  Consider sellers in a competitive market that use algorithms to adapt their
prices from data that they collect. In such a context it is plausible that
algorithms could arrive at prices that are higher than the competitive prices
and this may benefit sellers at the expense of consumers (i.e., the buyers in
the market). This paper gives a definition of plausible algorithmic
non-collusion for pricing algorithms. The definition allows a regulator to
empirically audit algorithms by applying a statistical test to the data that
they collect. Algorithms that are good, i.e., approximately optimize prices to
market conditions, can be augmented to contain the data sufficient to pass the
audit. Algorithms that have colluded on, e.g., supra-competitive prices cannot
pass the audit. The definition allows sellers to possess useful side
information that may be correlated with supply and demand and could affect the
prices used by good algorithms. The paper provides an analysis of the
statistical complexity of such an audit, i.e., how much data is sufficient for
the test of non-collusion to be accurate.
