In this paper, we study the dynamics of competition in the payment card market. This is done through a multi-agent based model, which captures explicitly the commercial transactions at the point of sale between consumers and mer-chants. Through simulation, we attempt to model the demand for payment instruments on both sides of the market. Constrained by this complex demand, a Generalised Population Based Incremental Learning (GPBIL) algorithm is applied to find a profit-maximizing strategy, which in addition has to achieve an average number of card transactions. In the present study we compare the performance of a profit-maximizing strategies obtained by the GPBIL algorithm versus the performance of randomly selected strategies. We found that under the search criteria used, GPBIL was capable of improving the price structure and price level over randomly selected strategies.
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