Collusion and Price Wars with Individual Demand

We analyze whether noncooperative collusive equilibria are harder to sustain when individual demand levels are not fixed but are able to fluctuate. To do this, we extend a Bertrand-type model of price competition to allow for fluctuating market shares when prices are equal. We find that, the larger the market share fluctuations may be, the higher the discount factor should be to sustain a collusive equilibrium in trigger strategies. The intuition behind this is fairly straightforward. When individual demand in the collusive state is suddenly low, the gains from collusion go down. Moreover, the firm with the low demand can capture a larger share of the market by deviating from the collusive strategy. The incentive to deviate therefore becomes larger when the individual market share decreases. We also look at the existence of a specific type of semi-collusive equilibrium when individual market shares are either common knowledge or private knowledge. We find that there exist equilibria in which competitive periods (price wars) occur with probability 1 and on the equilibrium path.