Directors’ dilemma: conflicted directors of the board

In this case study, you are a non-executive chairman of a publicly owned commercial company operating in a sector of national importance. The publicly owned commercial company is a monopoly supplier to this sector.
Board appointments are made by the government. The managing directors of two of the largest operators in the sector/customers of the monopoly supplier are well-known supporters of the political party in government. They have recently been appointed as non-executive directors to the board of the monopoly supplier.
You have received angry complaints from the remaining five large operators in the sector, who are concerned at the competitive advantage accruing to the two recently appointed directors on the ‘inside track’ with the monopoly supplier. The question of pricing of product to the sector/customers is an agenda item at the forthcoming board meeting.
How should conflicts of interest on the board be handled?