Abstract: Competing companies can achieve market segmentation and price discrimination through probabilistic selling strategy, thereby reducing competition and increasing sales profits. Cross holding is also popular among many companies of the same industry. Competitors can strengthen cooperation, soften competition and eliminate mistrust through cross holding. Therefore, this paper studies the probabilistic selling strategy between two oligopolistic firms that hold each other’s shares, aiming to find out the motivations behind their probabilistic selling strategy. This paper uses the Hotelling model to depict the characteristics of competing enterprises in the market and constructs a Nash static game model to study the probabilistic selling strategy of cross-holding companies in the products’ horizontally differentiated market. The results show that in the case of asymmetric cross holding, when the marginal cost is small, probabilistic selling strategy always benefits large-holding companies, but small-holding companies whose shares held by others exceed a threshold can also benefit from the probabilistic selling strategy.

Key words: probabilistic selling, cross holding, Hotelling model, competition