Mixed competition and horizontal shareholding in competing supply chains

We consider two-tier competing supply chains wherein downstream firms are engaged in mixed (Cournot-Bertrand or Bertrand-Cournot) competition and one downstream firm horizontally holds the rival firm's profit. Our results show that the type of mixed competition plays a crucial role in determining pricing and quantity decisions. The acquiring supply chain member's profit may be lower than the rival chain in Cournot-Bertrand retail competition. However, in Bertrand-Cournot retail competition, the upstream firm's profit of acquired supply chain is always higher, but the downstream firm's profit may be lower than the acquiring supply chain.