This paper addresses the bidding strategies of generating firms in a competitive market where the firms are provided with payment for generating reactive power. Reactive support for voltage control is an integral and critical part of power system operations. Since reactive support is unbundled in a competitive market under open access transmission, it is treated as one of ancillary services. The operation costs and opportunity costs for reactive support are compensated by payment to the firms, hence their bidding strategies will be affected. The opportunity costs are evaluated from the foregone profits of a generator in making sales in real power market by providing reactive support instead of real power. Game theory approach is used to analysis the transaction strategies of real power by the bimatrix method in this paper. Through computing the Nash equilibrium in a sample system, an incentive of a generator for improving the reactive generating capacity is found to be effective and the variations of the profits are analyzed as the demand power factor changes.