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The notion of charisma is found in many RPGs. Charisma is charm, attractiveness, authoritativeness. Well pumped charisma is needed for maximum success in interactions with NPCs. In Eve Online the concept of charisma is most closely associated with social and commercial skills — the groups of skills Social and Trade. The first group is very important for the players, often interacting with agents, because they allow to quickly enhance the «attitude» (or standing) of the agents towards themselves. This gives many advantages, such as reduced interest rates for ore processing. For mission-running the skills Communication, Negotiation, Rapid speech are helful. And since runnning missions for agents is the main income for many players, they should pay attention to these skills.
Trade skills speak for themselves. In addition to trade with the players there is trade with the NPC, and for this the level of charisma is very important. Trade with real players requires more real-world skills for doing business, and the character attributes are not to help here :)
Players who find combat missions to be the most important thing, often ignore the attribute Charisma, focusing on Willpower and Perception. In the first months of playing this is even correct, but if you want to be not just a pilot, but a commander with time, then sooner or later you'll have to train the skills from the  Leadership group, in which Charisma serves as the primary attribute. These are such skills as Leadership, which allows you to manage the squadron, Wing Command, which allows to command a wing of a fleet, Fleet Command, allowing to command a whole fleet, and others, 13 units in total. With each level of the above mentioned skills, you can create a larger grouping of fleets.
Thus the largest and most powerful fleets in the game are conducted by those who have highly-trained Charisma.