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In this paper, we consider an abstract market model for demand response where a supply function bidding is applied to match power supply deficit or surplus. We characterize the resulting equilibria in competitive and oligopolistic markets and propose distributed demand response algorithms to achieve the equilibria. We further show that the equilibrium in competitive market maximizes social welfare, and the equilibrium in oligopolistic market has bounded efficiency loss under certain mild assumptions. We also propose distributed demand response algorithms to achieve the equilibria.