Retractions in real time operation of transmission sector of electricity markets is the concern addressed here. This issue is resolved through the design of a socially stable pay-off vector in a Socially Structured Transferable Utility game based on cooperative game theory. Its algorithm requires an ordering of the players, here Discos, in a given social structure and a method of ranking them in a permutation and is devised to be endogenous to power markets. A transmission price is crafted to be used as the coalition value of the game, in order to identify trades with least impact on the grid. The development of power vectors signifying the strength of the players, ranking based on objective of the game and price design are in tune with the needs of an electricity market and a socially stable solution space. The game is applied to a five bus power system and results are analyzed. This work is important in the context of a still embryonic electricity market requiring a reliable, secure and harmonious transmission sector.