I appreciate the editor, Carlo Reggiani and two anonymous reviewers for their helpful and insightful suggestions which improve this paper significantly.

This paper proposes a game-theoretic model to analyze owners' vertical integration choices if they delegate pricing decisions to their managers. We find that all three vertical structures are possible Nash equilibrium outcomes. If the products are weak substitutes, then the outcome is that both owners adopt vertical integration. When the products are close substitutes, both owners adopt vertical separation in equilibrium. When substitution between the products is medium, the coexistence of vertical integration and vertical separation is the equilibrium outcome, and the owner corresponding to vertical separation offers exactly a profit-maximization contract to his or her manager under this situation.

Progress of hardware technologies and diffusion of computer knowledge enable consumers to crack software if they decide to use software illegally. This paper constructs a software market in which consumers are horizontally differentiated in accordance with social norms of copyright protection to examine the monopolistic producer’s software protection behaviors with considering partial compatibility between genuine and cracked software as well as utility loss from using cracked software. Our research presents the following results. First, when network externalities are weak, the monopolist would set a degree of protection which induces existence of software cracking to enhance consumers’ willingness to pay for genuine software by improving network benefits. Conversely, if network externalities are sufficiently strong, then software producer would set a degree of protection which stop software cracking completely. This implies that stopping software cracking is not possible without network effects. Second, if utility loss from using cracked software is severe (mild), then strengthening (weakening) network externalities or lowering (raising) compatibility may reduce the number of consumers using cracked software and increase software producer’s profits consequently. Finally, we show that the monopolistic producer tends to over-protect software when genuine and cracked software are highly compatible or network externalities are relatively weak which results in inadequate consumers using cracked software for social optimum.

A greater level of keenness on a rival system’s software intuitively motivates system manufacturers to raise their degrees of compatibility in order to capture more profit from selling software to rival system users. After constructing a game-theoretic model to investigate system manufacturers’ partial compatibility decisions, this paper surprisingly finds that when consumers are keener on a rival system’s software, hardware price competition is relaxed and system manufacturers reduce the degrees of compatibility. This paper also presents the following three results. First, partial compatibility occurs when the expenditure on system goods is relatively low. Second, the optimal degree of compatibility increases in the expenditure on system goods and decreases in hardware production cost. Third, system manufactures suffer losses on selling hardware when keenness on a rival system’s software is relatively low. According to Lee (2013), this result provides a theoretical interpretation of the phenomenon that platform providers often sell hardware platforms close or below cost in the US video game industry [Lee, R (2013). Vertical integration and exclusively platform and two-sided markets. American Economic Review, 103, 2960–3000].

It is common to observe software markets with competition between open-source software (OSS) and proprietary software (PS). This kind of market generally has some common features. First, as mentioned in Sen ( 2007), OSS is usually the late entrant which leads to the fact that PS has accumulated users as an installed base at the time of OSS entering the market. Second, due to asymmetric designs, compatibility between OSS and PS is not only asymmetric but also partial as well. If consumers buy PS, then they may enjoy full network benefits of PS installed base naturally. However, due to partial compatibility between OSS and PS, consumers can only enjoy network benefits of PS installed base partially if they use OSS. Third, PS usually has more