Playing the Meta-game
In honor of today’s Schelling-pointmas, a true Schelling-inspired story from a class I was in at a law school I did not attend:
As always, the class was dead silent as we walked to the front of the room. The professor only described the game after the participants had volunteered and been chosen; as a result, we rarely were familiar with the games we were playing, which the professor preferred because his money was on the line.
Both of us were assigned different groups of seven partners in the class. I was given seven slips of paper and my opponent was given six. Our goal was to make deals with our partners about how to divide a dollar, one per partner, and then write the deal down on a slip of paper. Whoever had a greater total take from the deals won $20. All negotiations were public.
The professor left the room, giving us three minutes to negotiate. The class exploded.
And then I hit a wall. Everybody with whom I was negotiating knew the rules, and they knew that I cared a hell of a lot more about the results of the negotiation than they did. I was getting offers on the order of $.20 and less—results straight from the theory of the ultimatum game—and no amount of begging or threatening was changing that.
Three minutes pass quickly under pressure. When the professor returned, I had written a total of $1.45 in deals: most people eventually accepted my meta-argument that they really didn’t want to carry small coins around with them, so they should give me a quarter and take three for themselves, but two people waited until the last second and took 90 cents each. Even then, I only got ten cents from those two by threatening not to accept one- or five-cent deals.
My opponent, on the other hand, had amassed a relative fortune: over five dollars. It turned out that he had been using the fact that he could make fewer deals than he had partners to auction off the chance to make a deal. His partners kept naming lower and lower demands, and he ended up getting the majority of each dollar with little effort.
I made a mock-anguished face, as the professor explained that the game was set up to demonstrate the effect of scarcity on the balance between merchants and customers. Yeah, yeah, monopolies are bad. Econ 101 stuff.
Then he turned to me and asked why I lost, when the odds were stacked in my favor. I asked him what he meant; after all, it was precisely because my partners knew that I could make seven deals that they could bargain against me.
He said, “But you could have torn up one of the slips.”
He was right. I was playing by the rules, when I should have been setting them.
Edit: extraneous and hyperbolic material removed
You’re in luck! The problem with your post is very easy to fix.
That’s where your post ended, and a fine post it was. Delete all the stuff after that. If only all writers had problems so simple!
Done. Thanks for the input—apparently I haven’t yet internalized de Saint Exupery’s admonition.
Now that only the story remains, you should also rename the post (gun/knife no longer make sense, if they ever did).
Renaming posts resends them in the RSS feed, please don’t. Post title still makes sense to me.
Never noticed that before… Should be considered a bug.
This is a bug with the site engine then (one I haven’t heard of before, with lots of posts having been renamed).
Apologies—just a few moments too late.
A good point. Fixed.
Call me dense if you will, but what does taming a fox have to do with editing a post?
Unless there was another admonition of Saint Exupery that I am not familiar with.
“A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.”
Yes… Of course (Doh! on my part)… This is Art School 101 stuff… I went to Art School (once upon a time), so why did I forget this application in relation to this post?
The Article does read much better at the current stopping point.
I thought that his admontion was about not caring about justice (as just desserts), only about getting people to act right in the future.
Hmm… I am thinking of the conversation between the Little Prince and the Fox, where the Fox says that one must take responsibility for what one tames.
I think it has been so long since I read any of St Exupery’s work to really recall what the admonition was. It was 30 years ago, I believe. I also recall in Night Flight that one of the Characters was admonished for the death of a pilot, and although the person had little to do with the death. The admonishing character later explains that what he did had little to do with right/wrong, but about making sure that pilots did not die.
Is that the admonishment to which you are referring?
Yes, that is what I was thinking of. I hadn’t read about the Little Prince and the Fox.
LOL.
It took me an unduly long time (five minutes, perhaps) to figure out that there were two main participants, who were in competition, with seven accessory participants each. Is it just me? (I wonder if this has anything to do with the unusually high amount of caffeine I had today.)
It wasn’t just you. I didn’t understand it ’till I read further into the post.
Ditto that. It took me two readings of the explanation of the game to make any sense of it. It also did not, at first, occur to me what the relationship of the strips of paper were to the game, either.
I wonder how the addition of a middle-man would have effected the game.
The Middle-Man’s job would be to negotiate the deals between the supplier and the 7 “buyers.” He would get a cut of the deals made (negotiated himself from each party of the deal). Now, there would need to be some incentive for the supplier or the buyer to go through this middle-man.
I was very confused by the description of the setup as well, but I just kept reading and sense emerged as the actual game was described.
