A probabilistic dealing strategy is proposed which allows all premium brands in an established market to earn nonnegative profits without cooperation. Following the strategy, brands take turns attracting deal‐responsive customers. Relative to a reactive competitive strategy, the proposed strategy improves the positions of all premium brands. With use of the strategy, average deal sizes are positively related to a brand's market share, the proportion of quality conscious customers, the proportion of informed customers, the span of regular prices in a market, and the range of customers' acceptable price