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.
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