If half the people who read the e-mail paid heed, it might cause maybe a nickel's worth of price differential between Exxon/Mobil and everyone else, with E/M going down 3 cents and everyone else up 2. Once the price differential reached a nickel, however, motorists would start going to E/M because they had the cheapest gas, thus causing the E/M price to stabilize or rise with everyone else's.
Even if there were a complete boycott of E/M and their prices dropped 50 cents, this would not in any way induce other companies to lower their prices because the boycott would mean they would not be in competition with E/M. The only way E/M's reduction of prices would have any effect on anyone else's prices would be if customers were leaving other stations for E/M, but if that happened E/M's prices would quickly rise to near their previous levels.