Due to economic turmoil, Southeast Asia saw a significant drop in tourism in the late 90s. Consequently, the demand for hotel rooms plummeted, and in Malaysia this caused a brutal price war between luxury hotels, consistently undercutting each other's prices and deteriorating margins. All luxury hotels but The Ritz.
The Ritz knew that their customer segment (wealthy tourists) was not very price sensitive, and thus, lowering the price was not very effective - especially not when you consider the harm it inflicted on the business. Therefore, James McBride (manager at the time) decided to win customers by offering additional value. Overnight, he introduced a new 24/7 "technology-repair room service" where customers could get their laptops and cellphones repaired around the clock; he arranged that guests were greeted with mimosas and music upon arrival; and that guests staying for more than 5 nights would receive a complimentary embroidered pillowcase.
The result: The Ritz won the war. Not only did James McBride's new initiatives add to the value that the customer got when booking a room at The Ritz; the other luxury hotels were actively depreciating their own value by offering lower prices (a cheap hotel is not really perceived as exclusive and luxurious). And so, the takeaway from this example is that sometimes, there may be external circumstances that suddenly decreases demand, and thus increases competition. And inevitably, this will force competing firms to offer value at a lower price: but if you operate in a market with low price sensitivity, you will be much better off increasing the value and keeping prices constant, rather than keeping value constant and lowering your prices.