Rotemberg and Saloner (1986) show price war during booms, in the sense that firms charge the monopoly price in the low state of demand whereas they charge below the monopoly price in the high state of demand if the discount factor falls in some region. However, we should notice that this price war does not necessarily imply countercyclical move of prices.

This is not a price war in the usual sense, because the price may actually be higher during booms than during busts; thus, that oligopoly prices move countercyclically is not an implication (but is consistent with) of the Rotemberg-Saloner model.
(Tirole, p.250)

Contrary to the Rotemberg-Saloner model, Green and Porter (1984) show that price wars are triggered by a recession. The latter develops the model that formalizes the issue of secret price cutting, in the setting of "imperfect public monitoring" called nowadays. In their model, price wars during recessions are involuntary, which give the incentive not to deviate when demand is not very low. (Remember, there is no private information and price wars are voluntary in Rotemberg-Saloner model.)

Tirole also mentions the following important point.

When price choices are perfectly observable, it makes sense to resort to extreme punishments because such punishments are never observed on the equilibrium path and therefore are costless to the firms (they are just threats). Under uncertainty, mistakes are unavoidable and maximal punishments (eternal reversion to Bertrand behavior) need not be optimal.
(Tirole, p.252)

References

Green and Porter (1984) "Non-cooperative Collusion Under Imperfect Price Information" Econometrica, 52
Rotemberg and Saloner (1986) "AQ Supergame-Theoretic Model of Business Cycle and Price Wars during Booms" AER, 76