote a post yesterday referring to the movie “A Beautiful Mind.”  The film is loosely based on John Forbes Nash’s life and his Nobel Prize Winning work on Game Theory and what is known as Nash Equilibrium.

Before discussing related topics more specifically, I’d like to prelude by saying:

“To the degree a social relationship does not practically and clearly create comparatively equal and good benefits for the parties involved, the relationship will likely struggle.”  – me, I said that.

Even if my above assertion is true, neither of the following would necessarily be true:

a)  A struggling social relationship struggles because of an imbalance in the perceived or actual benefits to either party, or

b)  All relationships, that don’t have roughly equal benefits for both parties, struggle.

Both of those statements are not true.

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Moving on to today’s post topics:

“Game Theory” as described in Wikipedia on April 14, 2008:

Game theory is a branch of applied mathematics that is used in the social sciences (most notably economics), biology, political science, computer science and philosophy.  Game theory attempts to mathematically capture behavior in strategic situations, in which an individual’s success in making choices depends on the choices of others.  While initially developed to analyze competitions in which one individual does better at another’s expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria.

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“Nash Equilibrium” as described in Wikipedia on April 14, 2008:

In game theory, the Nash equilibrium (named after John Forbes Nash, who proposed it) is a solution concept of a game involving two or more players, in which no player has anything to gain by changing only his or her own strategy unilaterally.  If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged, then the current set of strategy choices and the corresponding payoffs constitute a Nash equilibrium.

Stated simply, Amy and Bill are in Nash equilibrium if Amy is making the best decision she can, taking into account Bill’s decision, and Bill is making the best decision he can, taking into account Amy’s decision.  Likewise, many players are in Nash equilibrium if each one is making the best decision that they can, taking into account the decisions of the others.  However, Nash equilibrium does not necessarily mean the best cumulative payoff for all the players involved;  in many cases all the players might improve their payoffs if they could somehow agree on strategies different from the Nash equilibrium (eg. competing businessmen forming a cartel in order to increase their profits).

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“Zero-sum” as described in Wikipedia on April 14, 2008:

In game theory and economic theory, zero-sum describes a situation in which a participant’s gain or loss is exactly balanced by the losses or gains of the other participant(s).  It is so named because when the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero.  Go is an example of a zero-sum game:  it is impossible for both players to win.  Zero-sum can be thought of more generally as constant sum where the benefits and losses to all players sum to the same value of money and pride and dignity.  Cutting a cake is zero- or constant-sum because taking a larger piece reduces the amount of cake available for others.  In contrast, non-zero-sum describes a situation in which the interacting parties’ aggregate gains and losses is either less than or more than zero.

Situations where participants can all gain or suffer together, such as a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, are referred to as non-zero-sum.  Other non-zero-sum games are games in which the sum of gains and losses by the players are always more or less than what they began with.  For example, a game of poker, disregarding the house’s rake, played in a casino is a zero-sum game unless the pleasure of gambling or the cost of operating a casino is taken into account, making it a non-zero-sum game.

~ end of Wikipedia excerpts ~

 

Life is not a zero-sum game.

 

But sometimes people choose to confine their relationships and decision making considerations to self-imposed zero-sum structures.

And sometimes unnecessary and horrific problems arise when people perceive problems only through zero-sum considerations. 

I chose at differing points in my life to no longer live as if life was a zero-sum game.  And even though my unilateral changes of behavior would not likely lead the others involved to create more benefits for me and would not likely change their decisions, I still unilaterally chose to perceive and participate in the social games of life differently. 

I am not an exception to Nash Equilibrium expectations.  Rather, Nash Equilibrium does not generally apply because Nash Equilibrium applies primarily to zero-sum games.

I didn’t want to live in a world where social relationships were perceived as zero-sum games.  I had benefited too much from too many people working together for common good, outside of zero-sum structures and zero-sum mindsets.

Zero-sum thinking tends to ignore the ancillary benefits to other people involved.  While zero-sum thinkers tend to want to only focus on the benefits and detriments to the players they define as allowed to play the game, non-zero-sum thinkers tend to focus on the benefits and detriments for everyone involved, such as players past, present, and future – and even the spectators.

Zero-sum games are too often immature and simpleton.  They tend not to work as often toward cooperation, innovation, sharing, shared profits, and expansion.

Nash Equilibrium tends to break down when either irrational or unfair behaviors occur or when parties stop being intent on zero-sum outcomes.  Nash Equilibrium strategies and predictabilities lose reliability when the expected number of players in a game varies outside of the players’ expectations.  Nash Equilibrium tends to break down as each party to a game realizes there is not perfect information and communication available to each party.

I am sorry if this post creates more questions than answers.  But sometimes better answers are found by understanding there are so many questions that still remain without finite or certain answers. 

I think art sometimes makes the argument that the total chemistry of the combined parts does not always equal the sum of the parts.  The “total” is not always finite.  It is not always more.  And it is not always less.

I think art tends to consider the needs of more people, more than just the creator, more than the creator’s immediate social circle, more than the current majority opinions of the primary audience, and more than just what is considered important today.  

Art cares about tomorrow.   

Art cares about more.

Even when art focuses on the simple, the quiet, and the neglected, it is caring about more than most other people show concern for.

Life is not a zero-sum game.

Sexuality is not a zero-sum game.

Art is not a zero-sum game.

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