Italian is strictly better than Sandwiches, so it’s not, but Chinese has no alternatives going top-right.
I don’t understand the focus on the convex shape (which doesn’t seem to be the Pareto frontier here).
What if, to make it more obvious, Chinese was only slightly bottom-left of the Nash Equilibrium point. Would it still not be part of the shape? Would the choice still be between Sushi and Italian?
So, if you are limited to only pure strategies, for some reason, then yes, Chinese would be on the Pareto frontier. But if you can implement randomization, then Chinese is not on the Pareto frontier, because both sides agree that “flip a coin, Heads for Sushi, Tails for Italian” is just strictly better than Chinese.
The convex shape consists of all the payoff pairs you can get if you allow randomization.
Isn’t Chinese also on the Pareto frontier?
Italian is strictly better than Sandwiches, so it’s not, but Chinese has no alternatives going top-right.
I don’t understand the focus on the convex shape (which doesn’t seem to be the Pareto frontier here).
What if, to make it more obvious, Chinese was only slightly bottom-left of the Nash Equilibrium point. Would it still not be part of the shape? Would the choice still be between Sushi and Italian?
So, if you are limited to only pure strategies, for some reason, then yes, Chinese would be on the Pareto frontier.
But if you can implement randomization, then Chinese is not on the Pareto frontier, because both sides agree that “flip a coin, Heads for Sushi, Tails for Italian” is just strictly better than Chinese.
The convex shape consists of all the payoff pairs you can get if you allow randomization.