Competition in cascades
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Hydroelectric generation is the main source of energy production in many countries. When firms operate in the same river, or in cascades, the output of an upstream firm is the input of its downstream rival. We build a dynamic stochastic duopoly model of competition in cascades and show that the decentralized market is efficient at the critical times when rain is infrequent, but inefficient when rain is more frequent. Market power is an issue when peak prices are sufficiently higher than off-peak prices: Upstream firms delay production in off-peak times, limiting their rival downstream generators' production in peak times.