— It can be hot, if you accidentally put in too much chilli at Amanda’s wedding.

Yesterday my officemate and coauthor Michael Franke gave a talk on his Iterated Best Response model at the Logic Tea. It’s all about credibility of messages (at least the bit I’m writing about today is): roughly speaking, a message is credible if the speaker would only want you to believe it when it’s true. So “I owe you money” is credible (if it’s not true I certainly don’t want you to believe it) but “You owe me money” isn’t (I’m quite happy if you believe it, whether it’s true or not).

After the talk Jonathan Zvesper mentioned an interesting case of credible messaging: an ad campaign for Stella Artois in the UK, with the slogan “reassuringly expensive“.

What’s going on here? Stella want to say “our beer is better (than the common muck)” but that wouldn’t be credible (they would also want you to believe it if it were false). So they say something that is credible (in the UK it’s generally about 20p more expensive than whatever else is on offer, apparently) and implicate that this has some bearing on quality. And how does that work?

Well, in evolutionary biology (and game-theoretic economics, and possibly even our game-theoretic pragmatics) there’s something called the Handicap Principle. This says roughly that expensive messages can (in some circumstances) be credible where cheap ones would not. If I tell you “I’ve got lots of money” you’ve got no reason to believe me. But if at the same time I’m using a 100-dollar bill to light my cigar, you might just be convinced. So perhaps what Stella are doing is “burning money” to convince you?

Well, in the first instance that doesn’t seem to be the case. If they put the price up, they make more profit per unit, after all. But they probably sell less units, which seems to fit the Handicap Principle all right. So should we believe the advertising? Well, actually no: enter the Iterated Best Response model.

Micha’s insight is that you can’t always stop after just one round of calculation in checking if messages are credible. The first round actually changes the meaning of a message: it comes to mean only those things that the speaker would rationally have wished to convey with it. Sometimes this is widening: “Our beer is better” comes to mean “Our beer is better (or it isn’t but we don’t want you to know that)”. Other times the meaning narrows: “Our beer is more expensive” comes to mean “Our beer is more expensive and also better!” In both cases, though, you need to check if another round of best response calculation (“If that’s what the message seems to mean, when would the speaker want to use it?”) might change the picture.

And here it does. In the first round we conclude from “Stella is more expensive” that “Stella is more expensive and better” (the Handicap Principle). But now the drinkers are flocking to Stella, sales are soaring, and … there’s no handicap involved any more. A second round of Iterated Best Response reveals that the price hike is a cunning ploy, and the real meaning of the advertising slogan is “Our beer is more expensive and might be better, but if it’s not we’re satisfied so long as you buy it”.

But after all, what did you expect from advertising?

(This discussion was brought to you by the Eik en Linde, La Chouffe, and the letter BEER.)