Dynamic Price Competition with Capacity Constraints and Strategic Buyers

We analyse a set of simple dynamic models where sellers are capacity constrained over the length of the model. Buyers act strategically in the market, knowing that their purchases may affect future prices. The model is examined when there are single and multiple buyers, with both linear and non-linear pricing. We find that, in general, there are only mixed strategy equilibria and that sellers get a rent above the amount needed to satisfy the market demand that the other seller cannot meet. Buyers would like to commit not to buy in the future. Furthermore, sellers’ market shares tend to be maximally asymmetric with high probability, even though they are ex ante identical.