This paper looks at the influence of Financial Transmission Rights (FTRs) on the market value(Social Welfare; SW) in the competitive electricity market. The transmission line constraints make it difficult to compute the Nash Equilibrium (NE) due to causing a mixed strategy NE instead of a pure strategy NE. Computing a mixed strategy is more complicated in a multi-player game. The aim of this paper are to compute a mixed strategy NE and analyze SW in power transaction with FTRs. This paper introduces a formula and a technique for solving NE of multi-player game with FTRs. In addition, it analyzes the influence of holding of FTRs by generation company on SW and it proposes the SW at NE is influenced by Power Transfer Distribution Factor (PTDF) where holder of FTRs are located. The assertion is verified by calculating the mixed strategy utilizing the Cournot model widely used for studies on FTRs.