This paper focuses on the strategy choice issue of business expansion (i.e., envelopment and connection) of two competing software platforms. The envelopment strategy represents software platform will enter the hardware product market, while the connection strategy represents software platform will cooperate with third party hardware manufacturers. There are four strategies-both choose envelopment strategy (EE), both choose connection strategy (CC), one chooses envelopment strategy, and the other chooses connection strategy (EC/CE). This paper identifies the Nash equilibrium strategy and reveals the impact of different strategic choices on the price and quality decisions of hardware products and consumer surplus. The main findings are as follows. Firstly, EE is the unique Nash equilibrium strategy, and both EE and CC may be the Pareto optimality from the software platform's perspective. Both EE and CC can be the Nash equilibrium strategies, but only CC is the Pareto optimality from the platform system's perspective. Secondly, EE strategy may achieve a win-win outcome between software platforms and consumers, while CC strategy may achieve a win-win outcome between software platforms and platform system. Thirdly, no matter what strategy the competitor platform chooses, the envelopment strategy will always give the platform higher hardware product quality and product demand than the connection strategy, while the product price they provide may not necessarily be lower.