Based on previous feedback, there are a number of things in this story about which I was unclear, so it may very well have been on my end.
That said, I’m rather honored that you put in that degree of effort!
Oh dear. Being happy due to a bad thing is dangerous, you know.
An interesting story, followed by a lot of (unfounded) (self-)flattery. It’s unclear what’s your point.
As the consensus seems to be that the latter half of the story diminishes the impact of the former, I’ve deleted it.
Thanks for the suggestions—it’s great to have feedback.
Blast. Not what I was going for at all.
I was trying to focus on the framing issue, to suggest that arguing for rationalist positions in the normal manner is an uphill battle and that one solution is instead to highlight the many ways in which rationalism and its consequents can concretely improve people’s lives. The objective, then, would be to make people’s introductions to rationalism smoother by emphasizing the light at the end of the tunnel, rather than the (substantial) amount of things they have to internalize before they can get there.
I certainly wasn’t intending to flatter myself, and I’d hoped the links justified my statements about rationalism; is there a change you’d suggest that could fix that?
My reaction was kinda the same. The story was interesting, and a post with the story alone might have gotten an upvote from me. But the rest sounded a bit too much like an applause light. I didn’t feel like the end provided any new information. It just vaguely declared that rationalists could win by thinking outside the box and linked to a bunch of old posts.
I turned the lights out. Thanks for the suggestions!
I can certainly understand re: the applause lights; I suppose I was too positively affected by the Schelling-pointmas.
I probably should have framed the post as a reaction to the recent discussions about contrarianism, as I was in part hypothesizing that rationalism’s widespread adoption is impaired by being seen that way.
You should try writing a one-line self-contained description of the idea you wanted to communicate in the post, followed by a one-paragraph abstract and a several-items plan—that’ll help to focus the idea, bringing it closer to a legible explanation.
I still don’t understand your intended message. I know that my description doesn’t reflect the idea you wanted to communicate: but it never got through, and the above comment doesn’t help.
I made a couple of changes that might improve things a bit, summarizing particularly at the end.
I’m reflecting on my experience trying to bridge the inferential distance between myself and people with whom I am arguing, and I’m trying to suggest that we should re-frame our discussions with non-rationalists in a manner that shows we’re on their side, that we share their goals, in order to make our contrarian positions more easily accepted.
Better strategy: tear up a strip, make six deals… and then take another piece of paper out of your backpack to make the seventh. ;)
It’s true—we discussed that very point afterwards. A fraction of the class was arguing that I should have merely set aside one slip to be unused, made the deals, and then reversed myself and used the final one.
The argument was over whether that was a credible action—and I like your strategy better.
“When you break rules, break ’em good and hard.”—Nanny Ogg, Wyrd Sisters by Terry Pratchett
Where can I read more stories like these? Any links?
Hmm… I’ve been thinking about your question the last couple days and I’m really not sure. I haven’t really written up my experiences in the field very much, if that’s what you’re asking. If, on the other hand, you’re looking for stories of games played to illustrate game-theoretic concepts, there are lots of places to point for those.
Perhaps you could expand on the type of stories you’re looking for?
Yes that’s what I meant, but not restricted to game-theoretic concepts, psychological concepts interest me a lot also, and I think they are related of course.
Ahem, so, by tearing up two slips, you would’ve won?
I’m unfamiliar with anything like this, doesn’t seem likely that you could actually end up doing worse that those with fewer slips. Couldn’t you just refuse a ridiculously bad deal?
You’re right—and as my professor said, since I had a better initial situation, I should have been able to do at least as well as my opponent.
Tearing up two slips would have been unlikely to beat tearing up one—the latter creates the necessary scarcity (and causes the auction) while not diminishing the total number of deals that much. In fact, since my opponent beat five dollars, I couldn’t have won with two torn slips, but I should at least have been even with my opponent, and might (as my reply to CronoDAS notes) have been able to win via a trick.
I could refuse a bad deal, but my partners knew that I was trying to win $20, where they stood to lose at most a dollar relative to agreeing to the deal; they had less to lose, and thereby had a stronger bargaining position (the literature on Nash bargaining is relevant).
I wasn’t there, but it seems unlikely that the reason people bargained so hard as to almost refuse to give you anything (10-90 split) while the other side gave the other guy almost ALL of their money was merely that they realized you had an unfair advantage. Unless this was brought up frequently as the reason, I find it highly dubious, and would guess that the other guy was just more well liked in general than you were, such that the people in the class wanted him to win and didn’t care whether or not you won (or even wanted you to lose).
