The books reviewed by Phillips are Morals By Agreement by David Gauthier and Persons, Rights, and the Moral Community by Loren Lomasky. I have no extra knowledge of Mr. Gauthier. I have heard Stephan Kinsella mention Lomasky in various educational venues as a reference for an interesting theory of the rights of children.
Phillips recommends the books but I cannot recommend his review, which probably means I should not recommend the books either, but as I have not read the relevant books I should really not make a recommendation at all. I do plan to read both books however. I state that reluctantly, though, for I really don't give a damn about game theory models.
The purpose of these books, apparently, attempt to "arrive at a neo-liberal social philosophy from the starting point of quasi-Hobbesian individuals via contractarian methods". To paraphrase, both aim to figure out how rights can logically be derived using social contract methodology. As I reject social contract theory, I doubt I will find their arguments persuasive.
How do I derive rights? We live in a world of scarce resources, in which interpersonal conflict is unavoidable unless a coherent theory of rights can be deduced. The most coherent theory of rights is the praxeological method of Hoppe, otherwise known as argumentation ethics. Argumentation ethics demonstrates that all non-libertarian theories of rights are incoherent and, therefore, unjustified. What is the libertarian theory of rights? Ultimate decision-making authority over scarce resources, otherwise known as ownership, is assigned to the person (or persons) with the best claim to a specific scarce resource. For example, persons have the best claim to their own bodies and any other scarce resources that they have acquired via homesteading or contractual title-transfer. Owners have negative rights, meaning that non-owners must not interfere with the ability of owners to control their assigned scarce resources. Positive rights occur when owners voluntarily choose obligations towards other persons and/or other scarce resources. There's a theory of rights in one paragraph.