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Spectacularly non-obvious, 2: threeness games

Friday, October 30th, 2015

[ by Charles Cameron — my own three-way play, and a little goose ethology from Konrad Lorenz ]

lorenz goose geese gander pecking order from laws of the game
Konrad Lorenz, Paul Leyhausen, Motivation of human and animal behavior: an ethological view, p 129


Returning to the topic of ternary logics and scissors paper stone, here’s another old post of mine (Dec 2000):

I’ve always thought it was a training in the complete frustration of the assumption that conflict could be decided, most of all by means of skill of any kind. I mean, if you want to decide on a random basis, toss a coin, and if you want to decide on a basis of power or skill, set up a contest in which superior power or skill succeeds…

In scissors paper stone you have a setup where (as in heads and tails) no choice is superior to any other as far as chance is concerned, but there’s a troubling “threeness” about the thing which means it’s not aligned with an “either/or” logic but with a subtler logic altogether.

Two other places where this kind of “intransitivity” relation can be found would be (a) the geese studied by Konrad Lorenz which had a pecking order “a > b > c > a” (ie of the three particular geese, one would always defer to the second, which would always defer to the third, which in turn would always defer to the first) — and this is a perfectly “natural” effect which Lorenz encountered in “real life” — and (b) the impossible triangle devised by L S and R Penrose, which is clearly and unambiguously paradoxical (though logically equivalent to the Lorenz geese as far as I can tell).

Anyhow, what I’m trying to suggest is that “scissors paper stone” can work a little like a koan, it can somehow challenge our usual binary asusmptions and train us in a more flexible and “lateral” way of thinking..


Some thoughts about a game (real or agent-based) in which three players (or sides) compete, two teaming up against one in constantly different configurations of challenge and victory (June 2005):

The idea is simplicity itself, putting it into words unambiguously is difficult.

Yesterday I was at a hotel swimming pool where two sons of another guest and my own son Emlyn were playing around together, all aged around 10-12, with nobody else there, and I asked them to play a game where one of the three would be “top guy” and the other two would try to dunk and generally overthrow him, and as soon as it became clear that the top guy had been dunked and dethroned, there would be a new “top guy” (one of the two who had been doing the overthrowing and come out the obvious winner) and the other two would pounce on him…

They were not evenly matched, but any one of them was easily outmatched by the other two working together, and being “top guy” meant your head was above water and you were, so to speak, “comfortable” — so there was a real premium on being “top guy”, and the other two were (at any time) eager to collaborate to get the position.

And there was no tendency for the two brothers to gang up against my son, because the immediacy of two defeating one was more urgent and compelling than any ideas of teaming by kinship interests, minor differences in strength and skill, etc…


Prisoners’ Dilemma deals with the essence of twoness, as do many win / lose games such as tennis or chess, and this game deals with the essence of threeness, as (in a very different mode) does paper scissors rock.

My sense from PSR, and reason for being particularly interested in threeness in games, is that PSR involves thinking in flagrant defiance of our usual binary logic as humans.

I suspect my threeness game could be paradigmatic for cooperation and competition, in that each player at any given moment is either “top guy” or “member of the opposition” — and thus plays either “sole defender” (competing without a trace of collaboration) or “team attacker” (cooperating to compete) at any give moment, but with a very rapid turnover between the two.

The kids seemed to enjoy the in-the-pool version yesterday, until it the water-play got a bit too rough after about forty minutes or an hour of enthusiastic splashing and dunking.

And finally:

As a game designer, I want to think through this mode of play, two against one with switching, in a number of media — water play, three-person tag, possible card-game instantiations, board games, a chess variant perhaps, a variant on my own HipBone Games, etc — and as a conceptual matrix for game-theorizing, modeling, understanding conflict and conflict resolution, etc.

I wonder what ideas and possible uses the basic idea might trigger in others…

Trump as Cinderella’s Fairy Godmother

Monday, September 28th, 2015

[ by Charles Cameron — on finger-based decision theory ]

Surely this is the answer to Decision Theory and Human Behavior — don’t we all do it this way?

When win-win games get gamed

Monday, August 3rd, 2015

[ by Charles Cameron — a paradox I’m currently chewing on, courtesy of Richard Landes]

I want to take something that Richard Landes has been saying, abstract it from those conflicts to which Richard applies it, simplify it by removing one technical term that’s part of his detailed breakdown, and present it in as bare-bones a manner as I can manasge. You can see two of Richard’s own versions of the issue below.


The basic question, as I understand it, is this:

How does a non-zero-sum move look to a zero-sum player, and vice versa?

Let’s suppose your entire background and upbringing revolves around the idea of zero-sum, you-win-I-lose games. If you see any sign of your adversary gaining an advantage in a negotiation, that’s proof positive that you’ve been bamboozled: somehow, you must have lost. Your job is to make no concessions — to be the winner in a winner-takes-all contest.

Now suppose your background and upbringing have revolved around the idea of non-zero-sum, win-win games, in which both sides of a negotiation make some concessions so that both can emerge as winners. You offer concessions in good faith, and in return you expect similar concessions.

What happens when a zero-sum game player and a non-zero-sum game player meet in play?

It’s Landes’ suggestion that any generosity on the part of a win-win player offering his winner-take-all opponent a concession will be taken as evidence of weakness,. and the opponent, far from making a corresponding compromise, will press on and demand more — making further nmoves which will offer so little that the win-win player will be at a loss to explain why such a promising start to bnegotiations fell apart so badly.

A further supposition: so-called honor-shame societies are geared for zero-sum, winner-takes-all gameplay, while societies which rely on an innocence-guilt reading of human behavior will be no less inclined toeards playing non-zero-sum, win-win games.

