Hobbe's Leviathin

Hobbes’s Leviathan – Chapter 14
Every person has the right to pursue what is best for themselves. More specifically, everyone has the right to do whatever it takes to preserve their own life. Rational people will voluntarily choose what is in their best interests. If two people lived alone on an island and had no mutual agreement on how to live, then each one would separately do whatever was in his or her best interests. If that meant killing the other person for food then so be it. In such a situation each person would be living in fear of the other person. But being rational like humans are, each of the two people would realize that the best way to preserve their own lives would be to make peace with the other. The two people can agree to follow certain rules that will be in the best interests of each individual.
Every voluntary action a person makes is out of his or her own rational self interest. So if two people made peace then each individual would be voluntarily agreeing to a set of rules because the rules would be of self-interest to both individuals. The people would be in a sense giving up some rights, like the right to kill each other; however, the fact that each person gives up the right to kill the other means that each person is even more likely to survive than if they had not given up this right. Their initial right to do whatever it takes to live is enhanced by the peace that is made. After making peace, each individual no longer has to worry about the other person killing him or her. The peace allows each individual more freedom to exercise his or her own right to live because they won’t have to worry about the threat of the other individual. People are rationally led to make peace with other individuals because it is in a state of peace that a person is most likely to survive.
However, all the individuals must agree to this peace, or it will not work. If one human agreed to have peace and the other decided not to, then the one who agreed to peace would be slaughtered by the other. If it is unknown what the other person will do then neither person will make peace; this is the rational choice. But the best choice would be to agree to peace so that one would have an assurance that they were not going to be killed. So, in order to make peace there must be an agreement between every individual.
This kind of peace is what Hobbes calls a contract. Hobbes feels that these contracts are formed naturally by people acting rationally. Rationality leads people to voluntarily agree to some rules for the benefit of their own survival. If many people formed a contract like this then it would naturally flourish. A person who had entered into this peace would rationally decide not to violate the contract that he had made with his peers. If he did so and stepped out of the boundaries of peace by murdering another person who had joined the contract, then the other members of the group would become angry with the person. The person would then be punished or banned from the peaceful group. Without the group the man would once again be living in a world of every man for himself, and no longer have the security of the contract. A person involved in a peaceful contract would conclude that it is in their best interest not to violate the peace that they had made with their fellow humans, therefore the contract would be lasting.