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In the last decade, economic approaches based on computational markets have been proposed as a paradigm for the design and control of complex sociotechnical systems, such as urban road traffic systems. The control problem of an urban road traffic system can be modeled as a distributed resource-allocation problem to apply market-based techniques as solution methods. In this paper, we design a competitive computational market, where driver agents trade the use of the capacity inside the intersections with intersection manager agents. We show how the market dynamics influence the drivers' behavior, leading to a more efficient use of the urban road traffic system, in terms of lower average travel times and less congestion.