(1) The end was kind of surprising. for this kind of play to be stable in the long-run over many itterations, the player clearly needs to carry out his “promise” to play steal since (split,split) is the only pure-strategy outcome that is not an equilibrium of the game.

(2) This strategy trades a promise to split during the game for a promise to do so afterwards. It’s not clear why the latter should be more credible than the former.

(3) This strategy basically converts a pseudo prisoner’s dileme (psudo because it has weak rather than strict dominance) into an ultimatum game. How long until we see a player using the messaging strategy: “I will play steal. Since steal is a (weakly) dominant strategy for me, nothing you can say will change my mind. You should play split and then I will give you a fraction x of the money after the show”, where x is strictly less than 1/2?

April 20, 2012 at 2:54 pm

twicker

Re: (1) agreed that stability with this strategy is to carry out the promise (that builds credibility); disagree that (split, split) is not equilibrium. Given the right social norms, it’s pretty stable. I remember an honors micro course I took where we really aggravated the econ prof: we stayed at the equivalent of “split, split” for 8 rounds, with about 10 independent groups. Someone finally broke from the group at round 9, but he was visibly red before that – given that his dear theory was getting trounced. It would probably have been over by round 6 or 7 if we hadn’t been so annoyingly honest, altruistic, and altogether non-Homo economicus.

Of note, everyone assumed that I was the one who’d killed the cartel (it was the oil cartel game), because I’d forcefully made the, “Cooperation is not stable!” argument. In fact, my little group of 3 set our group up so that they would make the initial decision about how much oil to produce, and then they would give me the paper – and I could change or keep it, as I wished. Also of note, I wasn’t the one who broke the cartel; I had just come to believe what my other econ classes had sold me. Silly me.

(2) IMHO, the latter is more credible because it gives (what seems to be) patently honest information up front. If I say, “I’ll split it with you now,” I’m not really credible — too easy for me to cheat. If I say, “I’m going to play, ‘Steal,'” I’m more credible. I’ve established my position of power and offered two options: mutual annihilation or the possibility of gain. It’s a credible threat and, thus, provides more certainty – inherently more believable.

(3) Assuming players who claim they’ll play, “Steal,” really will, then the only thing making them keep any promise to split the money will be social pressure. If that social pressure is sufficient to have them split the money, they’ll have to split it 50/50 (otherwise, they’ll be outed as a liar). If it’s *not* sufficient, then they’ll keep well north of 50%, because they don’t care about being seen as a liar. The question then becomes whether they’ll give a little bit of money to assuage any guilt, or whether they’ll just keep all of it.

An ultimatum game, indeed.

April 20, 2012 at 11:16 pm

Joey

@ Greg re: (2)

The latter is not more credible than the former. It is the threat to play steal that is credible, as it is a dominant strategy. If you are faced with a promise to split during the game, your best option is to steal. If you are faced with a promise to split after the game, and a credible threat to steal in the game, then you are indifferent between in-game choices and the non-zero possibility of splitting after the game trumps the big fat nothing both players get with a {steal, steal}. This assumes that the bald player wouldn’t get any utility from schadenfreude; I might have tried to stick it to the other guy and chosen steal just to be spiteful.

April 8, 2013 at 12:38 am

Mike H

(2) it’s not relevant which promise is more credible. If I promise to split before, it’s still better for you to steal, whatever I actually do. If I promise to steal before and split after, and my promise to steal is credible, it’s better for you to split before no matter how much you doubt my word about what happens backstage.

April 20, 2012 at 4:37 pm

Evan

As the video was starting, my guess as to what the surprising strategy would be was that each person would agree to choose the other person’s ball (without knowing what was in it). This negates the prisoner dilemma problem and gives each person an expected value of 3/8 of the prize pool.

April 20, 2012 at 8:57 pm

jeff

Great idea! But why not go one step further. let each other inspect and choose the balls. what ball would you choose if you were choosing the other guy’s ball?

April 20, 2012 at 8:59 pm

jeff

i see that would not be allowed.

April 21, 2012 at 3:07 am

Emil

This sounds promising. Guy A can say right away “I’m not going to look at the balls and will pick blindly, but I’ll give you half my winnings if I end up taking the whole pot in the end”. Whether he looks or not is observable.
The other guy then has a choice between Steal (payoff 1/2*X+1/2*0) or Split (1/4*X+1/4*X). If guy B is risk averse at all, he’ll prefer 1/2*X for sure (assuming he believes the “split after the show” promise).

In the long run a promise not to look at the balls should be much more credible than a promise to Steal, considering how the guy in the video actually played Split.

What’s interesting in any case is that people find the promise to split after the show believable. For whatever reason, people think that promises regarding in-game actions are much less credible than promises regarding real-world actions. I would also be much more willing to trust someone who says they’ll give me money after the show, than someone who just promises to play Split. And this is despite the fact that splitting after the show probably involves some legal complications (e.g. accounting for taxes, or whether the payment is a lump-sum payment or not)

April 21, 2012 at 9:37 am

twicker

@Emil: I think you’re getting to the root of what’s happening. My hypothesis:
1) In-game, Player A’s threat to steal is more credible than any promise of splitting. If I’m Player B, my level of time-proximal trust in my counterpart is greater.
2) By providing me with a point of trust/credibility, my overall trust in Player A goes up. Thus, I have more faith in a more-distal promise, since I have proximal information suggesting the person can be trusted.

It also makes me think that the player who promised Steal and played Split did exactly what he needed to (though it hurts its efficacy in future rounds; then again, he’s not playing future rounds). Assume I’m the player promising, “Steal:”
+ If I play, “Steal,” and the other person trusts me and plays, “Split,” then we get to split the money.
+ If I play, “Split,” and the other person trusts me and plays, “Split,” then we get to split the money.
+ If I play, “Steal,” and the other person feels offended and plays, “Steal,” to spite me, then we get nothing (although I will have lived up to my word, albeit in a somewhat socially unacceptable way; note how people bristled when the guy threatened, “Steal”).
+ If I play, “Split,” and the other guy tries to spite me and plays, “Steal,” then the money still exists – and now there is a *huge* pressure on the other guy to actually split the money with me, since I’ve just visibly and very publicly demonstrated that, *if he had trusted me as a fellow human,* he would have had the guaranteed 1/2 the money. I have shown that he was wrong to *not* trust me, and that, if he *doesn’t* give me 1/2 the money, then *he* should not be trusted.

It comes down to that earlier implicit agreement to split the money: by setting that up, I set myself up as the good guy for everyone to see (including his family and friends). This works best in my favor if, after threatening “Steal,” I actually play, “Split.” Thus, I play, “Split” and let social pressure do the rest.

Very, very cool video. Again: Jeff – thanks for sharing!

April 21, 2012 at 10:16 am

David

Jeff, are there explicit rules forbidding the players from switching seats, for example? I’m having trouble finding game rules with that level of detail.

April 20, 2012 at 6:04 pm

wellplacedadjective

yeah, I was with evan… actually I thought they just wouldn’t look at the content of the balls.

April 21, 2012 at 8:14 am

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I saw the video elsewhere on the web and started a blog entry; fortunately I was just 2 lines in before I said “wait a minute, isn’t there a heck of a chance cheap talk may have covered this already…”
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The solution in the video appears in the comment thread on cheap talk from when you covered this in 2009! (proposed by Mike Hunter) Did the contestant read Cheap Talk 🙂 ? Florian had a different good solution there.

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