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

What the paper says

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.