Endogenous timing in a mixed duopoly with CSR and network effects

In a mixed duopoly (a public, welfare-maximizing firm competing with a private, profit-maximizing firm), as established by Amir, R., and G. De Feo. 2014. "Endogenous Timing in a Mixed Duopoly." International Journal of Game Theory 43: 629--58, the sequential order of moves (Stackelberg) is the sub-game perfect Nash equilibrium (SPNE), with indeterminacy of market leadership arising when the reaction functions are downward sloping (goods are strategic substitutes). The present study extends the framework of Amir, R., and G. De Feo. 2014. "Endogenous Timing in a Mixed Duopoly." International Journal of Game Theory 43: 629--58 by considering (separately and jointly) network goods and corporate social responsibility (CSR) objectives. The presence of network externalities or CSR alone enables a strict characterization of market leadership when goods are strategic substitutes. Remarkably, when both coexist, the simultaneous-move outcome (Cournot) can emerge as the SPNE, reversing the established result. This reversal is due to the interaction between the strength of the network effect and the degree of social concern of the private firm, rather than solely to its social focus. The paper also highlights the social welfare outcomes corresponding to the SPNEs.