Pareto Optimal - improving for one player, static for another This is very basic - 
Something is pareto optimal if you can't improve the outcome for one player without worsening the outcome for another.
But what about where one player gets the same but the other player gets more? Is one pareto optimal?
E.g.

           p1, p2
outcome 1: 2   2
outcome 2: 2   4

The move from outcome 1 to outcome 2 improves for p2 but it doesn't make the outcome worse for the other player.
I would say that outcome 2 is pareto optimal and that outcome 1-> outcome 2 is a pareto improvement.
 A: You are right, in your set of outcomes only outcome 2 is Pareto optimal. This is a direct application of the definition: for outcome 1, player 2's position can be improved, without worsening player 1's position. Thus, outcome 1 is not Pareto optimal.
These are exactly the kinds of comparisons you do in economics. Suppose you give away some item, and  two players have private information about how much they value the item, $\theta_1>0,\theta_2>0$. This is the "utility" they obtain when they receive the good. Suppose $\theta_1>\theta_2$. If transfers are allowed, it is only Pareto-optimal to give the good to the one with higher valuation, i.e., only giving it to $i=1$ is Pareto optimal. This is because with transfers, you can take away a transfer from $i=1$ and give it to $i=2$ such that $2$ is indifferent between getting the item (without transfers) and not getting it (being compensated by transfer), while player 1 strictly prefers getting the item with transfers. Hence, giving the item to player 2 is not Pareto optimal, because there is another allocation that makes player 1 bettor off, without making 2 worse off. (Note that this reasoning does not apply if transfers are not possible.)
