Gandhi's quote formalized Hello,
I hope this question is appropriate for Mathoverflow. Gandhi said, "Be the change that you wish to see in the world". I don't understand anything in Game/optimization theory (I don't know exactly what theory), but I am curious whether there are mathematical models, in which if the individual makes his local contribution the best, without thinking about the interaction with the decisions of the other, this makes the whole system act in the best possible way.
Thank you,
Sasha 
 A: The simplest example is an Edgeworth Box economy, or more generally a Walrasian equilibrium.
The fundamental insight is that when multiple individuals are faced with the same (linear) prices, they choose consumption bundles (or production bundles or something else, depending on the model) where certain level hypersurfaces are tangent to a particular hyperplane. Moreover, equilibrium requires these tangencies to occur at a common point. On the other hand, for one interpretation of "best possible" (i.e. Pareto optimality), the condition for a best possible outcome is that these level hypersurfaces should be tangent to each other.
Because hypersurfaces tangent to the same hyperplane at the same point are tangent to each other, the result follows.  This simple insight has been vastly generalized and underlies all of modern welfare economics.
A: I think in several cases "best self interest" can lead to overall poorer solutions than solutions with interaction. 
More formally, the self-interest maximizing version falls into the domain of traditional "Non-cooperative game theory" while the one with interactions falls  into "Cooperative game theory".
