I didn’t ever think that I’d comment on the game theory of the fashion industry, but hey the fashion industry contains profit-maximising firms that rely on a brand to maintain their profits, so why not? We’ve known for a while that various fashion houses employ many tactics to improve their branding, for example sending free products to celebrities so that their products are associated with these celebrities. This morning, though, I came across an article in which it was shown that fashion houses also send out their opponents’ products to sub-lebrities, that is, those people at the lower end of the celebrity spectrum with whom the fashion houses would rather not have their products associated in case it jeopardises their brand.  You get your opponents' customers to see that some loser sub-lebrity has their branded goods, which makes those customers come and buy your goods instead. Eureka!

But what the fashion house that started this didn’t realise is that the best policy with these kinds of games is not to commence playing them at all. Unless all the fashion houses can come to a simultaneous agreement to cease doing this 'unbranding' or ‘anti-branding’, they’ve now permanently increased their branding costs. Why? Not only do they have to pay for sending their products to celebrities, but they have to pay for sending their opponents’ products to sub-lebrities. I can see that the very first fashion house to do this thought “Wow! What a great idea! We can damage our opponents and increase our market share. We’re geniuses!” They didn’t realise they were initiating a multi-player prisoner’s dilemma in which each fashion house has an option to Cooperate (not anti-brand) and Defect (anti-brand).  How does this work? Well, for each fashion house, it’s in their interests to anti-brand if no other firm does (they defect, when the others cooperate) because they will end up looking like a superior brand at relatively low costs. Secondly, they would also much rather not be the firm that is not anti-branding when any other firm is anti-branding.  Together, these imply that Anti-branding is a strictly dominant strategy in the game.  Consequently, an All Anti-brand equilibrium obtains, at which all the firms are worse off than they would have been had no firm chosen to anti-brand, or at least chosen not to allow anti-branding into their set of potential strategies.

What do they need to do to get out of this situation? As someone who doesn't consume these goods, I don't really care, but the consumers of the goods should because the costs are probably going to be passed on to them (depending on the elasticity of demand for these goods, which might be quite great given that they are luxury goods).  Anyway, I suspect that they would like to alter the game so that the incentive to anti-brand is removed.  I suspect, though, that now all firms have done it, there is no credible way to get rid of it. All the firms will continue to do it, in the interests of attempting to get more market share, but ultimately damaging their profitability because if everyone does it, no single firm is likely to improve their market share.  Doh! Did no one at Gucci or Prada study game theory? What's probably even more frustrating for a consumer of these goods is that the outcome is not like the breakdown of cooperation in a cartel in which consumers might eventually benefit from lower prices, here, instead, consumers may suffer.  Poor fashionistas! Your Prada, Gucci and other famous brand's will cost more now.

Images: Gucci Bag from guccigoods.com, Snooki trio from americanchic.net