Presently, Independent System Operators (ISOs) in deregulated electricity markets in the U.S. use an auction method that minimizes the total bid cost when determining units to be on and their generation levels (Bid Cost Minimization or BCM). It has recently been shown that this method of auction does not provide minimal consumer payment costs for a given set of bids under the Market Clearing Price (MCP)-based or congestion-dependent Locational Marginal Price (LMP) scheme. Instead, an alternative auction method that directly minimizes the total consumer payment (Payment Cost Minimization or PCM) provides the payment-minimizing auction selection. Though the use of PCM minimizes consumer payments for a given set of bids for a day, it has not been fully illustrated that PCM minimizes payments over a longer time period with intelligent bidders that can adjust to the new auction mechanism. To address this important economic issue, a novel discrete game theoretic method of bidder behavior is used to model the competitive nature of generating companies in the day-ahead market. Numerical testing results show that PCM significantly reduces consumer payments with intelligent bidders. Simulation using a market simulator is also presented with similar results. Finally, insight into the potential benefits of PCM is briefly presented.