Any A student in the same economics class could scold Peritz for asserting that free markets exist only when bargaining power is equal. If Simpson had, by some measure, less bargaining power than large firms, this condition would be unfortunate for Simpson. However, this inequality by itself would not mean that the market is not free. Free markets exist whenever some minimum respect for private property rights prevails and government does not interfere with the peaceful use and voluntary exchange of these rights. As long as humans exist, each will have ample opportunity for mutually advantageous exchanges with others.
Bargaining power determines only the distribution of the resulting gains from trade.
Nothing in either the theory or the practice of free markets requires that the gains from trade always, or even generally, be divided equally. Although Peritz's book is not one to read for economic enlightenment, its subtitle does accurately promise to convey some history. Specifically, the book is a legal history of competition law and policy in the United States since 1888. But it is a peculiar history. It is a history only of lawyerly words.