This paper deals with an adaptive credit assignment algorithm to select strategies having higher capabilities in the learning classifier system (LCS) based upon the genetic algorithm (GA). We emulate a kind of prizes and incentives employed in the economies with imperfect information. The compensation scheme provides an automatic adjustment in response to the changes in the environment, and a comfortable guideline to incorporate the constraints. The learning process in the LCS based on the GA is realized by combining a pair of most capable strategies (called classifiers) represented as the production rules to replace another less capable strategy in the similar manner to the genetic operation on chromosomes in organisms. In the conventional scheme of the learning classifier system, the capability s(k, t) (called strength) of a strategy k at time t is measured by only the suitableness to sense and recognize the environment. But, we also define and utilize the prizes and incentives obtained by employing the strategy, so as to increase s(k, t) if the classifier provide good rules, and some amount is subtracted if the classifier k violate the constraints. The new algorithm is applied to the portfolio management. As the simulation result shows, the net return of the portfolio management system surpasses the average return obtained in the American securities market. The result of the illustrative example is compared to the same system composed of the neural networks, and related problems are discussed.