Philosophers have explored morality and justice over the centuries and arrived (broadly) at similar views. All philosophers seem to agree that we have a relatively weak moral sense, a "sentiment" (in David Hume's or Adam Smith's terminology) that dissipates rapidly beyond ourselves and family.
And yet, no civilised society can function if there is arbitrariness in the protection of each other's property rights. We necessarily need to be EQUALLY moral (just) towards others.
As Christ pointed out, "do unto others as you would have others do unto you" (Golden Rule), a sentiment that finds place in almost all religions. (This is the first formulation of the "ideal" Nash eqiulibrium in society, and indeed is very close to the "tit-for-tat" strategy that has been found experimentally to be optimal). The categorical imperative of Kant says pretty much the same thing.
The debate on matters of morality and justice is primarily two fold:
a) Rate of dissipation of the moral sentiment. David Hume objected to Hobbes's abrupt view about human nature (namely, "short, brutish" lives in the state of nature). "Nice" people like Locke, Hume, even Karl Marx don't admit to a rapid decline in this sentiment. They prefer to pretend that humans are nice to each other by nature. I'm not so sanguine and agree with Hobbes's assessment of the rapid dissipation rate of the moral sentiment. I've seen enough prejudice, hatred and ignorance in my life to somehow believe that people are "naturally" nice to each other. This is an empirical question, in the end, however, and philosophers should stay out of this.
b) What explains the puzzle that despite the dissipation of moral sentiment, societies do manage to get along? This is the second issue, namely, an explanation of why the society works, despite the (relatively rapid) dissipation of human goodwill towards others. In response to this, religions have sought to moralise (Golden Rule). Economists, on the other hand (starting with Adam Smith, but preceded in conception by Hobbes and Locke) have explained this as a strategic game-theoretic equilibrium ("enlightened self-interest").
David Hume explained this in his own way (see video below). Hume essentially pointed out that the strategic equilibrium ("enlightened self-interest") is not very stable, and so we need a justice system (an enforcer). That was exactly what Hobbes had said many decades before him, in a more blunt and forthright manner: the Leviathan. The dispute remains only about the nature of the justice system, not about its inevitability as part of the strategic equilibrium.