We have observed that both participants in the bike-selling game are better off if they make the transaction. This is the basis for one solution concept in cooperative games.First, we define a criterion to rank outcomes from the point of view of the group of players as a whole. We can say that one outcome is better than another (upper left better than lower right, e.g) if at least one person is better off and no-one is worse off. This is called the Pareto criterion, after the Italian economist and mechanical engineer, Vilfredo Pareto. If an outcome (such as the upper left) cannot be improved upon, in that sense -- in other words, if no-one can be made better off without making somebody else worse off -- then we say that the outcome is Pareto Optimal, that is, Optimal (cannot be improved upon) in terms of the Pareto Criterion.If there were a unique Pareto optimal outcome for a cooperative game, that would seem to be a good solution concept. The problem is that there isn't -- in general, there are infinitely many Pareto Optima for any fairly complicated economic "game." In the bike-selling example, every cell in the table except the lower right is Pareto-optimal, and in fact any price between $80 and $100 would give yet another of the (infinitely many) Pareto-Optimal outcomes to this game. All the same, this was the solution criterion that von Neumann and Morgenstern used, and the set of all Pareto-Optimal outcomes is called the "solution set."

概念：Pareto criterion（帕雷托标准）Pareto Optimality（帕雷托最优）Pareto Improvement (帕雷托改进) 在不使其他人境况变糟的情况下，而不可能再使另一部分人的处境变好。（No one can be made better off without making someone else worse off.）如果一种变革能够使没有任何人处境变坏的情况下，至少有一个人处境变得更好，我们就把这个变化称为帕累托改进。一般地说，如果一个社会的现状不是处在帕累托最优状态，就存在着帕累托改进的可能。相应地，如果没有任何帕累托改进余地，就意味着现状已经达到了帕累托最优的状态。