To better understand the evolutionary dynamics of cooperative strategies and their behavioral components in populations subjected to individual selection, a new classifier-system model (EvA) was developed. In EvA, strategies are encoded as algorithms composed of a fixed number of rules relating behavior remembered from the recent past to the present action to be taken. Each algorithm is the genotype of an individual within the population, and these individuals play the Iterated Prisoner's Dilemma game against each other to determine their relative contributions to the next generation. The rules are hierarchical, with more specific rules, when they apply, overriding more general rules. Maximal mutual cooperation was obtained when interaction sequences for each pair of individuals playing the game were long, when only the immediately preceeding plays in the game were remembered, and when the algorithms consisted of an intermediate number of rules (20-40). Under other conditions, mutual cooperation was reduced--even becoming less frequent than would be expected if behavior were completely random, with very few rules per algorithm. The algorithms that evolved could sometimes be recognized as Tit-For-Tat, Simpleton, or other well-known strategies; but when memory of several previous events was invoked by algorithms based on a substantial number of rules, the resulting strategies were considerably more complex. This approach shows considerable promise for providing a much deeper understanding of how cooperation may evolve in nature. Moreover, classifier-system models could prove to be broadly useful for addressing many optimization questions in biology.