Game Theory, Oligopoly, and Christmas Advertising


One of the surest signs that Christmas is approaching is that from November each year our screens are awash with expensive adverts by the major retailers — Marks and Spencer, Tesco, Asda and of course John Lewis. Why do these retailers advertise so much? It’s slightly odd, since, really, few people need to be reminded to buy food for Christmas, and the costs of these adverts are very high — according to Forbes, the John Lewis advert this year cost $8m. It is quite likely that the various retailers would be better off not advertising at all, and just enjoy the pure benefit of the increased Christmas spending. This, of course, is just what does not happen. And game theory helps to explain why.

Why do firms advertise at all? In most cases it’s not to increase total demand for the given product they make; it is, rather, to increase their share of the total market. Food adverts at Christmas will, probably, make each of us buy a bit more food. But the reason Asda or Sainsburys advertise is so that we buy our Christmas food from them and not some rival. The problem is, they are essentially locked in a Prisoner’s Dilemma.

Consider two rival retailers, Tesco and Sainsbury’s. Their payoffs from advertising are as follows (in millions of pounds). In each box the payoff to the Row player is given first (Tesco) and the payoff to the second player (Sainsbury’s) is given second.

The Nash Equilibrium for this game is for both firms to advertise, even though they would both be better off if neither advertised (so the outcome is similar to a Prisoner’s Dilemma, when both prisoners would be better off being silent but both confess). Starting with Tesco, if Sainsbury’s advertises, Tesco will need to advertise too, since if it does not its share of the Christmas market will be squeezed and its profits will be only £20m, whereas if it advertises its profits will be £30m. So we put a tick next to Tesco £30m payoff in the top left hand box. But if Sainsbury’s does NOT advertise, Tesco will benefit even more by advertising as it can gain market share from the silent Sainsbury’s, so hence we put a tick next to the payoff to Tesco of £70m in the top right hand box. Obviously, ‘Advertise’ is Tesco’s Dominant Strategy — it will run a Christmas advert whatever Sainsbury’s does.

The same reasoning applies for Sainsbury’s. So, if Tesco advertise, Sainsbury’s will do better to advertise too, since their payoff then will be £30m, compared to only £20m if they don’t advertise. So place a tick next to £30m for Sainsbury’s payoff in the top left hand box. And if Tesco do NOT advertise, Sainsbury’s will do even better and earn £70m if they advertise and thereby take market share off Tesco. So we place a tick next to £70m for Sainsbury’s in the bottom left hand box.

As can be seen, the only box with two ticks is the top left-hand box — where both shops run Christmas adverts and earn £30m in profits each. This is the Nash Equilibrium — which means that, in the light of what the other shop does, neither shop regrets its decision to run a Christmas advert campaign. By contrast, suppose Tesco had decided not to run a campaign and now it finds Sainsbury’s has — well then Tesco would regret that decision and would (if it could) reverse it, since by not advertising it makes only £20m profit to Sainsbury’s £70m. Advertise-Advertise is the only outcome that neither shop would change even if it could.

The irony is, of course, that both firms would be better off if they abandoned Christmas adverts altogether, for then each would earn £50m in profits compared to £30m. The problem is neither firm will occupy that position for, as we have seen, it is always in the individual shop’s interest to advertise irrespective of what the other shop does. Any shop seeking not to advertise and make the bottom right-hand box possible will be badly hit by the other firm that DOES advertise. So no one takes that chance and both firms advertise — and as a result our screens are saturated with Christmas adverts by oligopolistic retailers. Whether this is an optimal outcome for consumers is another question — though these adverts do seem to kick off the season of festive cheer!

By K Shah & Dr StJohn

Further reading:

Are big budget ads worth it?

Nash Equilibrium

Game Theory