Could it be that governments have always existed? The Hebrew bible comes close to providing an answer with the story of Saul. According to this story,members of the twelve tribes of Israel, each living under "his grape tree and fig tree" [read: state of nature] came to Samuel asking him to "make us a king" [read: constitute a government] so they would be as secure as "other nations." The old Hebrew prophet agreed to met his people's demand but not before he explained to them the nature of the trade-off associated with their request. With the benefit of the security they wished to obtain, so he argued, there would be a real cost to be paid in terms of their personal freedom.
Gideon Doron and Itai Sened (2001), Political Bargaining, p. 56
The next page gives the utility function for every agent i∈N from any σ∈σ to respect the law:
ui(σ) = ∑j≠ibiσi–ciσi