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The conversion of a one-player power sector (i.e., a natural monopoly) into a multiple-players power market brings not only benefits of competition but also the costs of complexity to the consumers. Between the two, an optimal number of players is found, corresponding to the minimum price of power to the consumers. Considering time as the third dimension, the optimum curve becomes a potential surface on which the evolution of the market entities is seen as oscillations (mergers and unbundling) along the valley of minimum price. Every oscillation triggers a price burst, which is detrimental to the consumers. To avoid this, the role of the regulator is better defined in the sense of smoothing the transition from monopoly to market. The example of the US and of the EU power sectors´ evolution is relevant here. In the above approach, long-range competition resulting from the future opening of power markets in Europe or from the penetration, 70 years ago, of the interconnection technology in the USA, is compared with the short-range (local) competition.