Competitive Advantage for Multiple-Memory Strategies in an Artificial Market

We consider a simple binary market model containing $N$ competitive agents. The novel feature of our model is that it incorporates the tendency shown by traders to look for patterns in past price movements over multiple time scales, i.e. {\em multiple memory-lengths}. In the regime where these memory-lengths are all small, the average winnings per agent exceed those obtained for either (1) a pure population where all agents have equal memory-length, or (2) a mixed population comprising sub-populations of equal-memory agents with each sub-population having a different memory-length. Agents who consistently play strategies of a given memory-length, are found to win more on average -- switching between strategies with different memory lengths incurs an effective penalty, while switching between strategies of equal memory does not. Agents employing short-memory strategies can outperform agents using long-memory strategies, even in the regime where an equal-memory system would have favored the use of long-memory strategies. Using the many-body `Crowd-Anticrowd' theory, we obtain analytic expressions which are in good agreement with the observed numerical results. In the context of financial markets, our results suggest that multiple-memory agents have a better chance of identifying price patterns of unknown length and hence will typically have higher winnings.