A new approach to designing bilateral power transaction bargaining models between two independent utilities in a deregulated electricity market is proposed. In the paper it is assumed that each utility (a seller or a buyer) knows its own operating costs but does not know those of its opponent. The bilateral power transaction problem is then considered as nonco-operative bargaining under incomplete information. Each participant develops its own bargaining strategy based on estimates of the opponent's operating costs and bargaining strategy. Two bargaining models are developed and examples are employed for demonstration.