Nash's bargaining formula revisited: A note on self-referential logic

The note focuses on the marginal rates of substitution (MRS) in Nash's product formula solution to bargaining and why the formula works. Two simple examples from duopoly and bilateral monopoly are used to demonstrate that the MRS's for both players are implicitly in the contract curve and the product formula. They are equal in the former by design. They become equal in the latter in equilibrium. The self-referential logic is evident. The bargaining model or system is self-contained and circular and is analogous to the proposition given by x = F(x).