Dynamic price competition with capacity constraints and strategic buyers

We analyze a dynamic durable good oligopoly model where sellers are capacity constrained over the length of the game. Buyers act strategically in the market, knowing that their purchases may affect future prices. The model is examined when there is one and multiple buyers. Sellers choose their capacities at the start of the game. We find that there are only mixed strategy equilibria. Buyers may split orders, preferring to buy a unit from both high and low price sellers to buying all units from the low price seller. Sellers enjoy 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 or hire agents with instructions to always buy from the lowest priced seller. Further, sellers’ market shares tend to be asymmetric with high probability, even though they are ex ante identical.