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The welfare of electricity producers and consumers depends on congestion in the transmission grid, generation costs that consist mainly of fuel costs, and strategic behavior. We formulate a game theoretic model of an oligopolistic electricity market where generation costs are derived from a fuel supply network. The game consists of a fuel dispatcher that transports fuels at minimum cost to meet generator demands, generators that maximize profit in Cournot competition, and an independent system operator (ISO) that sets nodal prices to balance electricity supply with linear demand functions. We prove the existence of an equilibrium. If fuel supplies are unlimited, the same equilibria hold in a simplified version of the game in which each generator optimizes its fuel acquisition from the network. In some very simple examples under different assumptions about the rationality of generators with respect to ISO decisions, paradoxical effects on total welfare can occur from expanding either electricity transmission capacity or the transportation capacity of low-cost fuel. We find some instances in which the paradox occurs only under bounded rationality of the generators, others where it occurs only if the generators are fully rational, and still others where it occurs to different degrees under the two rationality assumptions.