This paper proposes a game-theoretic framework for quantifying effects of strategic bidding behavior of load aggregators (LAs) on wholesale electricity market equilibrium. The independent system operator (ISO) employs double-sided auction design to settle transactions in the wholesale electricity market. Generating companies (GENCOs) and LAs submit their bids to the ISO in the economic model of supply function equilibrium. Under the smart grid paradigm, a LA participates in the electricity market on behalf of end-consumers to minimize their total payment for purchasing electricity. In this paper, bi-level programming (BLP) method is employed to determine optimal bidding strategy of self-interested market participants. In the upper level, the profit of intended market participant is maximized and in the lower level, the ISO clears the market via a bid-based security constrained economic dispatch (SCED). Also, competition of GENCOs and LAs is modeled as a non-cooperative game. To examine the effects of strategic bidding behavior of LAs on market equilibrium, the proposed model is applied to the IEEE 9-bus and the IEEE 30-bus test systems. According to numerical results, to allow the LAs to behave strategically along with the GENCOs makes the former better off and the latter worse off, while the net effect of this on total social welfare turns out to be case-contingent.