Evolutionary Learning of the Optimal Pricing Strategy in an Artificial Payment Card Market

Abstract

Summary. This paper introduces an artificial payment card market in which we model the interactions between consumers, merchants and competing card issuers with the aim of determining the optimal pricing structure for card issuers. We allow card issuers to charge consumers and merchants fixed fees, provide net benefits from card usage and engage in marketing activities. The demand by consumers and merchants is only affected by the size of the fixed fees and the optimal pricing structure consists of a sizeable fixed fee to consumers, no fixed fee to merchants, negative net benefits to consumers and merchants as well as a high marketing effort.

Market structure and information in payment card markets

“…Furthermore, the way competition enables merchants to attract consumers is usually not adequately considered. Addressing this issue, Alexandrova-Kabadjova et al [29] developed a multi-agentbased model to study competition among several competitors, which was further extended in [30,31], where the pricing strategy of the competitors is obtained by an evolutionary computation algorithm; see [32]. This line of research is being taken further in the present paper.…”

Natural Computing in Finance – A Review

“…The agents make their investment decisions by attempting to forecast the future return on the stock, using GA to generate, test, and evolve predictive rules. Other applications of ABM include the simulation of a foreign exchange market [55], the modelling of an artificial stock option market [40] and the modelling of an artificial payment card market [3]. A key output from the ABM literature on financial markets is that it illustrates that complex market behaviour can arise from the interaction of quite simple agents.…”

Profit-Maximizing Strategies for an Artificial Payment Card Market. Is Learning Possible?

“…Using the parameter setting described above, in the simulation eight of the nine competitors use the same profit-maximizing strategy, whereas one competitor applies a randomly generated strategy. We test five of the ten GPBIL-strategies presented in [17]. Each of the five exercises consists in comparing the evolved strategy against ten random strategies in independent executions of the model.…”

“…Given the complex domain of this vector, there exist multiple possibilities of sampling it. For instances, the authors applied a Generalised Population Based Incremental Learning (GPBIL) [17] algorithm in order to obtain profit-maximizing strategies, which in addition have to achieve an average number of card transactions.…”

“…Under this line of research, here we present a study that tests how efficient the GPBIL-strategies reported in [17] are. At this point the Box's statement: "all models are wrong, but some are useful" (p.424 in [20]) could not be more appropriate.…”