As a long term bidding behavior, bid shading is exhibited by wind farms participating in real Uniform Price (UP) markets. This signifies that the wind farm owners bid far below their true long run marginal cost. In this paper a method is proposed to consider the uncertainty of bidding admission in the long term expected revenue of wind farms. We show that this consideration could perfectly explain the observed bid shading behavior of wind farm owners. We use a novel market price model with a stochastic model of a wind farm to derive indices describing the uncertainty of bidding admission. The optimal behavior of the wind farm is then obtained by establishing a multi objective optimization problem and subsequently solved using genetic algorithm. The method is applied to the analysis of long term bidding behavior of a wind farm participating in a Pay-as-Bid (PAB) auction such as Iran electricity market. The results demonstrate that wind farm owners change their bid shading behavior in a PAB Auction. However, the expected revenue of the wind farm will also decrease in a PAB auction. As a result, it is not recommended to make an obligation for the wind farms to participate in a PAB auction as a normal market player.