Bertrand Competition when Rivals' Costs are Unknown, Journal of Industrial Economics
The conclusions of the Bertrand model of competition are substantially altered by the presence of asymmetric information about rivals' costs. Asymmetric information eliminates the discontinuity in the Bertrand model and significantly alters the properties of the market equilibrium. In the Bertrand-Nash equilibrium when rivals' costs are unknown, firms price above marginal cost and have positive expected profit. The analysis is extended to franchise competition. The market equilibrium is sensitive to market structure and yields incentives for entry.
Spulber, Daniel. 1995. Bertrand Competition when Rivals' Costs are Unknown. Journal of Industrial Economics. 43(1): 1-11.