Every essay — page 9
Geometry Analysis Algebra Discrete Topology Probability Number Dynamics Logic Computation Applied What's new Ladders Concepts Search
Applied
A rule for choosing, stated exactly, and what it forces on whoever adopts it.
The value from both sides
Two choosers move at the same instant, and each asks the cautious question — how much can be guaranteed, whatever the other does. With pure choices the two answers are usually different numbers; allow a probability and they are forced to be the same one.
The road that makes everyone later
An equilibrium is a state nobody can improve alone, which is a much weaker thing than a state anybody would choose. Adding a link that costs nothing to use makes every traveller in this network strictly slower, and the arithmetic says by exactly how much.
A lottery over whole assignments
A table of shares in which every person's shares add to one task and every task is exactly covered is never anything more than a mixture of whole assignments — and finding the mixture is a matter of taking one complete assignment out at a time.