Research Digest Solving a paradox about firms' price setting 

In Price competition with capacity uncertainty – feasting on leftovers, published in Games and Economic Behavior, Wouter Vergote and his co-authors studied the impact of private information about capacities on firms' pricing strategies.

Why study this

Pricing strategies are important in firms' search for profit, and are an important variable in market equilibrium. In the established literature on price competition, the theoretical prediction is that larger firms tend to set higher prices than smaller firms, in a context of capacity constraints (i.e. there is a limit to firms' output). Yet empirical studies document the opposite behaviour. To solve this puzzle, the researchers examined the effect of private information about firms' production capacities.


  • The researchers analysed a duopoly model of price competition with homogenous goods (meaning consumers will buy from the cheaper seller) in which the capacity of each firm is private information.
  • They showed that a unique symmetric, monotone equilibrium exists when the type distribution of capacities and the demand function are both concave. 
  • Monotonically increasing price equilibria do not exist because charging the highest (equilibrium) price yields the same leftover demand regardless of the type of the “losing” firm but charging any lower price allows a firm with a higher capacity to expand more than a lower capacity firm is able to. 
  • Therefore, in equilibrium the highest price has to be charged by the firm with the lowest capacity. 
  • Without regularity assumptions on the demand and capacity distribution function, the monotonicity result does not always hold.

We show that private information about firms’ available capacity levels is a possible explanation for this puzzle.

Key insight

Firms have a better understanding of their actual production capacity compared to their rivals, despite the classical Bertrand-Edgeworth competition model's typical assumption to the contrary (i.e. that capacity levels of firms are observable to all market participants). This private information about capacities matters for pricing strategies.


The researchers provide a novel model of price setting with capacity constraints under incomplete information. This information assumption on capacities is relevant in many industries including airlines, hospitals, electricity markets and procurement.

Final takeaway

Intensive price competition (an auction-type interaction) is most likely to occur when the realized capacities are intermediate, while firms with low- or high-capacity levels compete less vigorously on the margin.


Robert Somogyi Robert Somogyi Assistant Professor at the Department of Finance of the Budapest University of Technology and Economics (Hungary)
Wouter Vergote - ESCP Business School Wouter Vergote Associate Professor of Economics at ESCP Business School (Madrid campus)
Gabor Virag Gabor Virag Associate Professor of Economic Policy & Analysis at the University of Toronto Mississauga and the Rotman School of Management (Canada)