That’s the idea expressed in game-theoretic terms, as simply as I can put it. To my mind, these game considerations are worth thinking through in their own right, absent the specifics to which Richard Landes brings them.


Here is Landes making the same point, in the context of Israeli relations with the Palestinians, the Arab and Muslim worlds, and European liberalism –all of the above broadly speaking:

And a text version, Cognitive Egocentrism, for those who find words fly home faster in print…


Help me think this through.

Takfir squared, Prisoners Dilemma and MC Escher

Friday, January 16th, 2015

[ by Charles Cameron — call it backlash, backfire, or blowback, somewhere they’re dclaring takfir on the takfiris ]

Ali Minai at BrownPundits has a worthwhile take on what he calls, paradoxically enough, Unreal Islam, from which I’ve excerpted this paragraph:

However, another version of takfir is now afoot in the world. Call it “reverse takfir”. Unlike the militant version, it is well-intentioned and self-consciously humane, but it is also dangerous. This “benign” version of takfir is epitomized by the idea that the acts of violence being committed by self-proclaimed holier-than-thou Muslims are not the acts of “real Muslims” and do not represent “real Islam”. In effect, it declares the terrorists to be infidels! The idea is widespread, and is espoused in three different contexts: By well-meaning non-Muslims (such as Presidents Bush and Obama) seeking to avoid stereotyping and the implication of collective guilt; by ordinary Muslims wishing to dissociate themselves from the beheaders; by Muslim sectarians wishing to separate their brand of orthodoxy from that espoused by terrorists; and – most ironically – by Muslim governments and security forces seeking an “Islamic” justification for attacking extremist fellow Muslims, thus implicitly buying into the central jihadi argument of apostasy as a capital offense. The urge to do this reverse takfir is understandable and not without factual basis: Most Muslims are indeed not violent extremists who wish to kill infidels. And it does help protect innocent Muslims from backlash, which is rather important. The problem, however, is that it also feeds the narrative of denial and deniability that allows the militancy to thrive.


Call it reversal, call it backlash, backfire, blowback, call it enantriodromia, eye-for-an-eye, tit-for-tat — the return of violence for violence seems both instinctual, in the sense that a desire for vengeance seems to spring unprompted in the individual, and culturally embedded, in that it can be found in Torah and Pashtunwali alike, and elsewhere, and elsewhere.

Whether the individual instinct can usefully be separated from cultural instinct is at least a question, perhaps a koan — but it was Axelrod‘s insight, working on the Prisoners Dilemma in game theory, that the “strategy” of tit-for-tat may best be considered as an iterative process, .. for-tit-for-tat-for-tit-for-tat-for .. rather than as an isolated instance, tit-for-tat-period.

Gandhi made the same leap to iterative thinking when he said:

An eye for an eye makes the whole world blind

— or did he?


Iteration requires that we pull back, to see not just “my / our” response — which is probably self-evident, if not so all-consuming as to be omnipresent and invisible — but to see “both sides”.

We move from:

Escher one hand drawing

— which is the natural or “default” view, equivalent to the righteous indignation of one’s own side in a conflict, to:

Escher drawing_hands

— which definitely seems paradoxical on the face of it, and which notably doesn’t give preference to one side or one hand over the other — Doug Hofstadter‘s celebrated diagram illustrates the process thus:

Hofstadter Escher hands


Lincoln uses this strategy in his Second Inaugural, in describing the Civil War:

Each looked for an easier triumph, and a result less fundamental and astounding. Both read the same Bible and pray to the same God, and each invokes His aid against the other. It may seem strange that any men should dare to ask a just God’s assistance in wringing their bread from the sweat of other men’s faces, but let us judge not, that we be not judged. The prayers of both could not be answered. That of neither has been answered fully.

It is to a large extent the elevation of Lincoln’s comments above partisanship into inclusivity, surely, which gives that great speech its greatness.


For your further consideration:

Robert Axelrod:

  • The Evolution of Cooperation, 1984
  • The Complexity of Cooperation, 1997
  • The Evolution of Cooperation, revised 2006
  • Doris Schattschneider:

  • M.C. Escher: Visions of Symmetry
  • An interesting pattern I’ll call Piggy in the Middle

    Thursday, December 12th, 2013

    [ by Charles Cameron — on the travails of negotiators & peacemakers ]

    I’m thinking of the simple, three-player version of the children’s game called Piggy in the Middle. Two plays face each other and toss a ball back and forth, while a third player standing between them attempts to intercept the ball in passing. In the case below (upper panel), Phillip Smyth is “piggy in the middle”.

    I’m suggesting there’s a pattern here that’s worth watching for. Bill Keller, opining in the NYT under the title Iran’s Hardliners, and Ours (lower panel, above), thinks that if you’re piggy in the middle, “you’ve probably done something right.”

    That’s a thought that might have comforted my childhood, though I don’t think it’s true in an “always applicable” sense. I do think it suggests that both sides in a fierce argument may often have something to be said for them, and that a skillful negotiator will be one who can “hear the truth” in both sides and winnow them out of the turmoil as the basis for a rapprochement

    And BTW, it’s clearly a lot more work being “piggy in the middle” that either of the two other players — for one thing, you’re constantly forced to spin around to catch a ball you just missed, as it whistles by in the opposite direction to the one it was going in when you just missed it. Blessed are the peacemakers.


    Wikipedia’s entry on Piggy in the Middle is titled Keep Away. As of this writing, it contains what is undoubtedly my current favorite comment on any game in the entire literature of play up to this point in time:

    The game has a worldwide use of playing; mostly in many countries.

    That’s good to know, and or maybe not.

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