An important way to learn new actions and behaviors is by observing others, and several evolutionary games have been developed to investigate what learning strategies work best and how they might have evolved. In this paper we present an extensive set of mathematical and simulation results for Cultaptation, which is one of the best-known such games.

We derive a formula for measuring a strategy's expected reproductive success, provide algorithms to compute near-best-response strategies and near-Nash equilibria, and provide techniques for efficient implementation of those algorithms. Our experimental studies provide strong evidence for the following hypotheses:

1. The best strategies for Cultaptation and similar games are likely to be conditional ones in which the choice of action at each round is conditioned on the agent's accumulated experience. Such strategies (or close approximations of them) can be computed by doing a lookahead search that predicts how each possible choice of action at the current round is likely to affect future performance.

2. Such strategies are likely to exploit most of the time, but will have ways of quickly detecting structural shocks, so that they can switch quickly to innovation in order to learn how to respond to such shocks. This conflicts with the conventional wisdom that successful social-learning strategies are characterized by a high frequency of innovation; and agrees with recent experiments by others on human subjects that also challenge the conventional wisdom.