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Power supplier's behaviors have great effects on their strategic bidding. With exponential utility function, the optimal bid, reckoning the risk type of power supplier and the possible loss due to bidding failure, is obtained. The bidding strategies of the power suppliers vary with their risk types. Under uniform clear pricing method, no matter what risk type the power supplier takes, the optimal bid always appears as its cost minus the possible loss due to bidding failure plus a markup, which depends on the risk type taken by the suppliers. With the same cost, the optimal bid of a risk-taker is proved to be higher than that of a risk-avoider. The ultimate reason that power supplier bids under its cost is to avoid loss of bidding failure and risk types.