So in the toothpaste wars, we have Sensodyne and Colgate, choosing to
advertise or not to advertise. We found that it's a dominant strategy
for Sensodyne to always advertise because whatever Colgate does, if they don't
advertise, Sensodyne will advertise. If they do, again, Sensodyne will want to
advertise. And by the same token, Sensodyne choosing
to advertise means that Colgate is best off to advertise.
And if Sensodyne does not advertise again, Colgate will want to advertise.
So in this case, our Nash Equilibrium is for both firms to run the advertising
campaign. And this is actually what's called a
Prisoners' Dilemma. Because what's interesting in this
situation is that both Sensodyne's and Colgate's profits would be higher if they
chose not to advertise, right? Just go back, they both make 2.5 million
right now. But if they both could choose not to
advertise, they would make 5 million. So they could double their profits by
choosing not to run the ad campaign. But why don't they do it then?
What's the problem? Well, they have individual incentives to
advertise anyway. Regardless of what the other player does.
Remember, we talked about dominant strategies.
Dominant strategy here is to advertise, meaning that it doesn't matter if the
other firm advertises or not. It's always best, it's always profit
maximizing for a particular firm, Sensodyne or Colgate, to run the ad
campaign. All right.
So, it doesn't matter if the overall outcome will be best,
I will always choose to run the advertising campaign.
It doesn't matter what the other firm does.
