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Electricity markets based on power pools, in which the owners of generating units submit their marginal-price schedules, implicitly leave the problem of unit commitment and its associated constraints and costs aside. The paper addresses the unit-commitment problem faced by participants if they are to self-commit their units in a market structure. This strategic problem is formulated through a probabilistic-dynamic-programming model, where the probability of a particular generator being online during a specific market period is set by its owner. The solutions adopted for that problem are Nash equilibria in mixed strategies. The paper presents an example with a small group of generating units, where a comparison is made between the results for the integrated utility and for the market structure. This example is solved making use of a direct Monte Carlo method.