Non-discriminating renegotiation in a competitive insurance market

A variant of the Rothschild-Stiglitz model of a competitive insurance market is considered, where each uninformed firm is allowed to renegotiate the contracts that its customers initially sign, subject to the restriction that renegotiated contracts be offered to all the firm's customers. Such non-discriminating renegotiation is shown to weaken the profitability of cream skimming to the extent that there exists a unique equilibrium outcome. This outcome is that of Miyazaki and Spence i.e., the incentive-compatible pair of zero-profit contracts, if efficient; and the incentive-compatible, zero-profit pair of contracts maximizing low-risk utility, otherwise.