Assume Kim Kardashian and Angelina Jolie spend 30 minutes each day applying their own make-up. Should Kim and Angelina apply make-up or should they use no make-up at all?
Let’s say if Kim and Angelina stopped using make-up they each receive a payoff of 30 because they do not need to spend 30 minutes each day applying their own make-up. Let’s also assume that, if Kim believes Angelina will not use make-up, Kim will use make-up to look more attractive and she will receive a payoff of 200. This will make Angelina look less attractive so she receives a payoff of -50. Assume that Angelina will reason the same so the vice versa is also true. If both Kim and Angelina use make-up they receive a payoff of 0 because they both look equally more attractive than before so it has not changed who looks more attractive than the other and they now lose 30 minutes of their day applying make-up.
If Kim believes Angelina will use no make-up then Kim will want to use make-up to look more attractive than Angelina and receive a payoff of 200 rather than 0. Angelina will reason the same way. So both Kim and Angelina will play their dominant strategy and apply make-up.
Both Kim and Angelina using make-up means they will each receive a payoff of 0 because both Kim and Angelina using make-up does not change who looks more attractive and yet they waste 30 minutes applying their own make-up. So the Nash equilibrium (Make-Up, Make-Up) makes Kim and Angelina worse off than if they both use no make-up. As long as Kim and Angelina do not trust each other to use no make-up, they will both use make-up. If Kim and Angelina could collude and make an agreement or if they trust each other then they could both use no make-up.