  We give examples of situations -- stochastic production, military tactics,
corporate merger -- where it is beneficial to concentrate risk rather than to
diversify it, that is, to put all eggs in one basket. Our examples admit a dual
interpretation: as optimal strategies of a single player (the `principal') or,
alternatively, as dominant strategies in a non-cooperative game with multiple
players (the `agents').
  The key mathematical result can be formulated in terms of a convolution
structure on the set of increasing functions on a Boolean lattice (the lattice
of subsets of a finite set). This generalizes the well-known Harris inequality
from statistical physics and discrete mathematics; we give a simple
self-contained proof of this result, and prove a further generalization based
on the game-theoretic approach.
