We propose to study market efficiency from a computational viewpoint.
Borrowing from theoretical computer science, we define a market to be
\emph{efficient with respect to resources S} (e.g., time, memory) if no
strategy using resources S can make a profit. As a first step, we consider
memory-m strategies whose action at time t depends only on the m previous
observations at times t−m,...,t−1. We introduce and study a simple model of
market evolution, where strategies impact the market by their decision to buy
or sell. We show that the effect of optimal strategies using memory m can
lead to "market conditions" that were not present initially, such as (1) market
bubbles and (2) the possibility for a strategy using memory m′>m to make a
bigger profit than was initially possible. We suggest ours as a framework to
rationalize the technological arms race of quantitative trading firms