Always possible, but I wasn’t suggesting that I had an unfair advantage. Quite the opposite: game-theoretically, my opponent was in a vastly preferable position, as long as I didn’t tear up one of my slips.
To see this, imagine there were only two partners per player. One player can make a deal with each partner, where the other player can only make one deal total. The partners of the former player are playing the Nash bargaining game; the partners of the latter are participating in an auction for the right to play the Nash bargaining game.
Since the theoretical/canonical outcome of the bargaining game is that the person in the stronger bargaining position (the person with less to lose from walking away) takes a larger share of the money, it’s not a big leap to see how the outcomes should differ. When I could make a deal with each partner, they were in the stronger bargaining position (not being eligible for the $20 meta-prize). In the other case, they knew that they could only get some money if they were allowed to come to the table, so to speak, and so they competed with each other in essentially a bidding war for that opportunity.
Does that make sense? As further evidence that I wasn’t simply unusually unpopular, I should note that the outcome I described was standard, happening year after year in the class. Indeed, the professor relied on it turning out that way to make a point; he would have looked rather foolish if I had come out on top despite the apparent structural disadvantages.
If that happens every year then I think that is strong evidence that the reasons you provide are correct. Surprising and interesting…
If you are interested in those kind of social dynamics, I highly recommend studying game theory—it’s absolutely full of surprising results and predictions.
In one class, we proved that for a certain model of soccer penalty kicks, if a kicker got better at shooting (increased the chance of scoring, ceteris paribus) but only in one direction (left or right), he actually was less likely to score because it was easier for the goalie to predict which side he would favor.
That doesn’t sound right. Why couldn’t you simply choose to keep on randomizing 50/50? (Or better yet, calculate an optimal mixed strategy which should be at least as good as randomizing. But my immediate reaction is just generated by the heuristic that capability improvements should never hurt you because you can always choose to go on doing what you would have done previously.)
Ah, of course, I forgot a prepositional phrase: he actually was less likely to score on that side because it was easier for the goalie to predict which side he would favor.
(Incidentally, this proposition has been empirically tested in G.C. Moschini, Economics Letters 85 (2004) 365–371)
However, we do have to be careful in games of strategy in selecting what we call capability improvements. Increasing my payoff in a single cell can change the relationship between cells, preventing me from credibly committing to a particular strategy and thereby diminishing the outcome of the game.
As an example, imagine we have a game defined as follows:
(U,L) ⇒ (1,1)
(U,R) ⇒ (0,0)
(D,L) ⇒ (0,0.9)
(D,R) ⇒ (1,0)
where the pairs are (x strategy, y strategy) mapped to (payoff to x, payoff to y).
The unique Nash equilibrium is (U,L), so each player receives a payoff of 1.
Now “improve” player y’s capabilities by making (U,R) ⇒ (0,1.1). Now there is no equilibrium in pure strategies, and the unique mixed strategy equilibrium is: Pr(U) = 0.9, Pr(L) = 0.5. Expected payoff to the “improved” player is 0.99, and to the other player 0.5, both down from their previous equilibrium values of 1 each, and the magnitude of the effect damaging player y increases as her payoff to (D,L) decreases (derivations available on request).
Of the top of my head, I suspect your heuristic applies in zero-sum games, but not necessarily elsewhere. Unless the players could read each other’s source code...
Related: here’s a fascinating recent Reddit thread about generating random numbers with your brain while playing poker. I’m curious if the LW community can come up with better ways, because the ones proposed there strike me as inadequate. IMO, memorizing a longish string of random digits beforehand was the best strategy proposed.
As a further note, though, if by
you mean I should be able even without tearing up a slip or otherwise limiting my own options, then no—I was in a weaker bargaining position at the beginning, and game-theoretically I should have ended up worse than my opponent. That was a key finding of Thomas Schelling’s, though he applied it to nuclear warfare (see The Strategy of Conflict and also the link at the beginning of this post for more info on his bare-knuckle game theory).
He could, but as long as he had all the slips of paper, he can’t but gain by going back on the commitment not to trade below a certain split. He can only deal once with each person, so with the same number of slips and co-players, everyone dealing with him knows there’s no substantial chance he’ll wind up not trading with them at all as long as they’re willing to give him a penny of the dollar. As much of the dollar that slip represents as they’re willing to hold out for already belongs to them—since if he doesn’t use it, he gets nothing, and if he does, he gets some non-zero amount. Only by taking away his own option to use the last slip does there come to be any credible chance that somebody doesn’t get to split a buck with him.
Tearing up two slips would likely have lost him the game, however, since the actual winner had obtained over five dollars, and one couldn’t manage that with only five slips.