  The multi-armed bandit problem (MBP) is the problem of finding, as accurately
and quickly as possible, the most profitable option from a set of options that
gives stochastic rewards by referring to past experiences. Inspired by
fluctuated movements of a rigid body in a tug-of-war game, we formulated a
unique search algorithm that we call the `tug-of-war (TOW) dynamics' for
solving the MBP efficiently. The cognitive medium access, which refers to
multi-user channel allocations in cognitive radio, can be interpreted as the
competitive multi-armed bandit problem (CMBP); the problem is to determine the
optimal strategy for allocating channels to users which yields maximum total
rewards gained by all users. Here we show that it is possible to construct a
physical device for solving the CMBP, which we call the `TOW Bombe', by
exploiting the TOW dynamics existed in coupled incompressible-fluid cylinders.
This analog computing device achieves the `socially-maximum' resource
allocation that maximizes the total rewards in cognitive medium access without
paying a huge computational cost that grows exponentially as a function of the
problem size.
