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.
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.