Lets leave aside philosophy for a moment and go to the behaviour of animals and humans. Science have shown that animals and humans both engage in war and collaborate. Peter Kropotkin in his book "Mutual Aid: A factor of Evolution" http://www.theanarchistlibrary.org/HTML/Petr_Kropotkin__Mutual_Aid__A_Factor_of_Evolution.html
showed that the not so visible side of success in species survival is collaboration inside the species against others or in mere self-survival.
Egoism can be said to be the direct logical linguistic opposite of altruism yet like every binary operation it is not that simple. Max Stirner himself said: "Who, then, is “self-sacrificing?”[Literally, “sacrificing”; the German word has not the prefix “self.”] In the full sense, surely, he who ventures everything else for one thing, one object, one will, one passion. Is not the lover self-sacrificing who forsakes father and mother, endures all dangers and privations, to reach his goal? Or the ambitious man, who offers up all his desires, wishes, and satisfactions to the single passion, or the avaricious man who denies himself everything to gather treasures, or the pleasure-seeker, etc.? He is ruled by a passion to which he brings the rest as sacrifices.
And are these self-sacrificing people perchance not selfish, not egoist? As they have only one ruling passion, so they provide for only one satisfaction, but for this the more strenuously, they are wholly absorbed in it. Their entire activity is egoistic, but it is a one-sided, unopened, narrow egoism; it is possessedness."
So one can be egoistic and also be altruistic at the same time if this things outside me is of my love or desire. It is clear "egoism" and "self interest" is involved here but of course it is also altruistic. And so for example gift economies (http://en.wikipedia.org/wiki/Gift_economy
) could be superficially identified and mostly altruistic relationships but this is not exactly the case. Anarchist antropologist David Graeber when speaking about french antropologist Marcel Mauss says:
"Instead, what anthropologists were discovering were societies where economic life was based on utterly different principles, and most objects moved back and forth as gifts and almost everything we would call “economic” behavior was based on a pretense of pure generosity and a refusal to calculate exactly who had given what to whom. Such “gift economies” could on occasion become highly competitive, but when they did it was in exactly the opposite way from our own: Instead of vying to see who could accumulate the most, the winners were the ones who managed to give the most away. In some notorious cases, such as the Kwakiutl of British Columbia, this could lead to dramatic contests of liberality, where ambitious chiefs would try to outdo one another by distributing thousands of silver bracelets, Hudson Bay blankets or Singer sewing machines, and even by destroying wealth sinking famous heirlooms in the ocean, or setting huge piles of wealth on fire and daring their rivals to do the same...In gift economies, Mauss argued, exchanges do not have the impersonal qualities of the capitalist marketplace: In fact, even when objects of great value change hands, what really matters is the relations between the people; exchange is about creating friendships, or working out rivalries, or obligations, and only incidentally about moving around valuable goods. As a result everything becomes personally charged, even property: In gift economies, the most famous objects of wealth heirloom necklaces, weapons, feather cloaks always seem to develop personalities of their own."
David Graeber. "Give It Away" http://www.theanarchistlibrary.org/HTML/David_Graeber__Give_It_Away.html
So gift economies include motivations that don´t appear out of something similar to "christian love" but of other "egoistic" tendencies such as the desire of prestige and recognition as well as keeping good relations with those who can help me in the future.
Hakim Bey thus establishes this bridge in this way:
"The essence of the party: face-to-face, a group of humans synergize their efforts to realize mutual desires, whether for good food and cheer, dance, conversation, the arts of life; perhaps even for erotic pleasure, or to create a communal artwork, or to attain the very transport of bliss — in short, a “union of egoists” (as Stirner put it) in its simplest form — or else, in Kropotkin's terms, a basic biological drive to “mutual aid.” (Here we should also mention Bataille's “economy of excess” and his theory of potlatch culture.) "
So a union of egoists is a form of mutual aid. Mutual Aid is not the same as "christian love". Mutual aid is something done in the self-interest of both sides.