Finite and Infinite Games

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Finite and Infinite Games Empty Finite and Infinite Games

Post by wodouvhaox on Thu Nov 29, 2018 8:40 pm

by James Carse

In the early ‘Eighties, NYU Professor William Zartman gathered about a dozen faculty from as many departments to discuss game theory, each from the perspective of our own academic field. Zartman was in Political Science. Math and the sciences were well represented, as were the social sciences. I was to be the philosopher. Game theory, it became clear at once, is a maddeningly subtle subject, especially in its mathematical and scientific expressions.

As the weekly discussions–and the presented papers–made clear, game theory had chiefly to do with winning conflicts, or minimizing losses where winning was impossible. Without advanced mathematical skills, I found myself reflecting on the nature of play itself, especially play that saw no value in winning, or even play that actively avoided winning.

The result was a 150 page book initially published in 1986 by The Free Press. Still in print and published in a dozen or more languages, the entire first chapter reads:

There are at least two kinds of games. One could be called finite, the other infinite. A finite game is played for the purpose of winning, an infinite game for the purpose of continuing the play.

Although it may be obvious, it is worth stressing that “play,” as it is used here does not mean merely “playing around.” Play, in this discussion, is a metaphor for any number of complex human engagements whenever they take on a competitive, or cooperative, character. Corporations, for example, not only compete with each other but are in themselves populations of strivers, each trying to supplant another, each struggling for higher incomes and titles. The same applies to schools and colleges where attaining superior grade averages, degrees, and honors absorb the lives of students. Sexuality and marriage are often finite battle grounds with winners and losers. In fact, the features of play–finite and infinite–are essentially the same whether we are children playing jacks or soldiers caught up in a war between nations.

As this rather simple idea developed there were unexpected features of play–especially competitive (or finite) play–that came into sudden view. If the purpose of a finite game is to conclude play as a winner, then play itself acquires distinctly negative quality. Since your opponents seek only to make you a loser, the play actually stands in the way of their desired result. Winning ends the game at once.  Finite players find themselves in a strange situation: they are playing against play itself.

This contradiction has a number of consequences. For one, a combatant will appraise the strengths and weakness of the opponent so as to have a faultless strategy. If this is done perfectly, there is basically no game at all, merely the appearance of one. The combatant has become what I call in the text, a Master Player. A true Master Player completes a game only for the theater of it. The outcome was determined in advance. Master Players are rare, of course, but it is somewhere in the fantasy of every serious competitor to be one. We saw in the previous century how a self-identified Master Race collectively believed they had won the contest for superiority over all other races even before the contest began; they were winners at birth.  History stopped with them. (It also stopped them.)

A second insight yielded by this simple distinction is that finite play in itself has any number of desirable values. A group of friends meets every Thursday at a club to play poker. They have been doing it for years and almost never does one of them miss the occasion. The rules are precise and never broken; the competition is fierce; each one of them obsesses over being the Master Player among the four of them. Suddenly the playing is over and they leave for home, delighted to have had such a lively evening with friends. To use the language of the book, they were playing a finite game (poker) within an infinite game (life-long friendships). A finite game begins to have ugly consequences when it is played within another finite game. Let’s say some of our poker players have truly decided they cannot continue living unless they emerge winners–every time. That is, Master Players. That’s their game. Poker is only part of it. How often it happens that open hostility emerges; friendship turns to hatred; alcohol is involved; then fists; occasionally guns.

The question gets very complicated. Did President Putin bomb Syrian civilians out a long friendship with Assad, or was it a move to be the Master Player over his corner of the world? What was the longer game in the American invasion of Iraq and Afghanistan? What, for instance, is meant by the term, “American exceptionalism?” Are Americans born with history on their side?

Our simple distinction now makes us look directly at the nature of an infinite game. If the purpose of such human engagement with the world is to continue the play, it would mean there are no winners–and no losers. The essential strategy would be to keep everyone in play. Finite players play within strict rules, else they cannot say who has won or who has lost; infinite players play with rules, because they must be constantly adjusted in response to changing circumstances. Master Players do what they can to prevent surprise; infinite players expect to be surprised. History did not end with their birth; neither will it end with their dying. The future is open and unpredictable. This is why the play of an infinite player is not a play but true play. It is not a scripted repetition of the past but the creative labor of imagining an open future, a future that stays open.


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