Passive cross holding as a strategic entry deterrence

•We study cross holding in a market with an incumbent and a potential entrant.•We show that the incumbent uses cross holding as a strategic device to deter the other firm's entry.•Firms' joint profit is maximized when the incumbent monopolizes the market.•The incumbent distributes part of its monopoly profit to compensate the entrant for staying out.

This paper builds a duopoly model to study the strategic effects of cross holding on entry deterrence. We show that, in equilibrium, the incumbent optimally chooses strictly positive cross holdings in each other to deter entry for the potential entrant.