Diplomacy in Beyond Earth is driven by your actions and Affinity. Each Sponsor has a unique personality and preferences. You can improve relations by offering favorable trade deals, sending gifts of Energy, or agreeing to their requests. Conversely, aggressive actions, such as attacking their units or settling too close to their borders, will worsen relations. Pay attention to their Opinion of you, displayed in the Diplomacy screen. A 'Friendly' opinion opens up opportunities for alliances and joint ventures, while 'Hostile' can lead to war. Consider establishing Trade Routes with friendly Sponsors to gain valuable Energy, Food, or Production. These routes also generate diplomatic points, further improving relations. Remember that your Affinity choice will naturally align you with some Sponsors and put you at odds with others.
