Cross-Ownership and Endogenous R&D Risk in Cournot Triopoly

Xing, Mingqing and Zhang, Ally Quan (2026) Cross-Ownership and Endogenous R&D Risk in Cournot Triopoly. The Manchester School. (In Press)

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Abstract

We examine how cross-ownership influences firms’ endogenous R&D risk-taking in a Cournot triopoly, where two "insider'' firms hold passive equity stakes in each other, and a third firm remains unaffiliated. Firms invest in stochastic R&D that lowers marginal costs and choose their risk level---measured by outcome variance---prior to quantity competition. Cross-ownership affects insiders through financial alignment and R&D spillovers, both intensifying with stronger equity links. Solving the two-stage game, we find that cross-ownership yields asymmetric, nonlinear impacts on innovation strategy. When spillover sensitivity is low, insiders undertake higher-risk R&D than the outsider; when sensitivity is high, this ranking may reverse. Increased cross-ownership always dampens the outsider’s R&D risk, while insiders’ risk rises with cross-holdings when spillovers are weak, but follows a U-shaped pattern when spillovers are strong. Enabling R&D collaboration does not affect the outsider, but can reduce insiders’ risk-taking when spillovers are substantial. However, when spillovers are exogenous and independent of equity ties, insiders’ risk increases monotonically with cross-ownership. These results identify information-sharing sensitivity as the key moderator of ownership networks’ innovation risk-taking, offering implications for competition and innovation policy.