What is a Pareto Optimal Allocation and How do we use an Edgeworth box to Show it?

Question

How can we use an edgeworth box to see if an allocation is Pareto Optimal? What doe Pareto optimal mean?

Answer 1

A Nash Equilibrium is Pareto Optimal if neither player can be made better off without making the other worse off.

For example, if the Nash Equilibrium of a game involves payoffs (0,0) but there is another node with payoffs (1,-20), then (0,0) is Pareto Optimal, because even though I may improve my own outcome by getting 1 instead of 0, you then must lose utility.