Competition in supply functions has been used to model several markets, in particular the spot market for electricity but also management consulting or airline pricing reservation systems. The models considered typically do not allow for private information. Private information on costs is a relevant situation in many instances where it is not realistic to assume that there is common knowledge on costs.
Instead each firm has an estimate of its own costs and uses it, together with whatever public information is available, to make inferences about the costs of rivals. In this paper we study supply function competition when firms have private information about costs and compare it with Cournot competition, a leading modeling contender. Our aim is to explore the impact of private information on price-cost margins, competitiveness, and welfare.
Competition in supply schedules has been studied in the absence of uncertainty by Grossman (1981) and Hart (1985) showing a great multiplicity of equilibria. A similar result is obtained by Wilson (1979) in a share auction model. Back and Zender (1993) and Kremer and Nyborg (2004) obtain related results for Treasury auctions. Some of the equilibria can be very collusive. Klemperer and Meyer (1989) show how adding uncertainty in the supply function model can reduce the range of equilibria and even pin down a unique equilibrium provided the uncertainty has unbounded support.
In this case the supply function equilibrium always lies between the Cournot and competitive (Bertrand) outcomes. Kyle (1989) introduces private information into a double auction for a risky asset of unknown liquidation value and derives a unique symmetric linear Bayesian equilibrium in demand schedules when traders have constant absolute risk aversion, there is noise trading, and uncertainty is normally distributed.
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Strategic Supply Function Competition with Private Information
