This paper proposes an offering strategy for a wind power producer (WPP) that participates in both day-ahead (DA) and balancing oligopoly markets as a price maker. Penetration of demand response (DR) resources into smart grids is modeled by intraday demand response exchange (IDRX) architecture. A bilevel optimization framework is proposed based on multiagent system and incomplete information game theory. Modeling the WPPs in high penetration of wind power as price makers can reflect the capability of this market player to directly affect the market prices. Simulation results indicate that the price-taker model of WPP is not accurate for WPPs that have significant market shares. By comparing the results obtained from modeling the WPPs as price makers with the ones as price takers, it can be concluded that WPPs have the market power not only to increase the prices of both DA and balancing markets, but also to reduce the amount of DR through IDRX market mechanism.